Determination of the Minimum Time for Binder Removal and Optimum Geometry for Three-Dimensional Porous Green Bodies

A model is developed to optimize two aspects of the thermal removal of binder from green ceramic components. The model, which accounts for flow in porous media arising from the thermal decomposition of binder in three-dimensional bodies with anisotropic permeability, describes the pressure within the body as a function of position, time, and temperature during the heating cycle. The model is used with variational calculus to predict the heating profile that minimizes the cycle time for the thermal removal of binder. The model is also used to determine which body geometry maximizes the buildup of pressure in parallelepipeds, a common shape of multilayer ceramic capacitors.     

Effect of Decomposition Kinetics and Failure Criteria on Binder-Removal Cycles From Three-Dimensional Porous Green Bodies

A previously developed algorithm can be used to predict the minimum time for the thermal removal of binder from porous green ceramic bodies. The algorithm combines a variational statement on internal pressure, which is generated by binder decomposition, with a transport model that treats the convective flow of binder decomposition products in a porous medium. The minimum time heating cycles depend on a number of coupled transport, kinetic, and dimensional parameters. The predicted minimum time heating cycles depend on the decomposition kinetics (activation energy, preexponential factor, and decomposition mechanism) and on the temperature and pressure at which failure occurs in the green body.     

Minimum Time Heating Cycles for Diffusion‐Controlled Binder Removal from Ceramic Green Bodies

An algorithm based on variational calculus has been developed to predict the minimum time heating cycle (MTHC) for thermal binder removal from a ceramic green body when diffusion, as described by the free volume theory, is the governing mass transport mechanism. The algorithm uses a previously derived analytic solution for the diffusant concentration, which was obtained from the governing reaction–diffusion differential equation. Either a constraint on diffusant concentration or on the equilibrium pressure of diffusant is used to predict the MTHC for both a stationary binder model and a shrinking core binder model. For these four cases, the dependence of the MTHC has been determined on a number of model parameters, including the threshold concentration or pressure, the body size, and the reaction order of the binder degradation kinetics. The algorithm determines two important aspects of the MTHC, namely, the starting temperature of the heating cycle and how temperature varies with time during the cycle. The duration and shape of the temperature‐versus‐time heating schedule, whether increasing, decreasing, or almost constant, depends sensitively on parameters in the model.     

Role of Length Scale on Pressure Increase and Yield of Poly(vinyl butyral)–Barium Titanate–Platinum Multilayer Ceramic Capacitors during Binder Burnout

The binder-burnout kinetics of poly(vinyl) butyral from BaTiO₃ multilayer ceramic capacitors with platinum metal electrodes were analyzed by combining thermogravimetric analysis with infrared spectroscopy. The rate of weight loss was accelerated when both BaTiO₃ and platinum metal were present, and the presence of both metal and ceramic enhanced the production of CO₂. The activation energy and pre-exponential factor were determined by analysis of the weight-loss data with a first-order kinetics model. Then, the decomposition kinetics were incorporated into a coupled heat- and mass-transport model to predict pressure increases as a function of the heating cycle. The heating cycles determined in this manner then were used to evaluate the yield of capacitors 1.3–3.8 cm long and 0.3–1.3 cm high. The optimum yield was realized at an aspect ratio (height:length) of 1:3.     

Heat Transfer in Porous Green Bodies During Binder Removal by Minimum Time Heating Cycles

Heat transfer in ceramic green bodies is examined during rapid binder removal cycles predicted by a variational calculus algorithm. Both the heat transfer and the mass transfer problems are described by one-dimensional spatial models, for which analytical solutions are available. During the minimum time heating cycles, the temperature difference within the green body is shown to depend on the thermal diffusivity, on the permeability, on the threshold pressure at which failure of the green body occurs, and on a number of other kinetic and transport parameters. The temperature difference within the green body is smallest during the early part of the minimum time heating cycle, when the constraint on pressure buildup within the green body limits the rate at which the temperature can be increased.     

