Skip to main content

2011 | OriginalPaper | Buchkapitel

Modeling of Polymer Phase Equilibria Using Equations of State

verfasst von : Gabriele Sadowski

Erschienen in: Polymer Thermodynamics

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The most promising approach for the calculation of polymer phase equilibria today is the use of equations of state that are based on perturbation theories. These theories consider an appropriate reference system to describe the repulsive interactions of the molecules, whereas van der Waals attractions or the formation of hydrogen bonds are considered as perturbations of that reference system. Moreover, the chain-like structure of polymer molecules is explicitly taken into account. This work presents the basic ideas of these kinds of models. It will be shown that they (in particular SAFT and PC-SAFT) are able to describe and even to predict the phase behavior of polymer systems as functions of pressure, temperature, polymer concentration, polymer molecular weight, and polydispersity as well as – in case of copolymers – copolymer composition.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat van der Waals JD (1873) Over de Continuiteit van den gas- en vloeistoftoestand. Sijthoff, Leiden van der Waals JD (1873) Over de Continuiteit van den gas- en vloeistoftoestand. Sijthoff, Leiden
2.
Zurück zum Zitat Soave G (1972) Equilibrium constants from a modified Redlich–Kwong equation of state. Chem Eng Sci 271:197–1203 Soave G (1972) Equilibrium constants from a modified Redlich–Kwong equation of state. Chem Eng Sci 271:197–1203
3.
Zurück zum Zitat Peng D-Y, Robinson DP (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15:59–64CrossRef Peng D-Y, Robinson DP (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15:59–64CrossRef
4.
Zurück zum Zitat Sanchez IC, Lacombe RH (1976) An elementary molecular theory of classical fluids: pure fluids. J Phys Chem 80:2352–2362CrossRef Sanchez IC, Lacombe RH (1976) An elementary molecular theory of classical fluids: pure fluids. J Phys Chem 80:2352–2362CrossRef
5.
Zurück zum Zitat Kleintjens LA, Koningsveld R (1980) Liquid–liquid phase separation in multicomponent polymer systems XIX. Mean-field lattice-gas treatment of the system n-alkane/linear polyethylene. Colloid Polymer Sci 258:711–718CrossRef Kleintjens LA, Koningsveld R (1980) Liquid–liquid phase separation in multicomponent polymer systems XIX. Mean-field lattice-gas treatment of the system n-alkane/linear polyethylene. Colloid Polymer Sci 258:711–718CrossRef
6.
Zurück zum Zitat Beret S, Prausnitz JM (1975) Perturbed Hard-Chain Theory: an equation of state for fluids containing small or large molecules. AIChE J 21:1123–1132CrossRef Beret S, Prausnitz JM (1975) Perturbed Hard-Chain Theory: an equation of state for fluids containing small or large molecules. AIChE J 21:1123–1132CrossRef
7.
Zurück zum Zitat Cotterman RL, Schwarz BJ, Prausnitz JM (1986) Molecular thermodynamics for fluids at low and high densities. Part 1. Pure fluids containing small or large molecules. AIChE J 32:1787–1798CrossRef Cotterman RL, Schwarz BJ, Prausnitz JM (1986) Molecular thermodynamics for fluids at low and high densities. Part 1. Pure fluids containing small or large molecules. AIChE J 32:1787–1798CrossRef
8.
Zurück zum Zitat Morris WO, Vimalchand P, Donohue MD (1987) The Perturbed-Soft-Chain Theory: an equation of state based on the Lennard–Jones potential. Fluid Phase Equilib 32:103–115CrossRef Morris WO, Vimalchand P, Donohue MD (1987) The Perturbed-Soft-Chain Theory: an equation of state based on the Lennard–Jones potential. Fluid Phase Equilib 32:103–115CrossRef
9.
Zurück zum Zitat Barker JA, Henderson D (1967) Perturbation theory and equation of state for fluid II. A successful theory of liquids. J Chem Phys 47:4714–4721CrossRef Barker JA, Henderson D (1967) Perturbation theory and equation of state for fluid II. A successful theory of liquids. J Chem Phys 47:4714–4721CrossRef
10.
Zurück zum Zitat Weeks JD, Chandler D, Anderson HC (1971) Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54:5237–5247CrossRef Weeks JD, Chandler D, Anderson HC (1971) Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54:5237–5247CrossRef
11.
