Diffusion-limited kinetics modeling of one-step polyimide formation

A diffusion-limited kinetic model was developed to describe the imidization of one-step polythioetherimide formation based on an endgroup diffusion model. The changes of conversion and viscosity during the imidization were monitored with thermogravimetric analysis and dynamic stress rheometry, respectively. It was observed that the imidization rate began to decelerate after a fast early stage, whereas the viscosity in the system increased dramatically after a period of low value. Amic acid and imide formations concurrently take place in the one-step polyimide formation, but the formation of amic acid is much slower than that of imide and is the rate-limiting step of imidization. When a second-order kinetic model was used to describe the imidization, the effect of viscosity on the diffusion resistance of reactive groups needed to be included. In order to predict the change of viscosity during the imidization, the Lipshitz-Macosko model was modified and introduced into the diffusion-limited kinetic model by the Stokes-Einstein equation. The comparison of the modeled results with experimental data indicated that the diffusion-limited kinetic model and the modified Lipshitz-Macosko model were able to efficiently predict the changes of conversion and viscosity with temperature and time during the one-step polythioetherimide formation. (C) 2001 John Wiley & Sons, Inc.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone). V: Estimation of temperature distribution during cure process

A numerical method to estimate temperature distribution during the cure of epoxy-terminated poly(phenylene ether ketone) (E-PEK)-based composite is suggested. The effect of the temperature distribution on the selection of cure cycle is evaluated using a suggested alternation criterion. The effect of varying heating rate and thickness on the temperature distribution, viscosity distribution and distribution of the extent of cure reaction are discussed based on the combination of the here-established temperature distribution model and the previously established curing kinetics model and chemorheological model. It is found that, for a thin composite (<=10mm) and low heating rate (<=2.5K/min), the effect of temperature distribution on cure cycle and on the processing window for pressure application can be neglected. Low heating rate is of benefit to reduce the temperature gradient. The processing window for pressure application becomes narrower with increasing thicknesses of composite sheets. The validity of the temperature distribution model and the modified processing window is evaluated through the characterization of mechanical and physical properties of E-PEK-based composite fabricated according to different temperature distribution conditions.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone) .3. Determination of the time of pressure application

The curing temperature, pressure, and curing time have significant influence on finished thermosetting composite products. The time of pressure application is one of the most important processing parameters in the manufacture of a thermosetting composite. The determination of the time of pressure application relies on analysis of the viscosity variation of the polymer, associated with curing temperature and curing time. To determine it, the influence of the time of pressure application on the physical properties of epoxy-terminated poly(phenylene ether ketone) (E-PEK)-based continuous carbon fiber composite was studied. It was found that a stepwise temperature cure cycle is more suitable for manufacture of this composite. There are two viscosity valleys, in the case of the E-PEK system, associated with temperature during a stepwise cure cycle. The analysis on the effects of reinforcement fraction and defect content on the composite sheet quality indicates that the width-adjustable second viscosity valley provides a suitable pressing window. The viscosity, ranging from 400 to 1200 Pa . s at the second viscosity valley, is the optimal viscosity range for applying pressure to ensure appropriate resin flow during curing process, which enables one to get a finished composite with optimal fiber volume fraction and low void content. (C) 1997 John Wiley & Sons, Inc.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone) .4. Cure cycle simulation

Epoxy-terminated poly(phenylene ether ketone) (E-PEK) developed in this Institute is a candidate matrix resin for polymer composites as structural materials. Cure cycles for this reaction system were simulated according to the previously established processing model. It is found that for the E-PEK system, the curing process is best completed by a stepwise cure cycle comprising two isothermal processes at different temperatures, T-1 and T-2. The cure cycles over a wide range of processing parameters simulated, based on the established processing model, indicate that the processing window is width-adjustable. Analysis of the mechanical properties of the composite sheets showed that the simulated cure cycles are acceptable and reliable. (C) 1997 John Wiley & Sons, Inc.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone) .1. DSC characterization of curing reaction

The curing reaction process of epoxy-terminated poly(phenylene ether ketone) (E-PEK) with 4,4'-diaminodiphenyl sulfone (DDS) and hexahydrophthalic acid anhydride (Nadic) as curing agents was investigated using isothermal differential scanning calorimetry (IDSC) and nonisothermal differential scanning calorimetry (DDSC) techniques. It was found that the curing reactions of E-PEK/DDS and E-PEK/Nadic are nth-order reactions but not autoaccelerating. The experimental results revealed that the curing reaction kinetics parameters measured from IDSC and DDSC are not equivalent. This means that, in the curing reaction kinetics model for our E-PEK system, both isothermal and nonisothermal reaction kinetics parameters are needed to describe isothermal and nonisothermal curing processes, The isothermal and nonisothermal curing processes were successfully simulated using this model. A new extrapolation method was suggested. On the basis of this method the maximum extent of the curing reaction (A(ult)) that is able to reach a certain temperature can be predicted. The A(ult) for the E-PEK system estimated by the new method agrees well with the results obtained from another procedure reported in the literature. (C) 1997 John Wiley & Sons, Inc.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone) .2. Chemorheological modeling

