Modeling diffusion in miscible polymer blend films

Recent experiments designed to probe polymer transport in the bulk and in the vicinity of surfaces have examined the interdiffusion of multilayer sandwiches of isotopically labeled polymers. The measured time dependent concentration profiles normal to the surface are typically fit to Fick's law, with a single fitting parameter, the mutual binary diffusion coefficient (MBDC). The resulting MBDCs are found to vary over a broad range of film thicknesses and time, with the time dependence being viewed as a unique signature of the reptation mechanism of long chain motion, and the thickness dependence being attributed to the slowing down of chain dynamics near surfaces. Since the experiments are conducted at finite concentration, the MBDC, which is a product of the bare mobility and the concentration derivative of the chemical potential, could be dominated by the time and thickness dependence of this second term (which is ignored in Fick's law). To quantify this conjecture we consider the more rigorous Cahn formulation of the diffusion problem in terms of chemical potential gradients. We use square gradient theory to evaluate chemical potentials, and fit the resulting time dependent concentration profiles to the analytical solution of Fick's law. By thus mimicking the experimental analysis we find that the apparent MBDCs vary with time as t(-1/2) at short times, in good agreement with existing experiments. We show that this time dependence reflects the system's desire to minimize concentration gradients, a fact ignored in Fick's law. Since these arguments make no reference to the mechanism of chain motion, we argue that the time dependence of MBDC derived from interdiffusion experiments does not provide unequivocal support for the reptation mechanism of long chain transport. The MBDC values, which also vary with the degree of confinement, are predicted to increase with decreasing thickness for model parameters corresponding to experimental systems. In contrast, since the experimental fits yield an opposite trend, we suggest that the bare mobility of the chains decreases strongly with decreasing thickness. These findings strongly support the idea that the chains are "pinned" irreversibly to the surfaces, in good agreement with other, independent experiments.     

Solvent effect in the polymerization of e-caprolactone initiated with diethylaluminum ethoxide

Kinetics of ϵ-caprolactone (ϵCL) polymerization initiated with diethylaluminum ethoxide in benzene (C₆H₆) and acetonitrile (CH₃CN) as solvents was studied and compared with the previously studied polymerization conducted in tetrahydrofuran (THF) solvent. Kinetic data were analyzed in terms of the kinetic scheme: “propagation with aggregation,” assuming that actually propagating active species (P_n*) aggregate reversibly into the unreactive (dormant) species . The determined equilibrium constants of deaggregation (K_da) decrease with decreasing solvent polarity, namely K_da (in mol²·L⁻²) = (1.3 ± 0.7)·10⁻² (CH₃CN), (1.8 ± 0.5)·10⁻⁵ (THF), (4.1 ± 0.7)·10⁻⁶(C₆H₆), whereas for the rate constants of propagation the opposite is true, k_p (in mol⁻¹·L·s⁻¹) = (7.5 ± 0.3)·10⁻³ (CH₃CN), (3.87 ± 0.01)·10⁻² (THF), (8.6 ± 0.9)·10⁻² (C₆H₆) (25°C). The latter effect is explained by a specific solvation (the stronger the higher solvent polarity) of the active species already in the ground state in the elementary reaction of the poly(ϵCL) chain growth: C₂H₅[OC(O)(CH₂)₅]_nO(SINGLE BOND)Al(C₂H₅)₂ + ϵCL → C₂H₅[OC(O)(CH₂)₅]_n+1O(SINGLE BOND)Al(C₂H₅)₂. © 1996 John Wiley & Sons, Inc.     

Thermodynamic and Kinetic Polymerizability of Cyclic Esters

Recent advances in the controlled ring-opening polymerization (ROP) of cyclic aliphatic esters are reviewed with a particular attention to thermodynamics and kinetics of the polymerization of industrially important monomers, namely: lactide (LA), 1,4-dioxan-2-one (DX), and ϵ-caprolactone (CL). For comparison, polymerization of β-lactones is discussed. Progress in stereocontrolled polymerization of monomers bearing centers of chirality [LA and β-butyrolactone (BL)] is also briefly reviewed.     

Living polymerization of cyclic esters – a route to (bio)degradable polymers. Influence of chain transfer to polymer on livingness

Polymerization of cyclic esters leads to (bio)degradable polymers of the increasing industrial importance. These polymerizations are of the living nature, although chain transfer to polymer with chain scission may cause deviations from the livingness and introduce structural differences (e.g. in end-groups), important for physical properties. Two different systems are discussed. In the first one two living macromolecules react one with another and reproduce two living macromolecules, retaining the same reactivities and the same end-groups. Polymerizations of ϵ-caprolactone and lactide belong to this category. On the other hand, polymerization of cyclic carbonates proceeds with chain transfer, in which disproportionation of the living chains takes place: from two living macromolecules one “dead” and one “doubly active” can be formed. Conditions of retaining the livingness in terms of the ratios of the rate constants of transfer, reinitiation, and propagation are discussed.     

On the difference of reactivities of various aggregated forms of aluminium triisopropoxide in initiating ring-opening polymerizations

The polymerization of ε-caprolactone (εCL) initiated with aluminium triisopropoxide (Al(OⁱPr)₃) trimer ( A ₃) and/or tetramer ( A ₄) was studied. The rate of A ₃ ⇔︁ A ₄ interconversions in the diluted (≤0,1 mol · L^-1) C₆D₆, C₆D₆/εCL, and THF/εCL solutions were found to be slow, when compared with the rate of propagation. Comparison of the ¹H NMR spectra of the initiators with those of the polymerization mixtures revealed that A ₃ is much more reactive than A ₄ in their reactions with εCL. From the initiator reacted with εCL all threeOⁱPr groups from Al(OⁱPr)₃ are transferred into the poly(εCL) as end groups. Kinetic studies of polymerization confirmed the large reactivity difference between A ₃ and A ₄.     

Living polymerization with reversible chain transfer and reversible deactivation: The case of cyclic esters

Polymerization of cyclic esters at the properly chosen conditions can be treated as living polymerization, in agreement with the tentative definition of the Nomenclature Commission of IUPAC (Macromolecular Division) requiring that no irreversible transfer or irreversible termination take place. For these processes the most kinetic or structural (end group) studies do not reveal any deviation. However, since in these polymerizations reversible transfer to backbones of macromolecules and/or reversible deactivation take place, the molar mass distribution can be Poissonian only at certain conditions. These processes have been studied quantitatively and the corresponding rate constants were determined. Thus, the importance of these processes could be established by comparing the rate constants of transfer and/or deactivation with rate constants of propagation. In this way, polymerizations of cyclic esters were used to illustrate the meaning and scope of the definition of “living polymerization”, a process from which irreversible transfer and deactivation are absent and in which living polymers are formed, i. e. composed of macromolecules that do not irreversibly loose their ability to grow.     

A Raman laser system for multi-wavelength satellite laser ranging

~~A Raman laser system for multi-wavelength satellite laser ranging@K.Hamal$Czech Technical University in Prague,Czech @I.Prochazka$Czech Technical University in Prague,Czech @J.Blazej$Czech Technical University in Prague,Czech1. Yang Fumin, Chen Wanzhen, Zhang Zhongping et al., Satellite laser ranging experiment with sub-centimeter single-shot ranging precision at Shanghai Observatory, Science in China, Ser. A, 2002, 32(10): 935-939. 2. Degnan, J. J., Millimeter accurac…