Polymer model validation

Polymer model validation was ensured by checking the convergence of the total energy at the end of the MD runs as well as the density value and cohesive energy density close to that of the experiment. Moreover, plotting the total, intra-,... 

This is consistent with our previous discussion (see Chap, 7), where we stressed that the continuous chain model, underlying naive two-parameter theory, is a valid representation of a general polymer model only close to the -point. 

Liotta, V. Sudol, E.D. El-Aasser, M.S. Georgakis, C. On-line monitoring, modeling, and model validation of semibatch emulsion polymerization in an automated reactor control facility. J. Polym. Sci. Pt. A Polym. Chem. 1998, 36 (10), 1553-1571. 

Stern, Frisch, and coworkers have extended Fujita s free-volume model to the permeation of light gases (31-33) (see Figure 3) and binary gas mixtures (34,25) (see Figure 4) through polymer membranes. The extended model was found to describe satisfactorily the dependence of permeability coefficients on pressure and temperature for a variety of light gases in polyethylene, as well the dependence on composition for several binary mixtures in the same polymer. The validity of the extended model is limited to total penetrant concentrations of up to 20-25 mol-%. 

When the bulk behavior is checked with fluorescence techniques, much smaller CAC values are observed, an order of magnitude smaller than for a more hydrophilic polyelectrolyte, sodium polyacrylate.4 Bulk association could explain why surface tension changes are only appreciable at high polymer concentration. In this case, the simple adsorption model valid for PAMPS would evidently not work, because it does not account for bulk complexes. 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

Polymer Model Studies. In order to complete our design studies of the solubility switch approach to positive tone imaging of water soluble resists, a model homopolymer 14 was designed to help ascertain the validity of our acetal cleavage concept, the last step in our overall imaging concept (Scheme 6). 

No.lO, 30th July 1998, p.1553-71 ON-LINE MONITORING, MODELLING AND MODEL VALIDATION OF SEMIBATCH EMULSION POLYMERISATION IN AN AUTOMATED REACTOR CONTROL FACILITY Liotta V Sudol E D El-Aasser M S Georgakis C Lehigh University,Emulsion Polymers Institute... 

Weber, A.Z. and Newman, J. (2004) Transport in polymer-electrolyte membranes. III. Model validation in a simple fuel-cell model. /. Electrochem. Soc., 151, A3 26. 

It is the model library for fixed-bed catalytic reaction, fluidised-bed and various polymer reactors and so on. Different tools are available in gPROMS software for simulation and modelling of various systems. Some of the following are (i) multi-scale modelling of complex processes and phenomena, (ii) State-of-the-art model validation tools allow estimation of multiple model parameters from steady-state and dynamic experimental data, and provide rigorous model-based data analysis, (iii) The maximum amount of parameter information from the minimum number of experiments, (iv) The gPROMS-CFD Hybrid Multitubular interface provides ultimate accuracy in the modelling of... 

This study deals with the development of a dynamic model for an industrial olefin polymerization plant (Borstar ). The model captures the dynamic behaviour of the different process units, and accounts for molecular polymer properties and thermodynamic properties of polymer mixtures using an advanced equation of state. The model validity is tested against industrial data. 

If the two-phase model of semicrystalline polymers were valid, the following relationship would hold beyond the glass transition temperature ... 

Santos AF, Pinto JC, McKenna TFL. On-hne monitoring of the evolution of number of particles in emulsion polymerization by conductivity measurements. Part n. Model validation. J Appl Polym Sci 2004 91 941-952. 

As already emphasized, any structural model of heterogeneous polymers claiming validity had to account explicitly for the smearing out of any sharp mathematical interface into physical BI finite thickness Ar. Apparently, this... 

