Critical Conversion Research Articles

Gel point determination for the copolymerization system of cardanyl acrylate and styrene and its critical conversion

AbstractThe copolymerization of cardanyl acrylate (CA) and styrene (S) with methyl ethyl ketone peroxide (MEKP) and cobalt salt as the initiator was studied by means of rheometry and isothermal DSC. The gel point of the CA‐S reaction system was determined by rheological measurements at 50 and 70°C. In addition, rheological measurements provide very useful information on the evolution of the physical properties of the system during curing, such as viscosity and shear modulus. We demonstrate that isothermal DSC experiments, using the Avrami model, can be used to obtain a more detailed description of the curing process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2385–2390, 2003

A kinetic study on bulk thermal polymerization of styrene

The kinetics of bulk thermal polymerization of styrene over the range of 100–200 °C has been studied based on three stage polymerization model (TSPM) in this paper. TSPM plots showed that the whole polymerization course only exhibits two stages, low conversion stage and gel effect stage, which is consistent with TSPM as the reaction temperature is higher than the glass transition temperature of polystyrene. It was found that the critical conversion, x 1, for the transition from low conversion stage to gel effect stage is independent of the reaction temperature and approximately equal to 0.5. In addition, the apparent reaction rate constants obtained from TSPM plots could be correlated to temperature by Arrhenius equation. Expressions predicting number-average molecular weight were also derived according to TSPM. Using the expressions to treat experimental data available in the literature, it was found that number-average molecular weight is independent of the conversion and relative to the reaction temperature at low conversion stage. However, it varies with the conversions at gel effect stage and the variations are more obvious as the reaction temperature rises.

Gasification reactivity of charcoal with CO 2. Part I: Conversion and structural phenomena

The gasification reaction of fir charcoal with CO 2 was studied by isothermal thermogravimetric analysis under kinetic control. The derived reaction rate ( r=d X/d t) as a function of the converted carbon mass ( X) was compared with random pore model predictions and found to be much higher at elevated conversion levels than predicted by theory. Similar enhanced reaction rate behaviour was evidenced after removing the natural alkali catalyst from the charcoal by acid washing, suggesting that with untreated charcoal the late reaction rate contribution stems from both, catalytic and additional structure effects. Literature attributes the unpredicted late reaction rate behaviour to the disintegration of the porous char particle into small fragments, which, in line with percolation theory predictions, seems to occur only after a critical conversion level has been reached. However, our gasification data reveal a gradual rise in the charcoal reactivity thereafter, suggesting a breaking up (embrittlement) of the solid phase accompanied by the exposure of fresh surface area from fracturing. The original random pore model derivation given by Bhatia and Perlmutter is extended to account also for these peculiarities and the resulting kinetic relation described our reaction rate data well over the entire conversion range.

Monte Carlo simulation of diepoxides and monoepoxides cured with amines

AbstractThe diepoxide–monoepoxide–diamine curing systems are investigated with a Monte Carlo simulation. The dependence of the molecular weight distribution (MWD), gel fraction, and cycle rank of the polymers on the differences in the epoxy reactivities and the contents of the monoepoxide as a reactive diluent are discussed. Before gelation, the MWD of the curing systems with a lower content of the monoepoxide is broader than the MWD of the curing systems with a higher content, and it leads to a lower critical conversion. The gel fraction and cycle rank of the polymers decrease with an increasing amount of the diluent. Even fully cured, the system with a 0.6 epoxy molar fraction of the monoepoxide still has a large fraction of sol, about 49%. Although the various reactivities of the monoepoxide result in different ways of forming gels during curing, the final gel fractions are always near 100% as long as the epoxy molar fraction of the diluent is no more than 0.2. The profiles of the molecular weights of the polymers calculated by the model are in agreement with the experimental data. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1857–1868, 2002

Radiation polymerization of acrylonitrile in a viscous system with styrene

Radiation polymerization of acrylonitrile in a viscous system with styrene was performed at ambient temperature by using γ-rays. It is found that the overall rate of polymerization was accelerated after critical conversion due to the gel effect. As the molar fraction of styrene in monomer feed (fSt) is increased, both the total polymer conversion and molar fraction of acrylonitrile in the copolymer feed (FAN) were decreased. The monomer reactivity ratios for acrylonitrile and styerne were determined to be r1 (AN) = 0.25 and r2 (St) = 2.0, respectively. The copolymers obtained were characterized by Fourier transformed infrared spectra (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), 1H-NMR, and pyrolysis mass spectrometry (PMS). It was found that the slight addition of styrene to acrylonitrile strongly changes crystallinity, morphology, and thermal decomposition of the resulting polymer. 1H-NMR measurment of AN/St copolymer showed the appearance of aromatic proton signals and shifted the resonance of the methylene proton to lower chemical shifts. The mass spectra of AN/St copolymers showed fragments of pyrolysates corresponding to oligonitriles with styrene end groups. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 268–275, 2002; DOI 10.1002/app.10324