Zurück zum Zitat Carnahan NF, Starling KE (1969) Equation of state for nonattracting rigid spheres. J Chem Phys 51:635–636CrossRef Carnahan NF, Starling KE (1969) Equation of state for nonattracting rigid spheres. J Chem Phys 51:635–636CrossRef
12.
Zurück zum Zitat Chapman WG, Gubbins KE, Jackson G, Radosz M (1989) SAFT: Equation-of-State Model for associating fluids. Fluid Phase Equilib 52:31–38CrossRef Chapman WG, Gubbins KE, Jackson G, Radosz M (1989) SAFT: Equation-of-State Model for associating fluids. Fluid Phase Equilib 52:31–38CrossRef
13.
Zurück zum Zitat Chapman WG, Gubbins KE, Jackson G, Radosz M (1990) New reference equation of state for associating liquids. Ind Eng Chem Res 29:1709–1721CrossRef Chapman WG, Gubbins KE, Jackson G, Radosz M (1990) New reference equation of state for associating liquids. Ind Eng Chem Res 29:1709–1721CrossRef
14.
Zurück zum Zitat Huang SH, Radosz M (1990) Equation of state for small, large, polydisperse, and associating molecules. Ind Eng Chem Res 29:2284–2294CrossRef Huang SH, Radosz M (1990) Equation of state for small, large, polydisperse, and associating molecules. Ind Eng Chem Res 29:2284–2294CrossRef
15.
Zurück zum Zitat Huang SH, Radosz M (1991) Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures. Ind Eng Chem Res 30:1994–2005CrossRef Huang SH, Radosz M (1991) Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures. Ind Eng Chem Res 30:1994–2005CrossRef
16.
Zurück zum Zitat Chen SS, Kreglewski A (1977) Applications of the augmented van der Waals theory of fluids I. Pure fluids. Ber Bunsen-Ges Phys Chem 81:1048–1052 Chen SS, Kreglewski A (1977) Applications of the augmented van der Waals theory of fluids I. Pure fluids. Ber Bunsen-Ges Phys Chem 81:1048–1052
17.
Zurück zum Zitat Wertheim MS (1987) Thermodynamic perturbation theory of polymerization. J Chem Phys 87:7323–7331CrossRef Wertheim MS (1987) Thermodynamic perturbation theory of polymerization. J Chem Phys 87:7323–7331CrossRef
18.
Zurück zum Zitat Song Y, Lambert SM, Prausnitz JM (1994) Equation of state for mixtures of hard sphere chains including copolymers. Macromolecules 27:441–448CrossRef Song Y, Lambert SM, Prausnitz JM (1994) Equation of state for mixtures of hard sphere chains including copolymers. Macromolecules 27:441–448CrossRef
19.
Zurück zum Zitat Song Y, Lambert SM, Prausnitz JM (1994) A perturbed hard-sphere-chain equation of state for normal fluids and polymers. Ind Eng Chem Res 33:1047–1057CrossRef Song Y, Lambert SM, Prausnitz JM (1994) A perturbed hard-sphere-chain equation of state for normal fluids and polymers. Ind Eng Chem Res 33:1047–1057CrossRef
20.
Zurück zum Zitat Gil-Villegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN (1997) Statistical associating fluid theory for chain molecules with attractive potentials of variable range. J Chem Phys 106:4168–4186CrossRef Gil-Villegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN (1997) Statistical associating fluid theory for chain molecules with attractive potentials of variable range. J Chem Phys 106:4168–4186CrossRef
21.
Zurück zum Zitat Chang J, Sandler SI (1994) A completely analytic perturbation theory for the square-well fluid of variable well width. Mol Phys 81:745–765CrossRef Chang J, Sandler SI (1994) A completely analytic perturbation theory for the square-well fluid of variable well width. Mol Phys 81:745–765CrossRef
22.
Zurück zum Zitat Hino T, Prausnitz JM (1997) A perturbed hard-sphere-chain equation of state for normal fluids and polymers using the square-well potential of variable width. Fluid Phase Equilib 138:105–130CrossRef Hino T, Prausnitz JM (1997) A perturbed hard-sphere-chain equation of state for normal fluids and polymers using the square-well potential of variable width. Fluid Phase Equilib 138:105–130CrossRef
23.