The general expectations embodied in Equations 7.12, 7.16, and 7.19 are borne out to be valid as shown by experiments in dilute solutions of uncharged polymers. Depending on the experimental conditions, the value of the size exponent changes and this change is directly manifest in D, rj, and t in terms of their dependencies on the molecular weight of the polymer and solvent conditions. In order to obtain the numerical prefactors for the above scaling laws and to understand the internal dynamics of the polymer molecules, it is necessary to build polymer models that explicitly account for the chain connectivity. The two basic models of polymer dynamics are the Rouse and Zimm models (Rouse 1953, Kirkwood and Riseman 1948, Zimm 1956), which are discussed next. 

Polymers can adsorb spontaneously from solution on to surfaces if the interaction between the polymer and the surface is more favorable than that of the solvent with the surface. For example, a polymer like poly(ethylene oxide) (PEO) is soluble in water but will adsorb on various hydrophobic surfaces and on the water/air interface. This is the case of equilibrium adsorption where the concentration of the polymer monomers increases close to the surface with respect to their concentration in the bulk solution. We discuss this phenomenon at length both on the level of a single polymer chain (valid only for extremely dilute polymer solutions), see Section II, and for polymers adsorbing from (semidilute) solutions, see Section III. In Fig. 2a we schematically show the volume fraction profile (p(z) of monomers as a function of the distance z from the adsorbing substrate. In the bulk, i.e., far away from the substrate surface, the volume fraction of the monomers is (p], whereas, at the surface, the corresponding value is (p > (p]. The theoretical models address questions in relation to the polymer conformations at the interface, the local concentration of polymer in the vicinity of the surface, and the total amount of adsorbing polymer chains. In turn, the knowledge of the polymer interfacial behavior is used to calcu-... 

MC simulations are well-suited to determine the phase behavior and properties of bubbles directly (i.e., without further approximations). Even in the framework of a coarse-grained polymer model these simulations pose an enormous computational and methodological challenge, but they are absolutely crucial for assessing the validity of the maze of approximations involved in the previous methods. They elucidate the role of fluctuations [70, 71, 72, 73] (both of the composition and at interfaces) and provide - at least in principle - direct information about the kinetics of phase separation. The last two topics cannot be addresses within the SCF theory or TPTl-equation of state, which are mean-field theories for thermal equilibrium. 

Shojaie, S. S., Krantz, W. B., and Greenberg, A. R. (1994). Dense polymer film and membrane formation via the dry-cast process. 1. Model validation and morphological study. J. Membr. Sci. 94, 281. 

Molecular models of SWNT embedded in a polymer block are constructed. The SWNT is of armchair configuration with outer diameter of 13.4 A and length of 20 A. The outer diameter of the polymer block consists of randomly oriented polymer chains, approximately 56 A about 20 A in thickness. No chemical bonding exists between the CNT and the polymer. To validate the polymer molecular model, the density for polyethylene (PE) and polypropylene are calculated to be 0.705 g/cm and 0.73 g/cm, respectively, agreeing well with those by Frankland et al. ... 

Polymer models consisting of one single chain of 300 monomers were created using a Monte Carlo-based method similar to the short-chain models described above. This was done to study the effect on diffusion and solubility of the presence in these short-chain models of too many chain ends (as compared to the real material) and, therefore, of added free volume. It has been suggested that this is one of the main factors for the discrepancy between simulated and experimental values. The models were validated using the similar procedure described in Section 9.2.I.I. 

Fiber crystallinity data for fibers spun from two polypropylene resins was obtained, on a commercial fiber line, using on-line Raman spectroscopy. The experimental data presented here will be used to validate fundamental fiber spinning models. Results from the model validation/refinement will be are presented in a separate paper. The validated models and experimental observations can be used to guide fiber spinning of hPP polymers for rapid product development. Some key results obtained from the online Raman measurements can be summarized as follows... 

It is only the contribution of AH to AG that we are discussing here, but we see the effect of this contribution-in the systems for which the approximation is valid-is that a solvent becomes less suitable to dissolve a polymer the greater the difference is between their 6 values. At best, when 61 = 62, the solvent effect is neutral. Cases for which a favorable specific interaction between solvent and polymer actually promotes solution are characterized by negative values of AH and are therefore beyond the capabilities of this model. 

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