Preservation theorems in linear continuous logic

Linear continuous logic is the fragment of continuous logic obtained by restricting connectives to addition and scalar multiplications. Most results in the full continuous logic have a counterpart in this fragment. In particular a linear form of the compactness theorem holds. We prove this variant and use it to deduce some basic preservation theorems.     

Preparation of Cationic Membrane of Polyethylene Film by γ-Irradiation

Grafting of acrylic acid onto PE film by a pre-irradiation method was studied. In order to prevent formation of homopolymer, Mohr salt (NH₄)₂Fe(SO₄)₂ · 6H₂O was used, and the reaction was carried out in the presence of a swelling agent, such as methanol. The influence of different factors, such as dose, dose rate, and temperature, on the kinetics of the reaction was studied. The infrared spectrum of the grafted acrylic acid onto PE shows bands characteristic of carboxylic acids, which demonstrates that grafting has occurred. The grafting sites were shown to be of a semi-spongy shape and irregular structure which is thought to be due to the copolymerization of acrylic acid onto PE film.     

Synthesizing UHMWPE Using Ziegler-Natta Catalyst System of MgCl2(ethoxide type)/ TiCl4/tri-isobutylaluminum

Summery: A Ziegler-Natta catalyst of MgCl₂ (ethoxide type)/TiCl₄ has been synthesized. In order to obtain ultra high molecular weight polyethylene (UHMWPE) tri-isobutylaluminum which is less active to chain transfer was used as cocatalyst. Slurry polymerization was carried out for the polymerization of ethylene while, dilute solution viscometry was performed for the viscosity average molecular weight (Mv) measurement. The effect of [Al]/[Ti] molar ratio, temperature, monomer pressure and polymerization time on the Mv and productivity of the catalyst have been investigated. The results showed increasing [Al]/[Ti] ratio in the range of 78–117, decreased the Mv of the obtained polymer from 7.8 × 10⁶ to 3.7 × 10⁶ however, further increase of the ratio, resulted in decreased of by much slower rate up to [Al]/[Ti] = 588. The higher pressure in the range of 1–7 bars showed the higher the Mv of the polymer obtained, while increasing temperature in the range of 50 to 90 °C decreased the Mv from 9.3 × 10⁶ to 3.7 × 10⁶. The Mv rapidly increase with polymerization time in the first 15 minutes of the reaction, this increase was slowly up to the end of the reaction (120 min). Increasing [Al]/[Ti] ratio raised productivity of the catalyst in the range studied. Rising reaction temperature from 50 to 75 °C increased the productivity of the catalyst however, further increase in the temperature up to the 90 °C decreased activity of the catalyst. Monomer pressure in the range 1 to 7 bars yields higher productivity of the catalyst. Also by varying polymerization conditions synthesizing of UHMWPE with Mv in the range of 3 × 10⁶ to 9 × 10⁶ was feasible.     

Membranes permselectives obtenues par greffage radiochimique des acides acrylique et methacrylique sur des films de poly(chlorure de vinyle)

Membranes were prepared by subjecting to gamma-rays PVC films swollen in a mixture of acrylic acid and methylene chloride. The kinetics of the reaction were investigated as a function of monomer concentration, temperature and dose-rate. The swelling properties of the resulting membranes were studied as well as those of PVC films grafted with methacrylic acid. It was found that PVC films grafted with methacrylic acid only swell slightly in water even for high grafting ratios and the swelling is very slow. At elevated temperatures the films swell more quickly and reach a higher limiting swelling, but the effect is small. PVC films grafted with acrylic acid swell much more quickly and reach much higher swelling ratios. The extent of swelling markedly increases with temperature but this effect is not reversible: once the membranes have reached a high swelling ratio at elevated temperatures, they keep the same ratio when dipped in water at 20°. The Arrhenius plot of the swelling ratio exhibits a break at 50–60° apparently corresponding to a glass transition temperature. In methanol the swelling is significantly higher for PVC films grafted with methacrylic than with acrylic acid. Swelling of the membranes was also investigated in mixtures of water with methanol and methanol with methylene chloride. The results are interpreted by assuming a strong dipole-dipole interaction between the grafted branches and the trunk polymer resulting in a quasimolecular dispersion of the carboxylic chains in the PVC matrix. The latter acts as a barrier against the penetration of water. Heat treatment favours a segregation of the two polymeric species into microphases and this non-reversible transformation is assumed to be responsible for the unexpected behaviour of PVC films grafted with acrylic acid. The significant differences between the properties of PVC films grafted with either acrylic or methacrylic acid are attributed to the much higher hydrophobic character of the methacrylic chains.     

Peculiar swelling properties of PVC films grafted with acrylic and methacrylic acids

It was found that PVC films grafted with methacrylic acid do not swell in either water or methanol, two solvents of poly(methacrylic acid), even for high grafting ratios. The swelling of these films was examined in mixtures of methylene chloride with methanol and curves of different shapes were obtained depending on the grafting ratio. PVC films grafted with acrylic acid readily swell in both water and methanol but they remain hard in the swollen state. The equilibrium swelling increases with swelling temperature but this process is not reversible; films swollen at high temperature keep a high degree of swelling even when the system is cooled.     

