Skip to main content
Top
Published in: Rheologica Acta 7/2009

01-08-2009 | Original Contribution

An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transition

Authors: H. Henning Winter, Miriam Siebenbürger, David Hajnal, Oliver Henrich, Matthias Fuchs, Matthias Ballauff

Published in: Rheologica Acta | Issue 7/2009

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Concentrated, non-crystallizing colloidal suspensions in their approach of the glass state exhibit distinct dynamics patterns. These patterns suggest a powerlaw rheological constitutive model for near-glass viscoelasticity, as presented here. The rheological parameters used for this model originate in the mode-coupling theory. The proposed constitutive model provides explicit expressions for the steady shear viscosity, the steady normal stress coefficient, the modulus-compliance relation, and the α peak of G″. The relaxation pattern distinctly differs from gelation.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

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!

Literature
go back to reference Abdel-Goad M, Pyckhout-Hintzen W, Kahle S, Allgaier J, Richter D, Fetters LJ (2004) Rheological properties of 1,4-polyisoprene over a large molecular weight range. Macromolecules 37:8135–8144CrossRefADS Abdel-Goad M, Pyckhout-Hintzen W, Kahle S, Allgaier J, Richter D, Fetters LJ (2004) Rheological properties of 1,4-polyisoprene over a large molecular weight range. Macromolecules 37:8135–8144CrossRefADS
go back to reference Baumgärtel M, Winter HH (1989) Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol Acta 28:511–519CrossRef Baumgärtel M, Winter HH (1989) Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol Acta 28:511–519CrossRef
go back to reference Baumgärtel M, Schausberger A, Winter HH (1990) The relaxation of polymers with linear flexible chains of uniform length. Rheol Acta 29:400–408CrossRef Baumgärtel M, Schausberger A, Winter HH (1990) The relaxation of polymers with linear flexible chains of uniform length. Rheol Acta 29:400–408CrossRef
go back to reference Baumgärtel M, DeRosa ME, Machado J, Masse M, Winter HH (1992) The relaxation time spectrum of nearly monodisperse polybutadiene melts. Rheol Acta 31:75–82CrossRef Baumgärtel M, DeRosa ME, Machado J, Masse M, Winter HH (1992) The relaxation time spectrum of nearly monodisperse polybutadiene melts. Rheol Acta 31:75–82CrossRef
go back to reference Bengtzelius U, Götze W, Sjölander A (1984) Dynamics of supercooled liquids and the glass transition. J Phys C 17:5915CrossRefADS Bengtzelius U, Götze W, Sjölander A (1984) Dynamics of supercooled liquids and the glass transition. J Phys C 17:5915CrossRefADS
go back to reference Boltzmann L (1874) Zur Theorie der elastischen Nachwirkungen. Sitzungsber kaiserlich Akad Wissen Math Naturwissen 70:275–306 Boltzmann L (1874) Zur Theorie der elastischen Nachwirkungen. Sitzungsber kaiserlich Akad Wissen Math Naturwissen 70:275–306
go back to reference Brambilla G, El Masri D, Pierno M, Berthier L, Cipelletti L, Petekidis G, Schofield AB (2009) Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition. Phys Rev Let 102:085703CrossRefADS Brambilla G, El Masri D, Pierno M, Berthier L, Cipelletti L, Petekidis G, Schofield AB (2009) Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition. Phys Rev Let 102:085703CrossRefADS
go back to reference Carri G, Winter HH (1997) Mapping of the relaxation patterns of polymer melts with linear flexible molecules of uniform length. Rheol Acta 36:330–344 Carri G, Winter HH (1997) Mapping of the relaxation patterns of polymer melts with linear flexible molecules of uniform length. Rheol Acta 36:330–344
go back to reference Chambon F, Winter HH (1985) Stopping of crosslinking reaction in a PDMS polymer at the gel point. Polym Bull 13:499–503CrossRef Chambon F, Winter HH (1985) Stopping of crosslinking reaction in a PDMS polymer at the gel point. Polym Bull 13:499–503CrossRef
go back to reference Chambon F, Winter HH (1987) Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J Rheol 31:683–697CrossRefADS Chambon F, Winter HH (1987) Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J Rheol 31:683–697CrossRefADS
go back to reference Crassous JJ, Siebenbürger M, Ballauff M, Drechsler M, Hajnal D, Henrich O, Fuchs M (2006a) Thermosensitive core-shell particles as model systems for studying the flow behavior of concentrated colloidal dispersions. J Chem Phys 125:204906PubMedCrossRefADS Crassous JJ, Siebenbürger M, Ballauff M, Drechsler M, Hajnal D, Henrich O, Fuchs M (2006a) Thermosensitive core-shell particles as model systems for studying the flow behavior of concentrated colloidal dispersions. J Chem Phys 125:204906PubMedCrossRefADS