Zurück zum Zitat Blas FJ, Vega LF (1997) Thermodynamic behaviour of homonuclear Lennard–Jones chains with association sites from simulation and theory. Mol Phys 92:135–150 Blas FJ, Vega LF (1997) Thermodynamic behaviour of homonuclear Lennard–Jones chains with association sites from simulation and theory. Mol Phys 92:135–150
24.
Zurück zum Zitat Gross J, Sadowski G (2001) Perturbed-Chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40:1244–1260CrossRef Gross J, Sadowski G (2001) Perturbed-Chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40:1244–1260CrossRef
25.
Zurück zum Zitat Gross J, Sadowski G (2002) Modeling polymer systems using the Perturbed-Chain SAFT equation of state. Ind Eng Chem Res 41:1084–1093CrossRef Gross J, Sadowski G (2002) Modeling polymer systems using the Perturbed-Chain SAFT equation of state. Ind Eng Chem Res 41:1084–1093CrossRef
26.
Zurück zum Zitat Tumakaka F, Gross J, Sadowski G (2002) Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilib 194–197:541–551CrossRef Tumakaka F, Gross J, Sadowski G (2002) Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilib 194–197:541–551CrossRef
27.
Zurück zum Zitat Boublik T (1970) Hard-sphere equation of state. J Chem Phys 53:471–472CrossRef Boublik T (1970) Hard-sphere equation of state. J Chem Phys 53:471–472CrossRef
28.
Zurück zum Zitat Mansoori GA, Carnahan NF, Starling KE, Leland TW Jr (1971) Equilibrium thermodynamic properties of hard spheres. J Chem Phys 54:1523–1525CrossRef Mansoori GA, Carnahan NF, Starling KE, Leland TW Jr (1971) Equilibrium thermodynamic properties of hard spheres. J Chem Phys 54:1523–1525CrossRef
29.
Zurück zum Zitat Kouskoumvekaki I, von Solms N, Michelsen ML, Kontogeorgis G (2004) Application of the Perturbed Chain SAFT equation of state to complex polymer systems using simplified mixing rules. Fluid Phase Equilib 215:71–78CrossRef Kouskoumvekaki I, von Solms N, Michelsen ML, Kontogeorgis G (2004) Application of the Perturbed Chain SAFT equation of state to complex polymer systems using simplified mixing rules. Fluid Phase Equilib 215:71–78CrossRef
30.
Zurück zum Zitat Jog PK, Chapman WG (1999) Application of Wertheim’s thermodynamic perturbation theory to dipolar hard sphere chains. Mol Phys 97:307–319CrossRef Jog PK, Chapman WG (1999) Application of Wertheim’s thermodynamic perturbation theory to dipolar hard sphere chains. Mol Phys 97:307–319CrossRef
31.
Zurück zum Zitat Karakatsani EK, Spyriouni T, Economou IG (2005) Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids. AIChE J 51:2328–2342CrossRef Karakatsani EK, Spyriouni T, Economou IG (2005) Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids. AIChE J 51:2328–2342CrossRef
32.
Zurück zum Zitat Gross J, Vrabec J (2006) An equation of state contribution for polar components: dipolar molecules. AIChE J 52:1194–1201CrossRef Gross J, Vrabec J (2006) An equation of state contribution for polar components: dipolar molecules. AIChE J 52:1194–1201CrossRef
33.
Zurück zum Zitat Karakatsani EK, Economou IG (2006) Perturbed-chain statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids. J Phys Chem B 110:9252–9261CrossRef Karakatsani EK, Economou IG (2006) Perturbed-chain statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids. J Phys Chem B 110:9252–9261CrossRef
34.
Zurück zum Zitat Gross J (2005) An equation of state contribution for polar components: quadrupolar molecules. AIChE J 51:2556–2568CrossRef Gross J (2005) An equation of state contribution for polar components: quadrupolar molecules. AIChE J 51:2556–2568CrossRef
35.
Zurück zum Zitat Vrabec J, Gross J (2008) A molecular based approach to dipolar und quadrupolar fluids: vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions. J Phys Chem B 112:51–60CrossRef Vrabec J, Gross J (2008) A molecular based approach to dipolar und quadrupolar fluids: vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions. J Phys Chem B 112:51–60CrossRef
36.
