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Flow birefringence of polymer melts: Application to the investigation of time dependent rheological properties

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Summary

Transient stresses including normal stresses, which are developed in a polymer melt by a suddenly imposed constant rate of shear, are investigated by mechanical measurement and, indirectly, with the aid of the flow birefringence technique. For the latter purpose use is made of the so-called stress-optical law, which is carefully checked.

It appears that the essentially linear model of the “rubberlike liquid”, as proposed byLodge, is capable of describing the behaviour of polymer melts rather well, if the applied total shear does not exceed unity. In order to describe also steady state values of the stresses successfully, one should extend measurements to extremely low shear rates.

These statements are verified with the aid of a method which was originally designed bySchwarzl andStruik for the practical calculation of interrelations between linear viscoelastic functions. In the present paper dynamic shear moduli are used as reference functions.

Zusammenfassung

Mit der Zeit anwachsende Spannungen, darunter auch Normalspannungen, wie sie sich nach dem plötzlichen Anlegen einer konstanten Schergeschwindigkeit in einer Polymerschmelze entwickeln, werden mit Hilfe mechanischer Messungen und indirekt mit Hilfe der Strömungsdoppelbrechung untersucht. Für den letzteren Zweck wird das sogenannte spannungsoptische Gesetz herangezogen, dessen Gültigkeit sorgfältig überprüft wird.

Es ergibt sich, daß das im Wesen lineare Modell der gummiartigen Flüssigkeit, wie es vonLodge vorgeschlagen wurde, sich recht gut zur Beschreibung des Verhaltens von Polymerschmelzen eignet, solange der im ganzen angelegte Schub den Wert Eins nicht überschreitet. Um auch stationäre Werte der Spannungen in die Beschreibung erfolgreich einzubeziehen, sollte man die Messungen bis zu extrem niedrigen Schergeschwindigkeiten ausdehnen.

Die gemachten Feststellungen werden mit Hilfe einer Methode verifiziert, die vonSchwarzl undStruik ursprünglich für die praktische Berechnung von Beziehungen zwischen Zustandsfunktionen entwickelt wurde, die dem linear viskoelastischen Verhalten entsprechen. In der vorliegenden Veröffentlichung dienen die dynamischen Schubmoduln als Bezugsfunktionen.

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Abbreviations

a T :

shift factor

B ij :

Finger deformation tensor

C :

stress-optical coefficient, (m2/N)

f (p jl ):

undetermined scalar function

G :

shear modulus, (N/m2)

G(t) :

time dependent shear modulus, (N/m2)

G′(ω) :

shear storage modulus, (N/m2)

G″(ω) :

shear loss modulus, (N/m2)

G″ r :

reduced shear storage modulus, (N/m2)

G″ r :

reduced shear loss modulus, (N/m2)

H(τ) :

shear relaxation time spectrum, (N/m2)

k :

Boltzmann constant, (Nm/°K)

n ik :

refractive index tensor

p :

undetermined hydrostatic pressure, (N/m2)

p ij ,p ik :

stress tensor, (N/m2)

p 21 :

shear stress, (N/m2)

p 11 –p 22 :

first normal stress difference, (N/m2)

p 22 –p 33 :

second normal stress difference, (N/m2)

q :

shear rate, (s−1)

t, t′ :

time, (s)

T :

absolute temperature, (°K)

T 0 :

reference temperature, (°K)

x :

the ratiot/τ

x :

position vector of a material point after deformation, (m)

x′:

position vector of a material point before deformation, (m)

α 0,α 1 :

constants in eq. [37]

β 0,β 1 :

constants in eq. [37]

γ :

shear deformation

γ(t, t′) :

time dependent shear deformation

δ ij :

unity tensor

Δn :

flow birefringence in the 1–2 plane

η(q) :

non-Newtonian shear viscosity, (N s/m2)

η * (ω) :

complex dynamic viscosity, (N s/m2)

|η * (ω)|:

absolute value of complex dynamic viscosity, (N s/m2)

η′(ω) :

real part of complex dynamic viscosity, (N s/m2)

η″(ω) :

imaginary part of complex dynamic viscosity, (N s/m2)

μ(t — t′) :

“memory function”, (N/m2 · s)

v :

number of effective chains per unit of volume, (m−3)

ρ :

temperature dependent density, (kg/m3)

ρ 0 :

density at reference temperatureT 0, (kg/m3)

τ :

relaxation time, (s)

τ′ :

integration variable, (s)

φ(x) :

approximate intensity function

φ 1 (x) :

error function

χ :

extinction angle

χ m :

orientation angle of the stress ellipsoid

ω :

circular frequency, (s−1)

1:

direction of flow

2:

direction of the velocity gradient

3:

indifferent direction

t :

time dependence

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Authors and Affiliations

  1. Laboratory of Physical Chemistry, Delft University of Technology, Julianalaan 136, Delft 8, The Netherlands

    F. H. Gortemaker & H. Janeschitz-Kriegl

  2. General Electric Research Laboratories, Schenectady, N. Y., USA

    M. G. Hansen

  3. Istituto di Principi di Ingegneria Chimica, University of Naples, Italy

    B. de Cindio

  4. Meß- und Prüflaboratorium, BASF Aktiengesellschaft, D-6700, Ludwigshafen/Rhein, BRD

    H. M. Laun

Authors
  1. F. H. Gortemaker
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  2. M. G. Hansen
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  3. B. de Cindio
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  4. H. M. Laun
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  5. H. Janeschitz-Kriegl
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Additional information

The present investigation has been carried out under the auspices of the Netherlands Organization for the Advancement of Pure Research (Z. W. O.).

North Atlantic Treaty Organization Science Post Doctoral Fellow.

Research Fellow, Delft University of Technology.

With 11 figures and 2 tables

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Gortemaker, F.H., Hansen, M.G., de Cindio, B. et al. Flow birefringence of polymer melts: Application to the investigation of time dependent rheological properties. Rheol Acta 15, 256–267 (1976). https://doi.org/10.1007/BF01521126

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