A process control algorithm for reaction-diffusion minimum time heating cycles for binder removal from green bodies

Minimum time heating cycles have been simulated for binder removal from ceramic green bodies where the product of binder decomposition exits the green body via diffusion. The model consists of the reaction-diffusion partial differential equation, ordinary differential equations describing the reaction kinetics and a heating function, and algebraic equations, one of which imposes a constraint on concentration or pressure to avoid failure of the green body. Two solution approaches were compared: an earlier approximate method based on the pseudo-steady state assumption combined with a variational calculus algorithm and a new approach based on the finite element method combined with a process control algorithm. The agreement between the two solution strategies reinforces the validity of the pseudo-steady state approximation and the utility of the process control methodology. The latter, which was also applied to problems in which no approximate solution was obtainable, is thus a general method for obtaining minimum time heating cycles.     

Determination of rapid heating cycles for binder removal from open pore green ceramic components

Abstract

Rapid heating cycles have been determined for the thermal removal of binder from open pore green ceramic components. The samples are multilayer green bodies with barium titanate as the dielectric, and the binder consists of poly(vinyl butyral) and dioctyl phthalate. The kinetics of binder decomposition, the gas permeability of the green body and the conditions at failure of the green body were determined from a combination of experiments and modelling. These results were then used with an algorithm based on variational calculus to develop successful rapid heating cycles without causing failure of the component.     

Permeability of Green Ceramic Tapes as a Function of Binder Loading

The permeability of green ceramic tapes was determined as a function of binder content for binder removed by air oxidation. The tapes were comprised of barium titanate as the dielectric, and polyvinyl butyral and dioctyl phthalate were the main components of the binder mixture. The flow in porous media through the tapes was analyzed in terms of models for describing Knudsen, slip, and Poiseuille flow mechanisms. The characteristic pore size was determined to be 1–2 μm, and thus Poiseuille flow was the dominant transport mechanism contributing to the flux. The permeability was then determined from Darcy's law for flow in porous media. The permeability was also determined from microstructural attributes in terms of the specific surface, the pore fraction, and a term to account for tortuosity and constrictions.     

Modeling of the Pressure Distribution in Three-Dimensional Porous Green Bodies during Binder Removal

A model is developed to describe flow in porous media from the thermal decomposition of binder in three-dimensional bodies with anisotropic permeability. The model is able to describe the pressure within the body as a function of position, time, and temperature during the heating cycle. The results from numerical solution of the un-steady-state partial differential equation are compared to those obtained from an analytical solution to the steady-state equation. Under many conditions that are representative of binder removal, the analytical solution provides a reasonable representation of the numerical solution. A criterion is also developed to determine when the analytical solution is valid. Scaling relationships for the buildup of pressure in terms of the dimensions of the body, the rate of reaction, and the permeability are also derived.     

Theoretical Models for Binder Burnout

The kinetics of binder burnout, from a ceramic green body, are considered for the case of an "unzipping" binder which decomposes to produce a volatile monomer. The process is considered to fail if the concentration of monomer in the green body exceeds that in equilibrium with vapor at 1 atm (≅10⁵ Pa), when an internal bubble would be expected to form. Steady-state diffusional calculations and computer simulations explore the size and temperature dependence of the process and are in agreement. The model suggests that it is not feasible to burn out a large flat piece greater than about 3 mm thick, without going to very long times of burnout. The kinetics are significantly improved if porosity develops in the piece during the early stages of decomposition, as opposed to the retreat of the binder into the piece on a uniform front.     