Zurück zum Zitat Cameretti L, Sadowski G, Mollerup J (2005) Modelling of aqueous electrolyte solutions with PC-SAFT. Ind Eng Chem Res 44:3355–3362CrossRef Cameretti L, Sadowski G, Mollerup J (2005) Modelling of aqueous electrolyte solutions with PC-SAFT. Ind Eng Chem Res 44:3355–3362CrossRef
37.
Zurück zum Zitat Held C, Cameretti L, Sadowski G (2008) Modeling aqueous electrolyte solutions. Part 1: fully dissociated electrolytes. Fluid Phase Equilib 270:87–96CrossRef Held C, Cameretti L, Sadowski G (2008) Modeling aqueous electrolyte solutions. Part 1: fully dissociated electrolytes. Fluid Phase Equilib 270:87–96CrossRef
38.
Zurück zum Zitat Behzad B, Patel BH, Galindo A, Ghotbi C (2005) Modeling electrolyte solutions with the SAFT-VR equation using Yukawa potentials and the mean-spherical approximation. Fluid Phase Equilib 236:241–255CrossRef Behzad B, Patel BH, Galindo A, Ghotbi C (2005) Modeling electrolyte solutions with the SAFT-VR equation using Yukawa potentials and the mean-spherical approximation. Fluid Phase Equilib 236:241–255CrossRef
39.
Zurück zum Zitat Tihic A, Kontogeorgis GM, von Solms N, Michelsen ML (2006) Application of the simplified perturbed-chain SAFT equation of state using an extended parameter table. Fluid Phase Equilib 248:29–43CrossRef Tihic A, Kontogeorgis GM, von Solms N, Michelsen ML (2006) Application of the simplified perturbed-chain SAFT equation of state using an extended parameter table. Fluid Phase Equilib 248:29–43CrossRef
40.
Zurück zum Zitat Danner RP, High MS (1993) Handbook of polymer solution thermodynamics. DIPPR, AIChE/Wiley, New York Danner RP, High MS (1993) Handbook of polymer solution thermodynamics. DIPPR, AIChE/Wiley, New York
41.
Zurück zum Zitat Sadowski G, Mokrushina L, Arlt W (1997) Finite and infinite dilution activity coefficients in polycarbonate systems. Fluid Phase Equilib 139:391–403CrossRef Sadowski G, Mokrushina L, Arlt W (1997) Finite and infinite dilution activity coefficients in polycarbonate systems. Fluid Phase Equilib 139:391–403CrossRef
42.
Zurück zum Zitat Becker F, Buback M, Latz H, Sadowski G, Tumakaka F (2004) Cloud-point curves of ethylene–(meth)acrylate copolymers in fluid ethene up to high pressures and temperatures – experimental study and PC-SAFT modeling. Fluid Phase Equilib 215:263–282CrossRef Becker F, Buback M, Latz H, Sadowski G, Tumakaka F (2004) Cloud-point curves of ethylene–(meth)acrylate copolymers in fluid ethene up to high pressures and temperatures – experimental study and PC-SAFT modeling. Fluid Phase Equilib 215:263–282CrossRef
43.
Zurück zum Zitat Kleiner M, Tumakaka F, Sadowski G, Latz H, Buback M (2006) Phase equilibria in polydisperse and associating copolymer solutions: poly(ethene-co-(meth)acrylic acid)–monomer mixtures. Fluid Phase Equilib 241:113–123CrossRef Kleiner M, Tumakaka F, Sadowski G, Latz H, Buback M (2006) Phase equilibria in polydisperse and associating copolymer solutions: poly(ethene-co-(meth)acrylic acid)–monomer mixtures. Fluid Phase Equilib 241:113–123CrossRef
44.
Zurück zum Zitat Krueger K-M, Pfohl O, Dohrn R, Sadowski G (2006) Phase equilibria and diffusion coefficients in the poly(dimethylsiloxane) + n-pentane system. Fluid Phase Equilib 241:138–146CrossRef Krueger K-M, Pfohl O, Dohrn R, Sadowski G (2006) Phase equilibria and diffusion coefficients in the poly(dimethylsiloxane) + n-pentane system. Fluid Phase Equilib 241:138–146CrossRef
45.
Zurück zum Zitat Goernert M, Sadowski G (2008) Phase-equilibrium measurement and modeling of the PMMA/MMA/carbon dioxide ternary system. J Supercrit Fluids 46:218–225CrossRef Goernert M, Sadowski G (2008) Phase-equilibrium measurement and modeling of the PMMA/MMA/carbon dioxide ternary system. J Supercrit Fluids 46:218–225CrossRef
46.