go back to reference Crassous JJ, Ballauff M, Drechsler M, Schmidt J, Talmon Y (2006b) Imaging the volume transition in thermosensitive core-shell particles by cryo-transmission electron microscopy. Langmuir 22:2403PubMedCrossRef Crassous JJ, Ballauff M, Drechsler M, Schmidt J, Talmon Y (2006b) Imaging the volume transition in thermosensitive core-shell particles by cryo-transmission electron microscopy. Langmuir 22:2403PubMedCrossRef
go back to reference Crassous JJ, Siebenbürger M, Ballauff M, Drechsler M, Hajnal D, Henrich O, Fuchs M (2008a) Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flow. J Chem Phys 128:204902PubMedCrossRefADS Crassous JJ, Siebenbürger M, Ballauff M, Drechsler M, Hajnal D, Henrich O, Fuchs M (2008a) Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flow. J Chem Phys 128:204902PubMedCrossRefADS
go back to reference Crassous JJ, Wittemann A, Siebenbürger M, Schrinner M, Drechsler M, Ballauff M (2008b) Direct imaging of temperature-sensitive core-shell latexes by cryogenic transmission electron microscopy. Colloid Polym Sci 286:805CrossRef Crassous JJ, Wittemann A, Siebenbürger M, Schrinner M, Drechsler M, Ballauff M (2008b) Direct imaging of temperature-sensitive core-shell latexes by cryogenic transmission electron microscopy. Colloid Polym Sci 286:805CrossRef
go back to reference Doi M (1981) Explanation for the 3.4 power law of viscosity of polymeric liquids on the basis of the tube model. J Polym Sci Polym Lett Ed 19:265CrossRef Doi M (1981) Explanation for the 3.4 power law of viscosity of polymeric liquids on the basis of the tube model. J Polym Sci Polym Lett Ed 19:265CrossRef
go back to reference Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York
go back to reference Franosch T, Götze W (1999) Relaxation rate distributions for supercooled liquids. J Phys Chem B 103:4011CrossRef Franosch T, Götze W (1999) Relaxation rate distributions for supercooled liquids. J Phys Chem B 103:4011CrossRef
go back to reference Friedrich C, Waizenegger F, Winter HH (2007) Relaxation patterns of long, linear, flexible, monodisperse polymers: BSW spectrum revisited. Rheol Acta 47(8):909–916CrossRef Friedrich C, Waizenegger F, Winter HH (2007) Relaxation patterns of long, linear, flexible, monodisperse polymers: BSW spectrum revisited. Rheol Acta 47(8):909–916CrossRef
go back to reference Fuchs M, Cates ME (2002) Theory of nonlinear rheology and yielding of dense colloidal suspensions. Phys Rev Lett 89:248304PubMedCrossRefADS Fuchs M, Cates ME (2002) Theory of nonlinear rheology and yielding of dense colloidal suspensions. Phys Rev Lett 89:248304PubMedCrossRefADS
go back to reference Götze W (1991) Liquids, freezing and glass transition. In: Hansen JP, Levesque D, Zinn-Justin J (eds) Session LI of Les Houches summer schools of theoretical physics. North-Holland, Amsterdam, pp 287 Götze W (1991) Liquids, freezing and glass transition. In: Hansen JP, Levesque D, Zinn-Justin J (eds) Session LI of Les Houches summer schools of theoretical physics. North-Holland, Amsterdam, pp 287
go back to reference Götze W, Sjögren L (1992) Relaxation processes in supercooled liquids. Rep Prog Phys 55:241CrossRef Götze W, Sjögren L (1992) Relaxation processes in supercooled liquids. Rep Prog Phys 55:241CrossRef
go back to reference Koumakis N, Schofield AB, Petekidis G (2008) Effects of shear induced crystallization on the rheology and ageing of hard sphere glasses. Soft Matter 4:2008–2018CrossRef Koumakis N, Schofield AB, Petekidis G (2008) Effects of shear induced crystallization on the rheology and ageing of hard sphere glasses. Soft Matter 4:2008–2018CrossRef
go back to reference Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press, Oxford Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press, Oxford
go back to reference Likhtman A, McLeish TCB (2002) Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 35:6332CrossRefADS Likhtman A, McLeish TCB (2002) Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 35:6332CrossRefADS
go back to reference Mason TG, Weitz DA (1995) Linear viscoelasticity of hard sphere suspensions near the glass transition. Phys Rev Lett 75:2770–2773PubMedCrossRefADS Mason TG, Weitz DA (1995) Linear viscoelasticity of hard sphere suspensions near the glass transition. Phys Rev Lett 75:2770–2773PubMedCrossRefADS