Binder jetting of ceramics: Powders,binders, printing parameters,equipment, and post-treatment

Binder jetting is expected to become the universal process for preparing ceramic parts because it can overcome multiple problems, such as the difficulty to prepare complex-shaped ceramic parts and the shrinkage of the sintering process, which appear in conventional ceramic preparation process. This paper introduces principles, steps, and applications of binder jetting printing ceramics. Furthermore, five key factors of binder jetting printing ceramics (powders, binders, printing parameters, equipment, and post-treatment process) have been investigated. Accordingly, effects of powders (including shape, particle size and distribution, and additives), binders (including binding method, droplet-formation mechanism, and droplet-infiltration kinetics), printing parameters (including layer thickness, saturation, solid binder, and printing orientation), equipment, and post-treatment (including de-powdering process, and densification process) on density, roughness, strength, accuracy, and resolution of ceramic parts have been discussed and summarized. This paper provides detailed analysis of techniques and mechanisms of binder jetting of ceramics, giving guidance on how to handle raw materials and select various processing parameters for achieving desired performance.     

Analytic Model for the Diffusant Concentration in Ceramic Green Bodies During Diffusion‐Controlled Thermal Binder Removal

The diffusion of the decomposition product of binder degradation has been modeled using the diffusion equation when a source term is present. An analytic solution to the governing nonlinear, unsteady‐state partial differential equations has been obtained for a planar body with two simplifications. The first approximation utilizes the pseudo‐steady‐state approximation whereas the second approximates the diffusivity, as given by the free volume theory, in terms of a single temperature‐dependent parameter. The analytic solution, which was compared to numerical solutions to establish the range of model validity, accurately describes the temporal and spatial distribution of the binder decomposition product during most of the heating cycle, especially when the concentration in the green body is the highest. The functional dependence of concentration within the body is established in terms of model parameters including the body size, degree of nonlinearity of the diffusivity, and the ratio of reaction rate to diffusivity.     

Minimum time heating cycles for diffusion‐ versus permeability‐controlled binder removal from ceramic green bodies

A comparison of minimum time heating cycles (MTHCs) was conducted for binder removal from ceramic green bodies for two mass transfer mechanisms: diffusion and gas permeability. The MTHCs were determined by combining approximate analytic solutions to the governing reaction‐diffusion and reaction‐gas permeability equations with a variational calculus algorithm containing a constraint on pressure buildup within the green body. Both the temperature‐time profile and duration of the MTHCs were sensitive to the operative transport process as well as to a number of model parameters including the pressure constraint, the total furnace pressure, the reaction kinetics, the gas permeability, and the diffusivity as described by the free volume theory. Strategies were identified which are most effective for decreasing the cycle time for each mass transfer mechanism.     

Binder Evolution from Powder Compacts: Thermal Profile for Injection-Molded Articles

Binder evolution information generated using thermal analysis techniques is used along with microstructural information to define a thermal cycle for debinderizing injection-molded articles. In addition, the roles of binder chemistry, powder morphology, binder loading, article size, heating rate, and environmental conditions in determining a satisfactory thermal cycle are investigated. Major binder evolution events and types of defects generated are identified. An improved binder removal cycle is developed from this evaluation for organics elimination of a honeycomb structure.     

Binder Distribution in Ceramic Greenware During Thermolysis

Capillary forces were shown to influence the distribution of polymer-plasicizer mixtures within ceramic green bodies during binder thermolysis. Isothermal thermogravimetric analysis was performed on tape-cast sheets of an aluminapoly(vinyl butyrall-dibutyl phthalate composite and direct observations were made of the binder distribution and pore growth after partial pyrolysis. This led to the investigation of a model system, an alumina-eicosane composite, by similar experimental techniques. The early stage of binder removal was found to be similar to the drying of particle beds in which capillary forces draw liquid into the smaller pores at the surface. The morphology of the binder distribution produced by these processes dictates which mass-transfer resistances may be controlling in binder burnout. A model is described that determines the length scale over which capillarity acts based on measurable physical parameters of the binder system and the packing of the ceramic particles.     