Radiation polymerization of acrylonitrile in a viscous system with styrene

AbstractRadiation polymerization of acrylonitrile in a viscous system with styrene was performed at ambient temperature by using γ‐rays. It is found that the overall rate of polymerization was accelerated after critical conversion due to the gel effect. As the molar fraction of styrene in monomer feed (fSt) is increased, both the total polymer conversion and molar fraction of acrylonitrile in the copolymer feed (FAN) were decreased. The monomer reactivity ratios for acrylonitrile and styerne were determined to be r1 (AN) = 0.25 and r2 (St) = 2.0, respectively. The copolymers obtained were characterized by Fourier transformed infrared spectra (FTIR), X‐ray diffraction (XRD), scanning electron microscopy (SEM), 1H‐NMR, and pyrolysis mass spectrometry (PMS). It was found that the slight addition of styrene to acrylonitrile strongly changes crystallinity, morphology, and thermal decomposition of the resulting polymer. 1H‐NMR measurment of AN/St copolymer showed the appearance of aromatic proton signals and shifted the resonance of the methylene proton to lower chemical shifts. The mass spectra of AN/St copolymers showed fragments of pyrolysates corresponding to oligonitriles with styrene end groups. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 268–275, 2002; DOI 10.1002/app.10324

Free-radical crosslinking copolymerization of acrylamide and N, N′-methylenebis acrylamide by used Ce(IV)/polyethylene glycol and Ce(IV)/diethylmalonate redox initiator systems

Acrylamide and N, N ′-methylenebis (acrylamide) (AAm–Bis) copolymerization has been investigated in water at a total monomer concentration of the 0.5 M. Conversion of monomer was measured as a function of the reaction time up to the onset of macrogelation. Experimental results indicate that the critical conversion at the gel point shows a minimum at 6 mol.% Bis when the monomer concentration was kept constant at 0.5 M and it was found that polymer formed with different Bis% are not dissolved in water, acetic acid, toluene or chloroform.

Off-lattice long-range percolation modelling of a network polymerisation

A system involving homopolymerisation of a 3-functional monomer has been studied by using an off-lattice long-range percolation model. The elementary reaction steps were controlled by substitution effects and by local concentrations of units. The latter were controlled by setting a constant value to a range-of-reaction parameter called the capture radius. The critical conversion at gelation in the system turned to the classical one as the value of capture radius increased.

Influence of seed polymer molecular weight on polymerization kinetics and particle morphology of structured styrene-butadiene latexes

Heterogeneous film-forming latexes were prepared using two-stage, seeded emulsion polymerization. The polymerization was performed in a calorimetric reactor with a control unit that monitored the reaction rate and controlled the charging rate of the monomers. Three types of styrene seed latexes were prepared at 70°C. The first was an unmodified polystyrene (PS) latex. The second had the molecular weight lowered by the use of carbon tetrachloride (CCl4) as a chain-transfer agent, added at the start of the polymerization. For the third one, divinylbenzene (DVB) was used as a comonomer. DVB was added under starved conditions near the end of the polymerization to achieve crosslinked particle shells and to introduce double bonds as possible grafting sites. The second polymerization step was performed at 80°C as a batch operation in a 200-mL calorimeter reactor. The second-stage polymer was poly(styrene-co-butadiene-co-methacrylic acid) (S/B/MAA). A fixed S/B ratio was used together with varying small amounts of MAA. Particle morphology and particle-size distributions were examined after the second stage using TEM after staining with osmium tetroxide. The particle morphology was found to depend on both the seed composition and the amount of MAA used in the second stage. Molecular weight and crosslinking of the DVB-containing seed influenced the internal particle viscosity, which gave differences in the polymerization rate and the particle morphology. Crosslinking of the second-stage polymer decreased the monomer concentration in the particles, which could be detected as a change in the slope the pressure/conversion curve. This phenomenon was used to indicate the critical conversion for crosslinking of the second-stage polymer. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 297–311, 2000

Percolative Fragmentation of Char Particles during Gasification

Percolative fragmentation was confirmed to occur during gasification of three microporous coal chars. Indirect evidence obtained by the variation of electrical resistivity (ER) with conversion was supported by direct observation of numerous fragments during gasification. The resistivity increases slowly at low conversions and then sharply after a certain conversion value, which is a typical percolation phenomenon suggesting the occurrence of internal fragmentation at high conversion. Two percolation models are applied to interpret the experimental data and determine the percolation threshold. A percolation threshold of 0.02-0.07 was found, corresponding to a critical conversion of 92-96% for fragmentation. The electrical resistivity variation at high conversions is found to be very sensitive to diffusional effects during gasification. Partially burnt samples with a narrow initial particle size range were also observed microscopically, and found to yield a large number of small fragments even when the particles showed no disintegration and chemical control prevailed. It is proposed that this is due to the separation of isolated clusters from the particle surface. The particle size distribution of the fragments was essentially independent of the reaction conditions and the char type, and supported the prediction by percolation theory that the number fraction distribution varies linearly with mass in a log-log plot. The results imply that perimeter fragmentation would occur in practical combustion systems in which the reactions are strongly diffusion affected.