Zurück zum Zitat Wohlfarth C (1994) Vapour-liquid equilibrium data of binary polymer solutions; physical sciences data 44. Elsevier, Amsterdam Wohlfarth C (1994) Vapour-liquid equilibrium data of binary polymer solutions; physical sciences data 44. Elsevier, Amsterdam
47.
Zurück zum Zitat Martin TM, Lateef AA, Roberts CB (1999) Measurements and modeling of cloud point behavior for polypropylene/n-pentane and polypropylene/n-pentane/carbon dioxide mixtures at high pressures. Fluid Phase Equilib 154:241–259CrossRef Martin TM, Lateef AA, Roberts CB (1999) Measurements and modeling of cloud point behavior for polypropylene/n-pentane and polypropylene/n-pentane/carbon dioxide mixtures at high pressures. Fluid Phase Equilib 154:241–259CrossRef
48.
Zurück zum Zitat Hasch BM (1994) Hydrogen bonding and polarity in ethylene copolymer-solvent mixtures: experiment and modeling. Ph.D. Thesis, Johns Hopkins University, Baltimore, MD Hasch BM (1994) Hydrogen bonding and polarity in ethylene copolymer-solvent mixtures: experiment and modeling. Ph.D. Thesis, Johns Hopkins University, Baltimore, MD
49.
Zurück zum Zitat Dietzsch H (1999) Hochdruck-Copolymerisation von Ethen und (Meth)Acrylsäureestern: Entmischungsverhalten der Systeme Ethen/Cosolvens/Poly(Ethen-co-Acrylsäureester) – Kinetik der Ethen-Methylmethacrylat-Copolymerisation. Ph.D. Thesis, Georg August-Universität zu Göttingen, Germany Dietzsch H (1999) Hochdruck-Copolymerisation von Ethen und (Meth)Acrylsäureestern: Entmischungsverhalten der Systeme Ethen/Cosolvens/Poly(Ethen-co-Acrylsäureester) – Kinetik der Ethen-Methylmethacrylat-Copolymerisation. Ph.D. Thesis, Georg August-Universität zu Göttingen, Germany
50.
Zurück zum Zitat Song Y, Hino T, Lambert SM, Prausnitz JM (1996) Liquid-liquid equilibria for polymer solutions and blends, including copolymers. Fluid Phase Equilib 117:69–76CrossRef Song Y, Hino T, Lambert SM, Prausnitz JM (1996) Liquid-liquid equilibria for polymer solutions and blends, including copolymers. Fluid Phase Equilib 117:69–76CrossRef
51.
Zurück zum Zitat Banaszak M, Chen CK, Radosz M (1996) Copolymer SAFT equation of state. Thermodynamic perturbation theory extended to heterobonded chains. Macromolecules 29:6481–6486CrossRef Banaszak M, Chen CK, Radosz M (1996) Copolymer SAFT equation of state. Thermodynamic perturbation theory extended to heterobonded chains. Macromolecules 29:6481–6486CrossRef
52.
Zurück zum Zitat Shukla KP, Chapman WG (1997) SAFT equation of state for fluid mixtures of hard chain copolymers. Mol Phys 91:1075–1081 Shukla KP, Chapman WG (1997) SAFT equation of state for fluid mixtures of hard chain copolymers. Mol Phys 91:1075–1081
53.
Zurück zum Zitat Gross J, Spuhl O, Tumakaka F, Sadowski G (2003) Modeling copolymer systems using the Perturbed-Chain SAFT equation of state. Ind Eng Chem Res 42:1266–1274CrossRef Gross J, Spuhl O, Tumakaka F, Sadowski G (2003) Modeling copolymer systems using the Perturbed-Chain SAFT equation of state. Ind Eng Chem Res 42:1266–1274CrossRef
54.
Zurück zum Zitat Chen S-J, Banaszak M, Radosz M (1995) Phase behavior of poly(ethylene-1-butene) in subcritical and supercritical propane: ethyl branches reduce segment energy and enhance miscibility. Macromolecules 28:1812–1817CrossRef Chen S-J, Banaszak M, Radosz M (1995) Phase behavior of poly(ethylene-1-butene) in subcritical and supercritical propane: ethyl branches reduce segment energy and enhance miscibility. Macromolecules 28:1812–1817CrossRef
55.
