Polymer properties modeling

The rotational isomeric state (RIS) model assumes that conformational angles can take only certain values. It can be used to generate trial conformations, for which energies can be computed using molecular mechanics. This assumption is physically reasonable while allowing statistical averages to be computed easily. This model is used to derive simple analytic equations that predict polymer properties based on a few values, such as the preferred angle... 

R. Keshavaraj, R. W. Tock, and D. Haycook, Feedforward Neural Network Modeling of Biaxial Deformation of Airbag Fabrics ANTEC 95 Proceedings, SPE Technical Papers, Modeling of Polymer Properties and Processes, Boston (May 1995). 

For copolymers of structure I, for both types of side-chains, there is a striking similarity with the optical properties of the corresponding models the absorption and photoluminescence maxima of the polymers arc only 0.08-0.09 eV red-shifted relative to those of the models, as shown in Figure 16-9 (left) for the octyloxy-substituted compounds. The small shift can be readily explained by the fact that in the copolymers the chromophorcs are actually substituted by silylene units, which have a weakly electron-donating character. The shifts between absorption and luminescence maxima are exactly the same for polymers and models and the width of the emission bands is almost identical. The quantum yields are only slightly reduced in the polymers. These results confirm that the active chro-mophores are the PPV-type blocks and that the silylene unit is an efficient re-conjugation interrupter. 

The distinctive properties of densely tethered chains were first noted by Alexander [7] in 1977. His theoretical analysis concerned the end-adsorption of terminally functionalized polymers on a flat surface. Further elaboration by de Gennes [8] and by Cantor [9] stressed the utility of tethered chains to the description of self-assembled block copolymers. The next important step was taken by Daoud and Cotton [10] in 1982 in a model for star polymers. This model generalizes the... 

In the past three decades, industrial polymerization research and development aimed at controlling average polymer properties such as molecular weight averages, melt flow index and copolymer composition. These properties were modeled using either first principle models or empirical models represented by differential equations or statistical model equations. However, recent advances in polymerization chemistry, polymerization catalysis, polymer characterization techniques, and computational tools are making the molecular level design and control of polymer microstructure a reality. 

The dynamical properties of polymer molecules in solution have been investigated using MPC dynamics [75-77]. Polymer transport properties are strongly influenced by hydrodynamic interactions. These effects manifest themselves in both the center-of-mass diffusion coefficients and the dynamic structure factors of polymer molecules in solution. For example, if hydrodynamic interactions are neglected, the diffusion coefficient scales with the number of monomers as D Dq /Nb, where Do is the diffusion coefficient of a polymer bead and N), is the number of beads in the polymer. If hydrodynamic interactions are included, the diffusion coefficient adopts a Stokes-Einstein formD kltT/cnr NlJ2, where c is a factor that depends on the polymer chain model. This scaling has been confirmed in MPC simulations of the polymer dynamics [75]. 

Before discussing details of their model and others, it is useful to review the two main techniques used to infer the characteristics of chain conformation in unordered polypeptides. One line of evidence came from hydrodynamic experiments—viscosity and sedimentation—from which a statistical end-to-end distance could be estimated and compared with values derived from calculations on polymer chain models (Flory, 1969). The second is based on spectroscopic experiments, in particular CD spectroscopy, from which information is obtained about the local chain conformation rather than global properties such as those derived from hydrodynamics. It is entirely possible for a polypeptide chain to adopt some particular local structure while retaining characteristics of random coils derived from hydrodynamic measurements this was pointed out by Krimm and Tiffany (1974). In support of their proposal, Tiffany and Krimm noted the following points ... 

With well defined goals for polymer properties and process, a technical person can develop the preferred procedure for the synthesis of a polymer with five days of computation efforts and two to five experimental runs. We estimate that without the use of the model, a two to three month effort is needed. 

The Instantaneous values for the initiator efficiencies and the rate constants associated with the suspension polymerization of styrene using benzoyl peroxide have been determined from explicit equations based on the instantaneous polymer properties. The explicit equations for the rate parameters have been derived based on accepted reaction schemes and the standard kinetic assumptions (SSH and LCA). The instantaneous polymer properties have been obtained from the cummulative experimental values by proposing empirical models for the instantaneous properties and then fitting them to the cummulative experimental values. This has circumvented some of the problems associated with differenciating experimental data. The results obtained show that ... 

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

The polymerization of halophenoxides by copper (II) mediated halide displacement is a mechanistically complicated reaction. Elucidation of the structure of the polymers is essential to an understanding of both the polymerization chemistry and the peculiar physical properties of the polymers. The physical tool which has yielded most information on the polymer structure is nmr. The first conclusion which derives from a study of the spectra of poly(dihalophenyleneoxides) is that regioselectivity in halogen displacement is more likely the source of the polymer properties than branching. A more rigorous confirmation of the polymer structures will depend on a detailed analysis of the spectra of model compounds for the chain segments. 

While both the Bicerano and van Krevelen systems model a significant number of polymer properties, most QSPR studies have focused on only a small number of key properties (which is mainly correlated to the availability of data for model development). 

Porter D (1995) Group interaction modeling of polymer properties. Marcel Dekker, New York... 

In thip appendix, a summary of the error propagation equations and objective functions used for standard characterization techniques are presented. These equations are Important for the evaluation of the errors associated with static measurements on the whole polymers and for the subsequent statistical comparison with the SEC estimates (see references 26 and 2J for a more detailed discussion of the equations). Among the models most widely used to correlate measured variables and polymer properties is the truncated power series model... 

Porter, D. Group Interaction Modelling of Polymer Properties. Marcel Dekker, Inc. New York, 1995. 

The gas-polymer-matrix model for sorption and transport of gases in polymers is consistent with the physical evidence that 1) there is only one population of sorbed gas molecules in polymers at any pressure, 2) the physical properties of polymers are perturbed by the presence of sorbed gas, and 3) the perturbation of the polymer matrix arises from gas-polymer interactions. Rather than treating the gas and polymer separately, as in previous theories, the present model treats sorption and transport as occurring through a gas-polymer matrix whose properties change with composition. Simple expressions for sorption, diffusion, permeation and time lag are developed and used to analyze carbon dioxide sorption and transport in polycarbonate. 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

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