Uphill motion of active brownian particles in piecewise linear potentials

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a ``high velocity'' or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current.

Correlation of critical current density and phase conversion at different final cooling rate in Ag-sheathed PbBi2223 tapes

As shown by Parrell et al., a final reduced cooling rate can produce an improvement of the optimum critical current in field. In this paper we present results on the critical current density and magnetic field dependence of Ag-sheathed (Pb,Bi)-2223 multifilamentary tapes as a function of the final sintering time for different cooling. Correlation between 2223 phase conversion, as determined by XRD, and the critical current density is also examined. For samples slow cooled to 800/spl deg/C at 1/spl deg/C/h followed by furnace cooling to room temperature, the critical current density remained almost constant at 20 KAcm/sup -2/ with different final sintering times between 10 to 150 hours. In contrast samples slow-cooled to 730/spl deg/C at 1/spl deg/C/h showed a decreased J/sub c/ of 7 KAcm/sup -2/ for a short final sintering time of 10 hours, rising gradually to 22 KAcm/sup -2/ at 200 hours. Corresponding to this, the samples cooled to 800/spl deg/C show a phase composition of 90% apparent (Pb,Bi)-2223 for all times, as opposed to a gradual increase of the (Pb,Bi)-2223 phase from 65% to 90% with increasing sintering time for samples slow cooled to 730/spl deg/C. As the conditions are exactly the same prior to the cooling below 800/spl deg/C, the reduced conversion for the samples slow cooled to 730/spl deg/C must be the result of 2212 precipitation from the apparent (Pb,Bi)-2223 phase present at 800/spl deg/C.

Preparation and end-linking of hydroxyl-terminated polystyrene star macromolecules

An up-scale synthesis of 3-arm hydroxyl-terminated polystyrene (PS) star polymers is reported. Subsequent end-linking of these hydroxyl-terminated star polymers with 2,4-toluene diisocyanate gave branched polymers. The extent of reacted groups was measured by UV spectroscopy. The quenched samples were characterized by static-dynamic light scattering. The experimental gel point (critical hydroxyl conversion, pOH, cr = 0.65) is shifted significantly from the theoretically predicted gel point (pOH,cr = 0.50), indicating extensive ring formation during the end-linking process. Analysis of the shrinking factors (gh, gs) and the molar mass dependencies of the radii of gyration Rg, hydrodynamic radii Rh, and the second osmotic virial coefficient A2 gave qualitative agreement with crosslinking theories. The deviations are discussed to arise from the large non-uniformity in the size distribution and from a cross-over of mean field to percolation behavior, as was previously found from the quantitative analysis of molar mass distributions.

Kinetic model of diepoxides with reactive diluents cured with amines

The systems of diepoxides cured with primary amine in presence of an monoepoxide, monofunctional reactive, under equal stoichiometric ratio has been analyzed by a generating function method. The average degree of polymerization, which changed with time or conversion, and gel point were calculated. The profiles of the degree of polymerization and critical conversion are dependent on the content of and relative reactivities of epoxy groups. For a system with the same ratio, the critical epoxy conversion increases with increasing reactivity. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2339–2348, 1998

Kinetic model of diepoxides with reactive diluents cured with amines

The systems of diepoxides cured with primary amine in presence of an monoepoxide, monofunctional reactive, under equal stoichiometric ratio has been analyzed by a generating function method. The average degree of polymerization, which changed with time or conversion, and gel point were calculated. The profiles of the degree of polymerization and critical conversion are dependent on the content of and relative reactivities of epoxy groups. For a system with the same ratio, the critical epoxy conversion increases with increasing reactivity. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2339–2348, 1998

An Evaluation of Free Volume Approaches to Describe the Gel Effect in Free Radical Polymerization

