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Determination of the weight-average molecular weight of polyamide-6 on the basis of melt viscosity

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Abstract

A theory of a two-point rheometrical method of determination of the weight-average molecular weightM w of polyamide-6 is presented. The method is based on the measurement of the instantaneous values of zero-shear-rate viscosity of the degrading polymer melt, and a formula is derived which enables the calculation of the initial value ofM w (i.e. at zero-residence-time in molten state) of the investigated sample. The experimental verification of the method proves its applicability. The considerations carried out may be regarded as a first step towards developing a theory of an in-line rheometer for a continuous determination ofM w .

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Abbreviations

a T :

temperature shift factor

A :

constant, Pa · s · (kg/kmol)−3.4

b M :

molecular weight shift factor

b M0 :

initial molecular weight shift factor

B :

activation energy of viscous flow, kJ/mol

[c]:

concentration of so called active agent

\(c_{\dot \gamma } \) :

shear rate shift factor

C :

frequency factor in Arndt-Arrhenius equation, Pa · s

C M :

Arndt-Arrhenius frequency factor in eq. (8), Pa · s

d t :

residence time shift factor

D :

constant in eq. (29), kg/kmol · (Pa · s)−0.294

k :

degradation reaction rate constant, s−1

k 1 :

polycondensation reaction rate constant, s−1

k 2 :

random chain scission rate constant, s−1

K :

Bueche constant, Pa · s (kg/kmol)

K T :

Bueche constant in eq. (9), Pa · s (kg/kmol)−3.4

[M]:

concentration of active end groups of polymer chains

M nt :

instantaneous number-average molecular weight of the polymer, kg/kmol

M wt :

instantaneous weight-average molecular weight of the polymer, kg/kmol

M w0 :

initial weight-average molecular weight of the polymer, kg/kmol

M w :

weight-average molecular weight of polymer melt, kg/kmol

(M w0 )solution :

M w0 determined using solution method by Matthes, kg/kmol

(M w0 )melt :

M w0 determined using “two-point” rheometrical method, kg/kmol

M 1 :

molecular weight of monomeric segment of the polymer chain, kg/kmol

m :

mass of the unit volume of polymer melt, kg

n t :

instantaneous number of polymer chains in the unit volume of polymer melt

N :

exponent in eq. (1)

N t :

instantaneous total number of joints between monomeric segments within alln t polymer chains

P nt :

instantaneous number-average polymerisation grade of the polymer

P wt :

instantaneous weight-average polymerisation grade of the polymer

q :

ratio, defined by eq. (A-19)

R :

gas constant,R = 8.315 J/mol η K

s t :

ratio, defined by eq. (A-5)

t :

residence time in molten state, s

t d :

limiting residence time in molten state, defined by eq. (35), s

T :

temperature, K

α :

frequency factor in eq. (4), s−1

β :

activation energy of the reaction rate constant, kJ/mol

\(\dot \gamma \) :

shear rate, s−1

δ :

relative error of the melt or solution viscosity determination

Δ sol :

relative error of the solution method by Matthes

Δ melt :

relative error of the two-point rheometrical method

η t :

instantaneous viscosity, Pa · s

η 0 :

zero-shear-rate viscosity, Pa · s

η 0t :

instantaneous zero-shear-rate viscosity, Pa · s

η 0,0 :

initial (at zero-residence time) zero-shear-rate viscosity, Pa · s

η 01 :

instantaneous zero-shear-rate viscosity att =t 1 , Pa · s

η 02 :

instantaneous zero-shear-rate viscosity att = t 2 , Pa · s

[η]:

intrinsic viscosity of the polymer

ϑ :

frequency factor in eq. (35), s

Λ t :

instantaneous rheological time constant in eq. (1), s

µ :

Newtonian viscosity, Pa · s

ρ :

density of the polymer melt, kg/m3

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Authors and Affiliations

  1. Institute of Chemical Engineering, Łódź Technical University, ul. Wólczańska 175, PL-90-924, Łódź, Poland

    Z. Kembłowski & J. Torzecki

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  1. Z. Kembłowski
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  2. J. Torzecki
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Kembłowski, Z., Torzecki, J. Determination of the weight-average molecular weight of polyamide-6 on the basis of melt viscosity. Rheol Acta 22, 186–196 (1983). https://doi.org/10.1007/BF01332371

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