Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
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Chapter 3.<br />
Analytical Methods and Designs <str<strong>on</strong>g>of</str<strong>on</strong>g> Experiments<br />
Figure 3.4: Schematic representati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> Ubbelohde viscosimeter.<br />
<strong>The</strong> viscometer is called “suspended level” because <str<strong>on</strong>g>the</str<strong>on</strong>g> liquid initially drawn into <str<strong>on</strong>g>the</str<strong>on</strong>g> small upper<br />
bulb is not c<strong>on</strong>nected to <str<strong>on</strong>g>the</str<strong>on</strong>g> reservoir as it flows down <str<strong>on</strong>g>the</str<strong>on</strong>g> capillary during measurement. <strong>The</strong> capillary is<br />
suspended above <str<strong>on</strong>g>the</str<strong>on</strong>g> reservoir. In c<strong>on</strong>juncti<strong>on</strong> with <str<strong>on</strong>g>the</str<strong>on</strong>g> pressure-equalizati<strong>on</strong> tube, this ensures that <str<strong>on</strong>g>the</str<strong>on</strong>g> <strong>on</strong>ly<br />
pressure difference between <str<strong>on</strong>g>the</str<strong>on</strong>g> top <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> bulb and <str<strong>on</strong>g>the</str<strong>on</strong>g> bottom <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> capillary is that due to <str<strong>on</strong>g>the</str<strong>on</strong>g> hydrostatic<br />
pressure, i.e. <str<strong>on</strong>g>the</str<strong>on</strong>g> weight <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> liquid.<br />
Capillary viscometry is c<strong>on</strong>ceptually simple: <str<strong>on</strong>g>the</str<strong>on</strong>g> time it takes a volume <str<strong>on</strong>g>of</str<strong>on</strong>g> polymer soluti<strong>on</strong> to<br />
flow through a thin capillary is compared to <str<strong>on</strong>g>the</str<strong>on</strong>g> time for a solvent flow. It turns out that <str<strong>on</strong>g>the</str<strong>on</strong>g> flow time is<br />
proporti<strong>on</strong>al to <str<strong>on</strong>g>the</str<strong>on</strong>g> viscosity, and inversely proporti<strong>on</strong>al to <str<strong>on</strong>g>the</str<strong>on</strong>g> density. <strong>The</strong> so called inherent viscosity or<br />
logarithmic viscosity number are defined by <str<strong>on</strong>g>the</str<strong>on</strong>g> following relati<strong>on</strong>ships:<br />
t solvent<br />
<br />
and<br />
<br />
solvent<br />
solvent<br />
t sol ' n<br />
<strong>The</strong> inherent viscosity is defined by <str<strong>on</strong>g>the</str<strong>on</strong>g> ratio:<br />
<br />
(3.3)<br />
<br />
sol'<br />
n<br />
sol'<br />
n<br />
inh<br />
ln rel<br />
t<br />
with soluti<strong>on</strong><br />
rel <br />
(3.4)<br />
C<br />
t solvent<br />
where C =c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> polymer in soluti<strong>on</strong> (in g/dL) and t =corrected flow time.<br />
For most polymer soluti<strong>on</strong>s at low c<strong>on</strong>centrati<strong>on</strong>s, soluti<strong>on</strong> / solvent 1<br />
. Thus, to a very good<br />
approximati<strong>on</strong>, <str<strong>on</strong>g>the</str<strong>on</strong>g> relative viscosity is a simple time ratio: t / t .<br />
rel<br />
soluti<strong>on</strong><br />
"Specific viscosity" represents <str<strong>on</strong>g>the</str<strong>on</strong>g> fracti<strong>on</strong>al change in viscosity up<strong>on</strong> additi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> polymer:<br />
sp<br />
soluti<strong>on</strong><br />
solvent<br />
solvent<br />
solvent<br />
(Unitless) (3.5)<br />
Both rel and sp depend <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> polymer c<strong>on</strong>centrati<strong>on</strong>, so to extract <str<strong>on</strong>g>the</str<strong>on</strong>g> “intrinsic” properties <str<strong>on</strong>g>of</str<strong>on</strong>g><br />
<str<strong>on</strong>g>the</str<strong>on</strong>g> polymer chain itself, <strong>on</strong>e must extrapolate to zero c<strong>on</strong>centrati<strong>on</strong>. Measuring at zero c<strong>on</strong>centrati<strong>on</strong> (C = 0)<br />
would be useless, but this c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> extrapolating to C = 0 is very important in polymer characterizati<strong>on</strong><br />
and in <str<strong>on</strong>g>the</str<strong>on</strong>g>rmodynamics generally. As shown <strong>on</strong> Figure 3.5, <str<strong>on</strong>g>the</str<strong>on</strong>g> [] intrinsic viscosity corresp<strong>on</strong>ds to <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
intercept to C = 0 <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> two quantities: <str<strong>on</strong>g>the</str<strong>on</strong>g> reduced viscosity (sp/C) and <str<strong>on</strong>g>the</str<strong>on</strong>g> inherent viscosity (C -1 .ln rel ).<br />
<strong>The</strong> intrinsic viscosity is given by <str<strong>on</strong>g>the</str<strong>on</strong>g> relati<strong>on</strong> [Russo et al., 1986]:<br />
<br />
<br />
<br />
C<br />
sp<br />
1<br />
lim limC<br />
ln<br />
. (3.6)<br />
rel<br />
C0<br />
C0<br />
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