This paper examines the use of free volume approaches to describe the gel effect in free radical polymerization, specifically testing the consistency of free volume in describing the effect of temperature on the critical onset conversion for the gel effect, Xcrit. Experimental polymerization results for both methyl methacrylate (MMA) and styrene in which the temperature, T, is varied while the molecular weight, M, is held nearly constant show that the critical onset conversion for the gel effect, Xcrit, is affected by T; i.e., a higher T leads to a higher Xcrit, consistent with free volume. Other studies purported to show a link between Xcrit and M did not account for variations in T in the data analyzed, and it is highly likely that part of the Xcrit trend reported to be caused by M was in fact related to T variations. Further examination of this issue via modeling indicates that the experimental results are consistent with the quantitative trend predicted by free volume for Xcrit as a function of T as well, indicating that free volume is an appropriate basis for modeling the gel effect as it adequately handles effects of temperature on termination. However, as it does not describe the concentration or potential molecular weight dependence of termination, free volume is not a complete theory for the gel effect. For this task, additional molecular-level insight is needed, a fact underscored by certain experimental trends not predicted by free volume, such as the effects of chain transfer and solvent quality on termination.

Layered motion estimation

A layered motion estimation algorithm is proposed that permits quasisimultaneous motion estimation/segmentation up to a fixed maximum number of layers. The estimation results in one motion parameter set per layer, and a segmentation map that assigns these sets to different parts of the image (motion layers). Motion in a layer is modelled with at maximum four parameters capable of describing pan, tilt and zoom. The concept shows some hierarchy, i.e. a ranking of the motion layers. In this way the motion parameter estimation concerning one layer excludes those parts of the image that have been described by a layer ranked higher in the hierarchy and are not polluted by parts of the image that are better described by layers ranked lower in the hierarchy. The concept results in a very low operations count. It has been shown to perform well even in critical scan rate conversion applications, particularly in picture rate up-conversion. A variant including three layers has been scheduled to run in real-time on a Philips TriMedia processor.

Real-Time FTIR and in Situ Rheological Studies on the UV Curing Kinetics of Thiol-ene Polymers

Real-time FTIR spectroscopy and in situ dynamic rheology were used to characterize the UV curing kinetics of a thiol-ene system containing trimethylolpropane tris(2-mercaptoacetate) and trimethylolpropane diallyl ether. The combination of these two techniques offered a powerful approach for monitoring changes in the chemical and rheological properties of the system during UV curing. Comparable gel times were independently obtained from both FTIR spectroscopy and rheology, thereby validating the comparison of data obtained from each method. The thiol conversion determined from FTIR spectroscopy was correlated with the elastic modulus obtained from rheology. The conversion increased very rapidly during the initial stages of UV curing. However, the elastic modulus did not have an appreciable value until after 65% of the thiol functional groups have reacted, following which the elastic modulus increased at a rapid rate. From the Flory−Stockmayer theory of gelation, the critical thiol conversion at the gel poi...

Formation and structure of polyacrylamide gels

Acrylamide and N,N′-methylenebis (acrylamide) (AAm–Bis) copolymerization has been in-vestigated in water at a monomer concentration of 1.8 w/v%. Conversion of monomer and pendant vinyl groups was measured as a function of the reaction time up to the onset of macrogelation. Experimental results indicate that 80% of pendant vinyl groups are consumed by cyclization reactions. When the monomer concentration was kept constant at 1.8%, the critical conversion at the gel point shows a minimum at 7.5 mol % Bits. The equilibrium degree of swelling of the polyacrylamide (PAAm) gels is independent of their crosslinker content. Calculation results show that the average reactivity of pendant vinyl groups for intermolecular links decreases as the Bis concentration increases. All these results suggest formation of PAAm microgels prior to the onset of macrogelation. As the reaction proceeds, microgels are connected to a macrogel through their peripheral pendant vinyls and radical ends, whereas those in their interior remain intact. The microgels seem to act as the junction points of the final inhomogeneous networks. © 1996 John Wiley & Sons, Inc.

Formation and structure of polyacrylamide gels

Acrylamide and N,N′-methylenebis (acrylamide) (AAm–Bis) copolymerization has been in-vestigated in water at a monomer concentration of 1.8 w/v%. Conversion of monomer and pendant vinyl groups was measured as a function of the reaction time up to the onset of macrogelation. Experimental results indicate that 80% of pendant vinyl groups are consumed by cyclization reactions. When the monomer concentration was kept constant at 1.8%, the critical conversion at the gel point shows a minimum at 7.5 mol % Bits. The equilibrium degree of swelling of the polyacrylamide (PAAm) gels is independent of their crosslinker content. Calculation results show that the average reactivity of pendant vinyl groups for intermolecular links decreases as the Bis concentration increases. All these results suggest formation of PAAm microgels prior to the onset of macrogelation. As the reaction proceeds, microgels are connected to a macrogel through their peripheral pendant vinyls and radical ends, whereas those in their interior remain intact. The microgels seem to act as the junction points of the final inhomogeneous networks. © 1996 John Wiley & Sons, Inc.