Modeling the dynamics of reactive foaming and film thinning in polyurethane foams

Flexible polyurethane foams are widely used in cushioning and packaging applications. A model for the dynamics of formation of polyurethane foams is presented, which includes thinning of foam lamellae. Experimental measurements for water blown flexible foam formulations at different water concentrations are presented to validate the model. Adiabatic temperature rise measurements during foaming are used to obtain the kinetic parameters of the reactions of isocyanate with polyol and water. The variation of foam density during foaming is studied by weight loss and video shooting methods and both are compared to estimate the amount of blowing gas lost during foaming. The average thickness of the foam lamellae of the solid foam is obtained by SEM measurements. The predictions of the model show good agreement with the experimental measurements of temperature and density with time and the final lamellar thickness. The results are important for understanding the cell opening process. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Process monitoring and kinetics of rigid poly(urethane–isocyanurate) foams

Process temperature profiles of a two‐component rigid poly(urethane–isocyanurate) foam system were studied and compared with the predictions of a one‐dimensional numerical simulation. This model is based on experimentally determined thermophysical properties including thermal diffusivity, enthalpy of reaction, and rate of reaction. Temperature profiles were measured at three positions within the foam and at the foam surface for mold temperatures of 25°C and 55°C. A high rate of reaction and heat of reaction, along with low thermal diffusivity, cause temperatures near the foam center to be insensitive to mold temperatures for thick samples. Thermal analysis was used for determination of thermophysical properties. Temperature‐dependent heat capacity, reaction kinetics, and heat of reaction were evaluated using temperature‐scanning DSC. Thermal conductivity was analyzed from steady‐state heat profiles. The system reaction kinetics indicated much faster kinetics than reflected by process cure temperature profiles made using thermocouples. The simulations accurately predict experimental results, allowing determination of demold time dependence on process conditions, including feed temperature, mold temperature programming, and sample thickness. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 374–380, 2000     

Mathematical model for the pultrusion of blocked PU–UP matrix composites

The thermokinetic behavior of blocked polyurethane (PU)–unsaturated polyester (UP)–based composites during the pultrusion of glass‐fiber‐reinforced composites was investigated utilizing a mathematical model that accounted for the heat transfer and heat generation during curing. The equations of continuity and energy balance, coupled with a kinetic expression for the curing system, were solved using a finite difference method to calculate the temperature profiles and conversion profiles in the thickness direction in a rectangular pultrusion die. A kinetic model, dP/dt = A exp(?E/RT)P^m(1 ? P)ⁿ, was proposed to describe the curing behavior of a blocked PU–UP resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry scans using a multiple regression technique, which was able to predict the effects of processing parameters on the pultrusion. The effects of processing parameters including pulling speed, die wall temperature, and die thickness on the performance of the pultrusion also were evaluated. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1996–2002, 2003     

Preparation and characterization of p-tert-butyl thiacalix[4]arene imbedded flexible polyurethane foam: An efficient novel cationic dye adsorbent

In this study, a new type of flexible polyurethane foam containing p-tert-butyl thiacalix[4]arene (TC4A) macrocycle was synthesized. TC4A macrocycle was incorporated into polyurethane foam as a part of crosslinking agent as well as glycerol. Structural, morphological, thermal and mechanical properties of this prepared foam were studied and compared with a polyurethane foam based on only glycerol as crosslinking agent, by Fourier transform infrared (FTIR), Scanning electron microscopy (SEM), Thermal gravimetric analysis (TGA), and dynamic mechanical thermal analysis (DMTA). The effect of introduction of TC4A crosslinker on cream time, rise time, apparent density, and water absorbency of the PU foams was evaluated. Moreover, it was shown that new TC4A-based polyurethane foam (TC-PUF) can be a high performance adsorbent for removal of malachite green from aqueous media using batch adsorption technique. The adsorption results indicated that TC-PUF has a high adsorption capacity of 58.82 mg/g for malachite green due to the presence of TC4A macrocycles in the structure of polyurethane foam. The kinetics of adsorption of malachite green was also investigated using the pseudo-first-order and pseudo-second-order kinetic models. The results of kinetic studies showed that the adsorption of malachite green onto TC-PUF followed pseudo-second-order kinetic model.     

