Fluoropolymers modeling

In the mid Atlantic ocean observed concentrations at A03 and A04 decrease gradually with depth, whereas A05 concentrations show an increase until 500 m and a decrease below. Modeled profiles show a similar pattern. Surface concentrations of model results are much lower than the observed ones. In addition to this the fact that profiles of all mid Atlantic sampling location are identical can be explained by missing discharge into the mid Atlantic ocean in the emissions scenario. Emissions from American fluoropolymer productions sites are released into the Atlantic Ocean solely at the mouth of St. Lawrence River. Discharge of PFOA into for example the Gulf of Mexico is not considered. 

The shortcomings of the force field notwithstanding, these preliminary molecular dynamics simulations indicate that modeling of the chain motions of crystalline fluoropolymers and their interactions is sure to be quite rewarding. Further, the results suggest that with additional refinement of the force field. 

A force field for solid state modeling of fluoropolymers predicted a suitable helical conformation but required further improvement in describing intermole-cular effects. Though victory cannot yet be declared, the derived force fields improve substantially on those previously available. Preliminary molecular dynamics simulations with the interim force field indicate that modeling of PTFE chain behavior can now be done in an all-inclusive manner instead of the piecemeal focus on isolated motions and defects required previously. Further refinement of the force field with a backbone dihedral term capable of reproducing the complex torsional profile of perfluorocarbons has provided a parameterization that promises both qualitative and quantitative modeling of fluoropolymer behavior in the near future. 

It was thus worth finding a model of the synthesis of fluoropolymers in order to predict their degree of polymerisation, their structure, and the mechanism of the reaction. 

The theoretical treatment presented (Eqs 4.1-4.5) is applicable also for direct wet electrochemistry on Pt cathode in aprotic electrolyte solution [12,13] (Table 4.1) and for some other chemical reductants, Rj, viz. benzoin dianion [14] and sodium dihydronaphthylide [15] (Table 4.1). Apparently, the decision between chemical and electrochemical carbonization may not be straightforward. The latter scenario requires a compact solid electrolyte with mixed electron/ion conductivity to be present at the interface. This occurs almost ideally in the reactions of solid fluoropolymers with diluted alkali metal amalgams [3]. If the interfacial layer is mechanically cracked, both electrochemical and chemical carbonization may take place, and the actual kinetics deviates from that predicted by Eq. 4.4 [10]. There is, however, another mechanism, leading to the perturbations of the Jansta and Dousek s electrochemical model (Eq. 4.4). This situation typically occurs if gaseous perfluorinated precursors react with Li-amalgam [4,5], and it will be theoretically treated in the next section. 

There are two approaches to characterizing fluoropolymers for injection molding. The more fundamental methodology centers around the measurement of physical properties such as melt viscosity and thermal diffusivity to generate data for mathematical modeling (simulation) of injection molding processes. 

Fluoropol Tners are used in critical applications where failure may have serious safety, environmental, and/or financial consequences. Modeling is an important tool in determining the root cause of the failure and its correction. The modeling of fluoropolymer components, like other polymer materials, continues to evolve in sophistication. This chapter introduces current and developing methodologies for mechanical analysis. These methodologies promise increasingly accurate predictions and analysis of fluoropolymer materials. 

Modeling of fluoropolymers can be based on several approaches, ranging from simple to complex and from phenomenological to those based on physical deformation processes. This chapter does not discuss all of the tools available for analysis. It does, however, provide a comparison and discussion of the values and ranges of applications for numerous analytical tools so an engineer or scientist can make informed decisions about how much effort and sophistication is appropriate for a given analysis. 

As stated in the introduction, there are numerous available techniques for modeling fluoropolymers. These can be divided into analytical and computational techniques, using more or less sophisticated material models within each technique. Table... 

Physically based constitutive models that accurately capture the behavior of fluoropolymers. 

There are a number of candidate materials models for predicting the behavior of fluoropolymers. Since the models have varying degrees of complexity, computational expense, and difficulty in determining the material parameters, it is a good idea to use the simplest material model that captures the necessary material characteristics for the application and situation at hand. Unfortunately, it is often difficult to determine, in advance, the required conditions needed by the material model. Hence, it is recommended that a more advanced model be used in order to ensure accuracy and reliability of the predicted data. At a later stage, a less advanced model can be attempted if the computational expense is too great. At that time, the accuracy of the different model predictions can also be tested and validated. 

Linear elasticity is the most basic of all material models. Only two material parameters need to be experimentally determined the Young s modulus and the Poisson s ratio. The Young s modulus can be directly obtained from uniaxial tension or compression experiments, and typical values for a few select fluoropolymers at room temperature are presented in Table 11.2. 

The theory behind linear viscoelasticity is simple and appealing. It is important to realize, however, that the applicability of the model for fluoropolymers is restricted to strains below the yield strain. One example comparing predictions based on linear viscoelasticity and experimental data for PTFE with 15 vol% glass fiber in the very small strain regime is shown in Fig. 11.4. 

A number of more advanced and general models attempting to predict the yielding, viscoplastic flow, time-dependence, and large strain behavior of fluoropolymers and other thermoplastics have recently been developed.in this section, we discuss the Dual Network Fluoropolymer (DNF) model. 

After a constitutive model has been chosen, calibrated, and validated for a particular fluoropolymer, it becomes as easy to perform multiaxial deformation simulations as it is to simulate uniaxial deformation. If the material model considers time dependence, temperature dependence, or damage evolution, then thermomechanical or fatigue loading can also easily be simulated. Since almost all commercial finite element (FE) software packages allow for nonlinear simulations including considerations of large deformations, the key component of performing accurate finite element simulations lies within the specification and calibration of the constitutive model. 

The physics of failure of fluoropolymers on the microscale is caused by thermally activated breakages of secondary and primary bonds in the material. The chain scission leads to crack and void formation and ultimate failure. To model and predict these events typically requires an investigation on a larger length scale where a continuum mechanics approach can be used. 

It is currently not well established which failure model is most appropriate for predicting failure of fluoropolymers that are monotonically loaded to failure. Commonly used approaches include the maximum principal stress, the maximum principal strain, the Mises stress, the Tresca stress, the Coulomb stress, the volumetric strain, the hydrostatic stress, and the chain stretch. In the chain stretch model, the failure is taken to occur when the molecular chain stretch, calculated fromPl... 

A direct comparison between these and other failure models has not been performed for fluoropolymers, but a recent study of UHMWPEl showed that, for UHMWPE, these models are very different. For example, it was shown that the chain stretch model is the most promising for predicting multiaxial deformation states, and that the hydrostatic stress, and the volumetric strain are not good predictors of failure. 

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