Zurück zum Zitat de Loos TW, Poot W, Diepen GAM (1983) Fluid phase equilibriums in the system polyethylene + ethylene. 1. Systems of linear polyethylene + ethylene at high pressure. Macromolecules 16:111–117CrossRef de Loos TW, Poot W, Diepen GAM (1983) Fluid phase equilibriums in the system polyethylene + ethylene. 1. Systems of linear polyethylene + ethylene at high pressure. Macromolecules 16:111–117CrossRef
56.
Zurück zum Zitat Kehlen H, Rätzsch MT (1980) Continuous thermodynamics of multicomponent mixtures. In: Proceedings of the 6th international conference on thermodynamics, Merseburg, Germany, pp 41–51 Kehlen H, Rätzsch MT (1980) Continuous thermodynamics of multicomponent mixtures. In: Proceedings of the 6th international conference on thermodynamics, Merseburg, Germany, pp 41–51
57.
Zurück zum Zitat Gualtieri JA, Kincaid JM, Morrison G (1982) Phase equilibria in polydisperse fluids. J Chem Phys 77:521–535CrossRef Gualtieri JA, Kincaid JM, Morrison G (1982) Phase equilibria in polydisperse fluids. J Chem Phys 77:521–535CrossRef
58.
Zurück zum Zitat Rätzsch MT, Kehlen H (1983) Continuous thermodynamics of complex mixtures. Fluid Phase Equilib 14:225–234CrossRef Rätzsch MT, Kehlen H (1983) Continuous thermodynamics of complex mixtures. Fluid Phase Equilib 14:225–234CrossRef
59.
Zurück zum Zitat Cotterman RL, Prausnitz JM (1985) Flash calculations for continuous or semicontinuous mixtures using an equation of state. Ind Eng Chem Proc Des Dev 24:434–443CrossRef Cotterman RL, Prausnitz JM (1985) Flash calculations for continuous or semicontinuous mixtures using an equation of state. Ind Eng Chem Proc Des Dev 24:434–443CrossRef
60.
Zurück zum Zitat Enders S (2010) Theory of random copolymer fractionation in columns. Adv Polym Sci. doi: 10.1007/12_2010_92 Enders S (2010) Theory of random copolymer fractionation in columns. Adv Polym Sci. doi: 10.1007/12_2010_92
61.
Zurück zum Zitat Buback M, Latz H (2003) Cloud-point pressure curves of ethene/poly(ethylene-co-meth acrylic acid) mixtures. Macromol Chem Phys 204:638–645CrossRef Buback M, Latz H (2003) Cloud-point pressure curves of ethene/poly(ethylene-co-meth acrylic acid) mixtures. Macromol Chem Phys 204:638–645CrossRef
62.
Zurück zum Zitat Beyer C, Oellrich LR (2002) Cosolvent studies bath the system ethylene/poly(ethylene-co-acrylic acid): Effects of solvent, density, polarity, hydrogen bonding, and copolymer composition. Helvetica Chimica Acta 85:659–670CrossRef Beyer C, Oellrich LR (2002) Cosolvent studies bath the system ethylene/poly(ethylene-co-acrylic acid): Effects of solvent, density, polarity, hydrogen bonding, and copolymer composition. Helvetica Chimica Acta 85:659–670CrossRef
63.
Zurück zum Zitat Bungert B, Sadowski G, Arlt W (1997) Supercritical antisolvent fractionation: measurements in the systems monodisperse and bidisperse polystyrene-cyclohexane-carbon dioxide. Fluid Phase Equilib 139:349–359CrossRef Bungert B, Sadowski G, Arlt W (1997) Supercritical antisolvent fractionation: measurements in the systems monodisperse and bidisperse polystyrene-cyclohexane-carbon dioxide. Fluid Phase Equilib 139:349–359CrossRef
64.
Zurück zum Zitat Behme S, Sadowski G, Arlt W (1999) Modeling of the separation of polydisperse polymer systems by compressed gases. Fluid Phase Equilib 158–160:869–877CrossRef Behme S, Sadowski G, Arlt W (1999) Modeling of the separation of polydisperse polymer systems by compressed gases. Fluid Phase Equilib 158–160:869–877CrossRef
Metadaten
Titel
Modeling of Polymer Phase Equilibria Using Equations of State
verfasst von
Gabriele Sadowski
Copyright-Jahr
2011
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/12_2010_94

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.