一种计算泡沫金属等效热导率的新模型

提出一种针对泡沫金属等效热导率预测的新模型,该模型基于泡沫金属Kelvin十四面体元胞结构建模,以凹面三棱柱近似金属韧带,并考虑韧带交汇处的结点特点,通过热阻分析得到计算等效热导率的表达式。研究表明：该模型对充填不同介质的不同材质泡沫金属等效热导率均有较高的预测精度（平均偏差均小于10%）,与文献其他半经验模型相比能更好兼顾预测精确性和通用性。     

Modeling of glycolysis of flexible polyurethane foam wastes by artificial neural network methodology

The glycolysis process as a useful approach to recycling flexible polyurethane foam wastes is modeled in this work. To obtain high quality recycled polyol, the effects of influential processing and material parameters, i.e. process time, process temperature, catalyst‐to‐solvent (Cat/Sol) and solvent‐to‐foam (Sol/Foam) ratios, on the efficiency of the glycolysis reaction were investigated individually and simultaneously. For the continuous prediction of process behavior and interactive effects of parameters, an artificial neural network (ANN) model as an efficient statistical‐mathematical method has been developed. The results of modeling for the criteria that determine the glycolysis process efficiency including the hydroxyl value of the recycled polyol and isocyanate functional group conversion prove that the adopted ANN model successfully anticipates the recycling process responses over the whole range of experimental conditions. The Cat/Sol ratio showed the strongest influence on the quality of the recycled polyol among the studied parameters, where the minimum hydroxyl value was obtained at a medium amount of the assigned ratio. For the consumed polyurethane foam, a higher value of this ratio led to an increase in the hydroxyl value and isocyanate conversion. © 2015 Society of Chemical Industry     

Modeling of a multizone gas‐phase polyethylene reactor with a cluster‐based approach

A circulating fluidized reactor of polyethylene was modeled with the proper hydrodynamics for a riser and downer and combined with a kinetic model based on the moment equations. The hydrodynamic model was able to predict the profiles of the following parameters through the riser and downer: cluster velocity, bed porosity, concentration of potential active sites, active sites, gas‐phase components, molecular weights, and reactor temperature. It was shown that one could control the monomer consumption and molecular weight, which are crucial in the reactor behavior and production properties, respectively, by setting different operating hydrodynamic conditions, such as the gas velocity in the riser and the solid circulation rate. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Simulation of liquid physical blowing agents for forming rigid urethane foams

A computer‐based simulation for rigid polyurethane foam‐forming reactions was compared with experimental data for six blowing agents including methyl formate and C5‐C6 hydrocarbons. Evaporation of blowing agent was modeled as an overall mass transfer coefficient times the difference in activity of the blowing agent in the gas foam cells versus the resin walls of the cells. Successful modeling hinged upon use of a mass transfer coefficient that decreased to near zero as the foam resin approached its gel point. Modeling on density agreed with experimental measurements. The fitted parameters allowed for interpretations of the final disposition of the blowing agent, especially, if the blowing agent successfully led to larger foam cells versus being entrapped in the resin. The only component‐specific fitted parameters used in the modeling was the activity coefficient that was lower for methyl formate than the value used for hydrocarbons. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42454.     

On the modeling and optimization of UV‐curable fluoro‐siloxane formulations and their solvent absorption and adhesion properties

A screening study was performed on a family of UV‐curable fluoro‐silicone polymers designed to coat aluminum. Solvent durability, adhesion, dimensional stability, and thermal oxidative stability were important physical parameters to control. An XVERT mixture experimental design was used to model the behavior of selected polymer formulations. A calibrated linear model showed excellent correlation with experimental data. The coefficients from this model were then used to predict and optimize the responses of the polymer formulations to specific requirements. It was shown that percent fluorination was a strong influence on the amount of solvent absorption and the level of thermal oxidative stability, while the amount of hydrocarbon‐based alcohol was shown to be necessary for adhesion to aluminum and a post cure polyurethane top coat. POLYM. ENG. SCI., 59:1678–1687 2019. © 2019 Society of Plastics Engineers     

Nanoclay filled soy‐based polyurethane foam

Polyurethane foam was fabricated from polymeric diphenylmethane diisocyanate (pMDI) and soy‐based polyol. Nanoclay Cloisite 30B was incorporated into the foam systems to improve their thermal stabilities and mechanical properties. Neat polyurethane was used as a control. Soy‐based polyurethane foams with 0.5–3 parts per hundred of polyols by weight (php) of nanoclay were prepared. The distribution of nanoclay in the composites was analyzed by X‐ray diffraction (XRD), and the morphology of the composites was analyzed through scanning electron microscopy (SEM). The thermal properties were evaluated through dynamic mechanical thermal analysis (DMTA). Compression and three‐point bending tests were conducted on the composites. The densities of nanoclay soy‐based polyurethane foams were higher than that of the neat soy‐based polyurethane foam. At a loading of 0.5 php nanoclay, the compressive, flexural strength, and modulus of the soy‐based polyurethane foam were increased by 98%, 26%, 22%, and 65%, respectively, as compared to those of the neat soy‐based polyurethane foam. The storage modulus of the soy‐based polyurethane foam was improved by the incorporation of nanoclay. The glass transition temperature of the foam was increased as the nanoclay loading was increased. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