Determination of thermal decomposition kinetics of low grade coal employing thermogravimetric analysis

The decomposition kinetics of low grade coals was studied and compared with the kinetics of higher grade coals using thermogravimetric analysis. The effect of atmospheres (air, O₂ and N₂) on coal decomposition kinetics was also investigated. Experiments were carried out under non-isothermal conditions from room temperature to 950 °C at a heating rate of 10 °C/min. Three kinetic models—multiple linear regression equation, unreacted shrinking core and continuous reaction—were used to determine the kinetic parameters of coal decomposition. From the kinetic parameters determined through the multiple linear regression equation, coal type and the atmosphere had an effect on coal decomposition kinetics. Also, there was some variation in the kinetic parameters of coal decomposition determined by the chosen kinetic models. However, the model employing multiple linear regressions yielded consistent results with respect to theoretical background. Under air, the order of the secondary decomposition of coal samples was found to be 0.88, 1.33, 1.69 and 1.52 for samples A, B, C and D, respectively. The order of the secondary decomposition of coal samples when operated under O₂ was 1.09, 1.45, 2.36 and 1.81 for samples A, B, C and D, respectively. Under N₂, the order of the secondary decomposition of coal samples was 0.72, 0.79, 1.15 and 1.02 for samples A, B, C and D, respectively.     

Thermogravimetric analysis of polystyrene: Influence of sample weight and heating rate on thermal and kinetic parameters

This article studies the influence of the heating rate and sample weight on the thermal decomposition of polystyrene (first-order kinetics). For this purpose, the kinetic parameters (i.e., frequency factor and activation energy), variables at the maximum decomposition rate (such as conversion, reaction rate, and temperature), as well as some characteristic temperatures have been determined for a series of experiments where the heating rate varies (0.5–11.5 K/min) and also, the sample weight (6.0–25.1 mg). Some mathematical equations have been developed that allow: (1) evaluation of the activation energy of thermal decomposition by different ways and comparing the results obtained; (2) relating different parameters between themselves, such as the heating rate with the temperature at the maximum decomposition rate or the frequency factor with the heating rate and sample weight. Finally, some theoretical explanations of the variation of thermal and kinetic parameters have been proposed. © 1996 John Wiley & Sons, Inc.     

Application of the kinetic composite methodology to autocatalytic-type thermoset prepreg cures

Using a commercial epoxy/carbon fiber prepreg as a model system, cure kinetics of an autocatalytic-type reaction were analyzed by a general form of conversion-dependent function first proposed for degradation kinetics of polymers and composites. The characteristic feature of conversion-dependent function was determined using a reduced-plot method where the temperature-dependent reaction rate constant was analytically separated from the isothermal data. Assuming two elementary reaction mechanisms that were expressed by the nth order and autocatalytic kinetic models, they were combined with a composite methodology capable of predicting overall kinetic behavior. The activation energies were determined and favorably compared for both isothermal and dynamic-heating differential scanning calorimetry experiments in the temperature region for standard epoxy cures at 177°C (350°F). Finally, the proposed model equation demonstrated excellent predictive capability and broad applicability in describing various types of thermoset polymer cure for both isothermal and dynamic heating conditions. © 1993 John Wiley & Sons, Inc.     

Hot-Stage Study of Bubble Formation During Binder Burnout

A technique for observing bubble formation during binder burnout in ceramics processing has been developed using the hot-stage microscope. Four sets of samples were designed to meet different objectives of the study. Bubble nucleation, growth, and shrinkage were observed. Influencing factors, such as initially trapped gas bubbles, amount of residual solvent, ceramic powder surface, and heating rate were studied.     

非等温热重法研究聚苯硫醚热分解动力学

采用非等温热重法对聚苯硫醚的热分解动力学进行研究,通过比较计算结果选定拟合结果更好的迭代法计算反应活化能,采用积分法结合36种动力学函数来判断聚苯硫醚热分解的机理函数。得到了聚苯硫醚热分解动力学参数平均活化能E、指前因子A和对应的热分解动力学方程。