Perturbed chain

Sequential IPN. The preceding analysis does not apply to the case of a sequential IPN. The formation of this system originates with the synthesis of the network (1). Then, network (1) is swollen with monomer (2) which is subsequently polymerized in situ to form a second network. Due to perturbed chain dimensions, the modulus of the first network is higher than the corresponding modulus in the unswollen state by a factor equal to v [ ] ... 

Investigation of the multivariate Gaussian distribution and the dipole moments of perturbed chains expansion factors for perturbed chains. 

In the perturbed chain the characteristic ratio C(q) is to be effectively multiplied by 5 (q), so that in the good-solvent case we have longer relaxation times [see Eqn. (3.1.11)] than in the unperturbed state, unlike the bad-solvent case. It must be remembered, though, that under collapse the Fourier modes that are significantly contracted are relatively few, being comprised between n, = 1 and n, N/nJ [see Eqn. (2.2.12), q = n nlN see also Figure 6]. 

Gross, J. and Sadowski, G., Perturbed-chain SAFT an equation of state based on a perturbation theory for chain molecules, Ind. Eng. Chem. Res., 40, 1244—1260, 2001. 

Tumakaka, F, Gross, J., and Sadowski, G., Modeling of polymer phase equilibria using perturbed-chain SAFT, Fluid Phase Equilibria, 541, 194—197, 2002. 

Such calculations, however, are based on crude geometrical models, and, so, cannot be considered to be rigorous. In fact, up to 88% of the positions of a primitive cubic lattice can be occupied, according to computer simulations, without the occurrence of ideal or perturbed chain bundles. So, space-filling problems do not hinder the dense packing of coiled molecules. 

To estimate Lc more accurately Yamakawa and Shimada [52] computed (5 ) of polymethylene-like rotational isomeric state models with excluded volume by a Monte Carlo method. They considered that bead-bead interactions higher than ones leading to the pentane effect contribute to excluded-volume effects. They found that the simulated polymer in the unperturbed state can be modeled by a wormlike chain and that (5 )/(4 rtK) of perturbed chains begins to deviate from those of unperturbed ones at uk of 3—5. Thus, the Lc by Yamakawa and... 

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT)... 

Gross, J., Sadowski, G., Perturbed-chain SAFT An equation of state based on a perturbation theory for chain molecules, oA. Eng. Chm. Res. 40 (2001) 1244-1260. Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M., New reference equation of state for associating liquids, Ind. Eng. Chem. Res. 29 (1990) 1709-1721. Diamantonis, N.I., Boulougouris, G.C., Mansoor, E., Tsangaris, D.M., Economou, LG. Evaluation of cubic, SAFT, cmd PC-SAFT equations of state for the vapor-liquid equilibrium modeling of CO2 mixtures with other gases, Ind. Eng. Chem. Res. 52 (2013) 3933-3942. 

The recently proposed Perturbed-Chain SAFT (PC-SAFT) model [75, 76] adopts the opposite idea here, a perturbation theory of second order is applied to the reference system of hard chains instead of hard spheres to develop a dispersion term for chain-Hke molecules ... 

J. Gross, G. Sadowski, Perturbed-Chain-SAFT development of a new equation of state for simple, associating, multipolar and polymeric compounds. In Supercritical Fluids as Solvents and Reaction Media, edited by G. Brunner, Elsevier, Amsterdam, 2004. 

Perturbed chain SAFT modei. Peng-Robinson-Stryjek-Vera equation of state. Sanchez-Lacombe hydrogen bond modei. 

The ability to model Selexol-based unit operations in Aspen Plus or Aspen HYSYS was recently made possible by the inclusion of the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) physical property model. As in Aspen HYSYS (see Section 6.1.1), a single chemical DEPG be used as a proxy for the mixture. Simple example files for using PC-SAFT with Selexol for one- or two-unit operations are included with the Aspen Plus distributiOTi, and an example for using PC-SAFT in Aspen HYSYS is available for download to subscribers of the Aspen Technology support website. 

Cameretti LF, Sadowski G, Mollerup JM (2005) Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory. Ind Eng Chem Res 44 3355-3362 ibid., 8944... 

Gonzalez et alP modeled the asphaltenes precipitation in live oils with the (Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) see Chapter 8 for additional material. It is not an easy task to apply a complicated model such as PC-SAFT to systems consisting of a very large number of chemical... 

FIGURE 3.9 Pressure-weight fraction plot of polypropylene(l)-diisopropyl ketone(2) at T = 318 K. Polypropylene molecular weight = 20,000. Comparison of experimental data with the predictions of original (solid line) and the simplified version (dotted line) of PC-SAFT. In both curves, the interaction parameter kij = 0. (From Fluid Phase Equilib., 215, Kouskoumvekaki, I. A., von Solms, N., Michelsen, M.L., and Kontogeorgis, G.M., Application of a simplified perturbed chain SAFT equation of state to complex polymer systems, 71-78, Copyright 2004, with permission from Elsevier.)... 

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