Polymerisation radiochimique de l''acide methacrylique en solution

The polymerization of methacrylic acid was investigated in various solvents under the action of gamma-rays. It was found that, as in the case of acrylic acid, solvents could be divided into groups according to the observed effects. The addition of methanol or dioxane up to 50 per cent does not significantly alter the polymerization rate. These two solvents do not dissociate the plurimolecular aggregates of methacrylic acid, the presence of which is demonstrated by the high viscosity of the medium. In the presence of either toluene or n-hexane, the rate gradually decreases and the aggregates are dissociated. Chloroform and CCl₄ also dissociate the aggregates but lead to acceleration of the reaction. This effect which was not observed with acrylic acid presumably results from an energy transfer process. The polymerization of methacrylic acid in bulk and in solution has a very small overall activation energy, 1·0–1·5 kcal/mole between 16 and 60°. All conversion curves are linear in contrast to the case of acrylic acid where auto-accelerated conversion curves were observed in most mixtures. A comparison of these results shows that the initial rates of polymerization of acrylic acid follow relationships similar to those observed for methacrylic acid except for the chlorinated solvents. It is concluded that the molecular aggregates produce the same influence on the polymerization of methacrylic acid as on the initial stages of the reaction for acrylic acid, but the “matrix effect” of poly(acrylic acid) does not appear in the case of poly(methacrylic acid).     

Modeling of Slurry Polymerization of Ethylene Using a Soluble Cp2ZrCl2/MAO Catalytic System

The slurry homopolymerization of ethylene catalyzed by a Cp₂ZrCl₂/MAO catalytic system was studied. A simple kinetic model including initiation, propagation, transfer to monomer and cocatalyst, spontaneous transfer and spontaneous deactivation was developed to predict dynamic yield of polymerization and molecular weight of final products. Kinetic constants were estimated by numerical solution of polymerization kinetic model, combined with Nelder‐Mead simplex method. The model predicts that the propagation reaction has the lower activation energy in relation to chain transfer reactions which leads to decrease of molecular weight at elevated temperatures. The initiation reaction has however, the highest activation energy that results in raising the peak of reaction rate at higher temperatures.

     

Thermodynamic Study of Poly(ethylene glycol) in Water/1-Propanol Solutions by Viscometry

In this work, the intrinsic viscosities of poly(ethylene glycol) with a molar mass of 20 kg⋅mol⁻¹ were measured in water/1-propanol solutions from 283.1 to 313.1 K. The expansion factors of the polymer chains were calculated from the intrinsic viscosity data. The thermodynamic parameters entropy of dilution parameter, the heat of dilution parameter, theta temperature, polymer–solvent interaction parameter and second osmotic virial coefficient were derived from the temperature dependence of the polymer chain expansion factor. The thermodynamic parameters indicate that mixtures of water/1-propanol become weaker solvents for poly(ethylene glycol) with increasing temperature. Also, the thermodynamic parameters indicate that the solvent ability of mixed water/1-propanol for poly(ethylene glycol) is less than that of pure water.     

Polymerisation de l'acide methacrylique en masse et en solution

In spite of the fact that the bulk polymerization of methacrylic acid proceeds under precipitating conditions, all conversion curves are linear and start from the origin. The overall activation energy of the gamma ray initiated reaction is very small: 1.3 kcal/mol. Methanol and water are solvents for the polymer but also form monomer-solvent complexes through H-bonds. It was found that, over a limited concentration range in these solvents, the reaction becomes auto-accelerating both in precipitating and homogeneous reaction media. Non-polar solvents (hydrocarbons) lead to a significant reduction in the polymerization rate but this effect is not as pronounced as for acrylic acid. Chlorinated derivatives reduce the polymerization rate of acrylic acid to the same extent as hydrocarbons but, for methacrylic acid, chlorinated derivatives lead to sensitization. By analogy with earlier results for acrylic acid, it is assumed that the auto-acceleration observed in water and methanol solutions is caused by a “matrix effect”. In bulk, the monomer undoubtly also associates with the polymer but, in view of the bulky methyl groups, the regularly oriented structure which favours propagation presumably never arises. The very small activation energy of the polymerization suggests that chain termination requires a significant activation energy. The mechanism of this process is not clear.     

Ziegler‐Natta/Metallocene Hybrid Catalyst for Ethylene Polymerization

A Ziegler‐Natta/metallocene hybrid catalyst was produced and utilized in the polymerization of ethylene with the aim of producing bimodal polyethylene. The MgCl₂ adduct was prepared by a melt quenching method and Cp₂ZrCl₂ and TiCl₄ catalysts were loaded, respectively, after treating the surface with TiBAl. The polymerization kinetics involved an induction period, followed by fragmentation and expansion of particles. SEM micrographs revealed that the spherical morphology was retained through the initial mild reaction conditions of induction period. The polymers produced showed bimodal molecular weight distribution patterns, suggesting that both components of the hybrid catalyst were active over the support.