New applications for foam composites of polyurethane and recycled rubber

In Portugal, most end‐of‐life tires are recycled through a process involving a cryogenic grinding technology. The purpose of this work was to envisage new applications for recycling rubber from end‐of‐life tires. In this work, rubber was supported in a polyurethane matrix generating two new products of distinct characteristics and properties. The choice of these products was ruled by the requests of potential clients: (a) Floating trays to withstand the load of plants capable of cleansing polluted water from lagoons, ponds, or basins; (b) Compression‐absorbing buoys to dampen the shocks and the compressive stresses between ships and docks. The polyurethane formulations developed herein were based on methylene diphenyl diisocyanate and a trifunctional polyol such that the final foam would be flexible. As the floating trays' density should be lower than the water density, the best formulation found comprised 150% of rubber, 4% of water (relative to the polyol mass), with an isocyanate index of 105% and a density of 89 kg m^?3. The foam that presented the optimal compression behavior to be applied in compression absorbing buoys, comprised 200% of rubber, 3% of water, with an isocyanate index of 105% and a density of 121 kg m^?3. In both cases, the composite foam materials obtained showed final properties compatible with the envisaged applications, pointing out that the implied methodology may be used in the future to recycle rubber from end‐of‐life tires. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Semiempirical,squeeze flow,and intermolecular diffusion model. II. Model verification using laser microwelding

This article reviews the application of a coupled squeeze flow and intermolecular diffusion model, which was used to predict the quality and size of microwelds in plastics. Weld widths predictions were compared with previously presented experimental results using moving heat source models and temperature fields. The motivation for this work was to develop and verify a model based on fundamental principles that could accurately predict weld size and strength for conventional plastic welding techniques as well as novel techniques such as laser microwelding. It is envisioned that the resulting model could be used to predict proper welding parameters, including laser power and travel speed, to produce welds of varying size. Although insight into weld quality can be derived from this model, it was not the goal of this work to accurately predict weld strength for laser microwelding because of the difficulty in measuring weld strength on the micron scale. However, as reported in Part 1, weld strength for impulse welds were accurately predicted. In this model it was found that variable temperature histories, rather than a single value of maximum weld temperature, allows more accurate modeling of the welding process. In this work (Part 2), microwelds as small as 11 μm in width were produced with transmission infrared welding. In addition, welds over 150‐μm wide were also generated and the model was able to predict the range of weld widths that were found experimentally. It was found that the predictions were in very good agreement with the experimental results. There was some deviation between the experimental data and the model at the extreme parameters and it is believed that this was due to the temperature‐dependent material properties as well as optical aberrations. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Controlled degradation of natural rubber and modification of the obtained telechelic oligoisoprenes: Preliminary study of their potentiality as polyurethane foam precursors

Telechelic oligoisoprenes were successfully prepared by the selective controlled degradation of natural rubber, a renewable source, via epoxidation and cleavage reactions. The molar mass of the oligoisoprene product obtained depends on the degree of epoxidation of the starting materials. The chemically modified structures obtained via epoxidation, hydrogenation, and ring opening of epoxide groups were also studied, and the chemical structures and thermal properties of the oligoisoprene products were determined. Moreover, the preliminary study of preparation of hydroxytelechelic natural rubber (HTNR)‐based polyurethane foam was performed. A novel HTNR‐based polyurethane foam was successfully prepared and its thermal properties were investigated and the results indicated that the HTNR‐based polyurethane foam has a good low temperature flexibility. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Kinetic finite element model to optimize sulfur vulcanization: Application to extruded epdm weather‐strips

A numerical two‐phase approach based on experimental scorch curve data fitting, to predict the optimal exposure time and cure temperature of extruded thick items is applied for the study of a real weather‐strip. In the first phase, an existing single equation kinetic model is used to predict the crosslinking density under sulfur vulcanization at variable temperatures. The model requires the calibration of only three kinetic constants. The variation with respect to temperature of such parameters is then evaluated by means of two experimental cure curves performed at two different temperatures. In the second phase, kinetic reaction parameters are implemented in finite element software, to perform thermal analyses on an extruded weather‐strip. Once evaluated the final mechanical properties of the item point by point, a set of compression tests is numerically simulated, assuming that the rubber behaves as a Mooney–Rivlin material under the large deformations. Elastic properties of the item are evaluated as a function of the vulcanization degree evaluated in the second phase. It is found that suboptimal vulcanizations result into lower elastic moduli and hence great deformability, sometimes incompatible with real scale engineering applications. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Dynamic compression characteristics of flexible foams. I. Similarity model,analysis, and experiments

A simple mathematical model is proposed, based on dimensional similarity parameters, to describe the characteristics of flexible plastic foams under impact conditions. The model assumes that the foam is rate-dependent material, when the dynamic stress is a function of the strain and the strain rate. The similarity parameters include the geometric dimension of the foam, the mass of the absorbing body, and the drop height. By using this model, one can predict the maximum deformation, the maximum decelerations, and the time-pulse period for a wide range of drop heights and masses, by conducting several drop tests. We verified the efficacy of this model by performing free-fall drop tests with flexible polyurethane foam having a uniform density of 240 kg/m³.     