go back to reference Mayer P, Miyazaki K, Reichman DR (2006) Cooperativity beyond caging: generalized mode coupling rheory. Phys Rev Lett 97:095702CrossRefADS Mayer P, Miyazaki K, Reichman DR (2006) Cooperativity beyond caging: generalized mode coupling rheory. Phys Rev Lett 97:095702CrossRefADS
go back to reference Milner ST, McLeish TCB (1998) Reptation and contour-length fluctuations in melts of linear polymers. Phys Rev Lett 81:725CrossRefADS Milner ST, McLeish TCB (1998) Reptation and contour-length fluctuations in melts of linear polymers. Phys Rev Lett 81:725CrossRefADS
go back to reference Schweizer KS (2007) Dynamical fluctuation effects in glassy colloidal suspensions. Curr Opin Colloid Interface Sci 12:297CrossRef Schweizer KS (2007) Dynamical fluctuation effects in glassy colloidal suspensions. Curr Opin Colloid Interface Sci 12:297CrossRef
go back to reference Schweizer KS, Saltzman EJ (2003) Entropic barriers, activated hopping, and the glass transition in colloidal suspensions. J Chem Phys 119:1181–1196CrossRefADS Schweizer KS, Saltzman EJ (2003) Entropic barriers, activated hopping, and the glass transition in colloidal suspensions. J Chem Phys 119:1181–1196CrossRefADS
go back to reference Siebenbürger M, Fuchs M, Winter HH, Ballauff M (2009) Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: comparison with mode-coupling theory. J Rheol 53:707–726CrossRefADS Siebenbürger M, Fuchs M, Winter HH, Ballauff M (2009) Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: comparison with mode-coupling theory. J Rheol 53:707–726CrossRefADS
go back to reference van Megen W, Underwood SM (1994) Glass-transition in colloidal hard spheres—measurement and modecoupling-theory analysis of the coherent intermediate scattering function. Phys Rev E 49:4206–4220CrossRefADS van Megen W, Underwood SM (1994) Glass-transition in colloidal hard spheres—measurement and modecoupling-theory analysis of the coherent intermediate scattering function. Phys Rev E 49:4206–4220CrossRefADS
go back to reference van Megen W, Underwood SM, Pusey PN (1991) Non-ergodicity parameters of colloidal glasses. Phys Rev Lett 67:1586–1589PubMedCrossRefADS van Megen W, Underwood SM, Pusey PN (1991) Non-ergodicity parameters of colloidal glasses. Phys Rev Lett 67:1586–1589PubMedCrossRefADS
go back to reference von Schweidler E (1907) Studien über die Anomalien im Verhalten der Dielektrika. Ann Phys (Leipzig) 24:711–770ADS von Schweidler E (1907) Studien über die Anomalien im Verhalten der Dielektrika. Ann Phys (Leipzig) 24:711–770ADS
go back to reference Winter HH (1987) Evolution of rheology during chemical gelation. Prog Colloid Polym Sci 75:104–110CrossRef Winter HH (1987) Evolution of rheology during chemical gelation. Prog Colloid Polym Sci 75:104–110CrossRef
go back to reference Winter HH, Chambon F (1986a) Analysis of linear viscoelasticity of a crosslinking polymer at the gel point. J Rheology 30:367–382CrossRefADS Winter HH, Chambon F (1986a) Analysis of linear viscoelasticity of a crosslinking polymer at the gel point. J Rheology 30:367–382CrossRefADS
go back to reference Winter HH, Chambon F (1986b) Rheology of crosslinking polymers at the gel point. Proc Bi-annual Meeting Polymer Networks Group, Elsinore Winter HH, Chambon F (1986b) Rheology of crosslinking polymers at the gel point. Proc Bi-annual Meeting Polymer Networks Group, Elsinore
go back to reference Winter HH, Mours M (1997) Rheology of polymers near their liquid–solid transitions. Adv Polym Sci 134:165–234CrossRef Winter HH, Mours M (1997) Rheology of polymers near their liquid–solid transitions. Adv Polym Sci 134:165–234CrossRef
go back to reference Winter HH, Mours M (2006) The cyber infrastructure initiative for rheology. Rheol Acta 45:331–338CrossRef Winter HH, Mours M (2006) The cyber infrastructure initiative for rheology. Rheol Acta 45:331–338CrossRef
Metadata
Title
An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transition
Authors
H. Henning Winter
Miriam Siebenbürger
David Hajnal
Oliver Henrich
Matthias Fuchs
Matthias Ballauff
Publication date
01-08-2009
Publisher
Springer-Verlag
Published in
Rheologica Acta / Issue 7/2009
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI
https://doi.org/10.1007/s00397-009-0377-5

Other articles of this Issue 7/2009

Rheologica Acta 7/2009 Go to the issue

Premium Partners