Chemorheology and corresponding models for an epoxy-terminated poly(phenylene ether ketone) (E-PEK) and 4,4'-diaminodiphenyl sulfone (DDS) system were investigated using a differential scanning calorimeter (DSC) and a cone-and-plate rheometer. For this system, the reported four-parameter chemorheological model and modified WLF chemorheological model can only be used in an isothermal or nonisothermal process, respectively. In order to predict the resin viscosity variation during a stepwise temperature cure cycle actually used, a new model based on the combination of the four-parameter model and the modified WLF model was developed. The combined model can predict the resin viscosity variation during a stepwise temperature cure cycle more accurately than the above two models. In order to simplify the establishment of this model, a new five-parameter chemorheological model was then developed. The parameters in this five-parameter model can be determined through very few rheology and DSC experiments. This model is practicable to describe the resin viscosity variation for isothermal, nonisothermal, or stepwise temperature cure cycles accurately. The five-parameter chemorheological model has also successfully been used in the E-PEK systems with two other curing agents, i.e., the diamine curing agent with the addition of a boron trifluride monoethylamine (BF3-MEA) accelerator and an anhydride curing agent (hexahydrophthalic acid anhydride). (C) 1997 John Wiley & Sons, Inc.

Physical modeling of localized scour for the Yangtze Estuary Waterway Improvement Project, Phase I

In order to examine the effectiveness of engineering protection against localized scour in front of the south groin-group of the Yangtze Estuary Waterway Improvement Project, Phase I, an undistorted physical model on a geometric scale of 1:250 is built in this study, covering two groins and their adacent estuarine areas. By use of rinsing fix-bed model as well as localized mobile-bed model the experiment is undertaken under bi-directional steady flow. According to the experimental results, waterway dredging leads to the increase in steram velocity, the increase being larger during the ebb than during the flood. Construction of the upstream groin has some influence on the flow patterns near the downstream groin. Localized scour in front of the groin-heads is controlled mainly by ebb flow. In the case of a riverbed composed entirely of silt, the depths of localized scour in front of the two groin-heads are 27 m and 29 m, respectively. In reality, the underneath sediment of the prototype riverbed is clay whose threshold velocity is much higher than the stream velocity in the Yangtze Estuary; therefore, the depths of localized scour will not be much larger than the thickness of the silt layer, i. e. 7.4 m and 4.7 m, respectively. The designed aprons covering the riverbed in fron of the groin-heads are very effective in scour control. Aprons of slightly smaller size can also fulfill the task of protection, but the area of localized scour increases significantly.

Periodical mixing of MORB magmas near East Pacific Rise 13N: evidence from modeling and zoned plagioclase phenocrysts

Thirty-six basalt samples from near East Pacific Rise 13N are analyzed for major and trace elements. Different types of zoned plagioclase phenocrysts in basalts are also backscatter imaged, and major element profiles scanned and analyzed for microprobe. Basalts dredged from a restricted area have evolved to different extents (MgO=9.38wt%-6.76wt%). High MgO basalts are modeled for crystallization to MgO of about 7wt%, and resulted in the Ni contents (28 ppm) that are generally lower than that in observed basalts (> 60 ppm). It suggests that low MgO basalts may have experienced more intensive magma mixing. High MgO (9.38wt%) basalt is modeled for self-"mixing-crystallization", and the high Ni contents in low MgO basalts can be generated in small scale and periodical self-mixing of new magma (high MgO). "Mixing-crystallization" processes that low MgO magmas experienced accord with recent 226Ra/230Th disequilibria studies for magma residence time, in which low MgO magmas have experienced more circles of "mixing-crystallization" in relatively longer residence time. Magma mixing is not homogeneous in magma chamber, however, low MgO magmas are closer to stable composition produced by periodical "mixing-crystallization", which is also an important reason for magma diversity in East Pacific Rise. Zoned plagioclase phenocrysts can be divided into two types: with and without high An# cores, both of which have multiple reversed An# zones, suggesting periodical mixing of their host magmas. Cores of zoned plagioclase in low MgO (7.45wt%) basalt differ significantly with their mantle in An#, but are similar in An# with microlite cores (products of equilibrium crystallization) in high MgO (9.38wt%) basalt, which further shows that plagioclase phenocryst cores in low MgO basalts may have formed in their parental magmas before entering into the magma chamber.

Modeling vertical heat transport in the wave affected surface layer of the ocean

In considering the vertical heat transport problems in the upper ocean, the flat upper boundary approximation for the free surface and the horizontal homogenous hypothesis are usually applied. However, due to the existence of the wave motion, the application of this approximation may result in some errors to the solar irradiation since it decays quickly in respect to the actual thickness of the water layer below the surface; on the other hand, due to the fluctuation of the water layer depth, it is improper to neglect the effects of the horizontal advection and turbulent diffusion since they also contribute to the vertical heat transport. A new model is constructed in this study to reflect these effects. The corresponding numerical simulations show that the wave motion may remarkably accelerate the vertical heat transferring process and the variation of the temperature in the wave affected layer appears in an oscillating manner.