Modeling of the Dynamics of Water and R-11 blown polyurethane foam formation

Polyurethane foam formation involves both polymerization and expansion processes. The dynamics of the water and R-11 blown foams depend on the rates of chemical and physical blowing processes, along with the rate of viscosity increase of the reacting mixture. Experiments were carried out to study the dynamics of free rising, water and R-11 blown rigid polyurethane foams. The density and temperature change during the foam formation were monitored. A theoretical model was developed to predict the density and temperature variation with time. In the model, the physical blowing agent (R-11) evaporation process is assumed to be heat generation–controlled and the carbon dioxide generation process to be controlled by the rate of the water-isocyanate reaction. The kinetic parameters of the reactions of isocyanate with polyol and water were obtained separately and were asssumed to be independent of each other. The water-isocyanate reaction appears to follow first-order kinetics with respect to concentration of water. The theoretical predictions of the model show good agreement with the experimental data for density variation with time. The model predictions for temperature rise also match experimental data, except at the later stages of foaming when it is found to be slower than the experimental measurements. However, this deviation does not affect the dynamics of density change since it occurs after the completion of the expansion process.     

Determination of adsorption and kinetic parameters for methyl acetate esterification and hydrolysis reaction catalyzed by Amberlyst 15

In this paper, the adsorption equilibrium constants, dispersion coefficients, and kinetic parameters were obtained for the liquid phase reversible reaction of methanol with acetic acid catalyzed by Amberlyst 15. The adsorption and kinetic parameters are determined corresponding to two different mobile phases, methanol and water. Such parameters are required for three different applications of the model reaction: namely, synthesis of methyl acetate, removal of dilute acetic acid from wastewater, and hydrolysis of methyl acetate. Experiments were conducted in a packed bed reactor in the temperature range 313–323 K using a rectangular pulse input. A mathematical model for a quasi-homogeneous kinetics was developed. The adsorption and kinetic parameters together with their dependence on temperature were determined by tuning the simulation results to fit the experimentally measured breakthrough curves of acetic acid, water (or methanol) and methyl acetate using a state-of-the-art optimization technique, the genetic algorithm. The mathematical model was further validated using the tuned parameters to predict experimental results at different feed concentrations and flow rates. The kinetics reported in this study was obtained under conditions free of both external and internal mass transfer resistance. The computed parameters were found to predict experimental elution profiles for both batch and plug flow reactors reasonably well.     

Constitutive modeling and simulation of energy absorbing polyurethane foam under impact loading

The compressive-stress strain response of polyurethane foam under uniaxial compressive impact loading has been studied. The development of a uniaxial constitutive model from strain rate controlled compression tests is detailed. Density and temperature functions have been added to the integral power model proposed by Schwaber, Meincke, and Nagy. The model assumes that the effects of density, temperature, strain and strain rate on stress are separable functions. The model correlated well with actual static compression tests and was used successfully to predict the impact response of energy absorbing polyurethane foam under uniaxial compressive loading.     

Reaction modeling of urethane polyols using fraction primary secondary and hindered‐secondary hydroxyl content

The effect of primary, secondary, and hindered‐secondary hydroxyl groups on reactions and temperature profiles of polyurethane gels was investigated and modeled using a computer simulation that simultaneously solves over a dozen differential equations. Using urethane gel reaction temperature profiles of the reference compounds 1‐pentanol, 2‐pentanol, and Voranol 360 reactivity parameters were determined for reference primary, secondary, and hindered‐secondary hydroxyl moieties. The reaction parameters, including Arrhenius constants and heats of reaction, were consistent with previous values reported in literature. The approach of using fractions primary, secondary, and hindered‐secondary hydroxyl content to characterize reactivity sets the basis for a powerful approach to simulating/predicting urethane reaction performance with limited data on new polyols and catalysts. This code can be used for all polyols, as the kinetic parameters are based on the fraction primary, secondary, and hindered‐secondary alcohol moieties, not the type of the polyol. Kinetic parameters are also specific to catalysts where at least one parameter specific to each catalyst is necessary to simulate the impact of that catalyst. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40388.