Influence of the Processes Parameters on the Properties of The ...

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Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments To describe <strong>the</strong> glass transition, <strong>the</strong> temperature <strong>of</strong> half-vitrification, T g , should be specified, i.e., <strong>the</strong> temperature at which <strong>the</strong> heat capacity is midway between that <strong>of</strong> <strong>the</strong> liquid and glassy states (cf. Figure 3.3). This temperature usually corresponds closely to <strong>the</strong> point <strong>of</strong> inflection in <strong>the</strong> heat capacity, and also to <strong>the</strong> breaks in <strong>the</strong> enthalpy or volume versus temperature curves at <strong>the</strong> glass transition. The onset temperature, T onset , is <strong>of</strong>ten given. 2 Intrinsic Viscosity 2.1 Molecular Mass <strong>of</strong> Polymer and Viscosity The M n number average molecular mass is <strong>the</strong> simple arithmetical average <strong>of</strong> each molecule as a summation, divided by <strong>the</strong> number <strong>of</strong> molecules. Ano<strong>the</strong>r measurement <strong>of</strong> average is <strong>the</strong> M w ‘weight’ average, and is an expression <strong>of</strong> <strong>the</strong> fact that <strong>the</strong> higher molecular mass fractions <strong>of</strong> a polymer play a greater role in determining <strong>the</strong> properties than do <strong>the</strong> fractions <strong>of</strong> lower molecular mass. Ma<strong>the</strong>matically, this is given by: Mw w M 1 1 (3.2) w1 where, w 1 represents <strong>the</strong> overall weight <strong>of</strong> molecules <strong>of</strong> molecular mass M 1 . The M w weight average molecular mass is invariably greater than <strong>the</strong> M n number average as its real effect is to square <strong>the</strong> weight. Several methods <strong>of</strong> measuring molecular weight are used and are summarized here: Osmometry. This is a vapour pressure method, useful for polymers <strong>of</strong> molecular mass up to about 25 000; membrane osmometry is used for molecular mass from 20 000 to 1 000 000. These are number average methods. Light scattering. This is a weight average method. Gel permeation chromatography. This is a direct fractionation method using molecular mass. It is relatively rapid and has proved to be one <strong>of</strong> <strong>the</strong> most valuable modern methods. Viscometry. This is a relative method, but <strong>the</strong> simplest, and its application is widespread in industry. Viscometry is <strong>the</strong> technique to measure <strong>the</strong> viscosity <strong>of</strong> materials noting <strong>the</strong> flow rate/efflux time by using different kinds <strong>of</strong> viscosimeters [Warson and Finch, 2001]. The absolute value <strong>of</strong> M w (molecular mass average) can only be determined by complex analytical methods such as light scattering. For linear and un-branched polymers, <strong>the</strong> viscosity average <strong>of</strong> molecular weight (M vis ) is approximately equal to <strong>the</strong> demi-sum <strong>of</strong> <strong>the</strong> M w molecular mass average and <strong>the</strong> M n number average molecular mass. 2.2 General Principle <strong>of</strong> Viscosity Measurement Intrinsic viscosity, which is measured from <strong>the</strong> flow time <strong>of</strong> a solution through a simple glass capillary, has considerable historical importance for establishing <strong>the</strong> very existence <strong>of</strong> polymer molecules. The most useful kind <strong>of</strong> viscometer for determining intrinsic viscosity is <strong>the</strong> “suspended level” or Ubbelohde viscometer, sketched Figure 3.4. - 64 -
Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments Figure 3.4: Schematic representation <strong>of</strong> <strong>the</strong> Ubbelohde viscosimeter. The viscometer is called “suspended level” because <strong>the</strong> liquid initially drawn into <strong>the</strong> small upper bulb is not connected to <strong>the</strong> reservoir as it flows down <strong>the</strong> capillary during measurement. The capillary is suspended above <strong>the</strong> reservoir. In conjunction with <strong>the</strong> pressure-equalization tube, this ensures that <strong>the</strong> only pressure difference between <strong>the</strong> top <strong>of</strong> <strong>the</strong> bulb and <strong>the</strong> bottom <strong>of</strong> <strong>the</strong> capillary is that due to <strong>the</strong> hydrostatic pressure, i.e. <strong>the</strong> weight <strong>of</strong> <strong>the</strong> liquid. Capillary viscometry is conceptually simple: <strong>the</strong> time it takes a volume <strong>of</strong> polymer solution to flow through a thin capillary is compared to <strong>the</strong> time for a solvent flow. It turns out that <strong>the</strong> flow time is proportional to <strong>the</strong> viscosity, and inversely proportional to <strong>the</strong> density. The so called inherent viscosity or logarithmic viscosity number are defined by <strong>the</strong> following relationships: t solvent and solvent solvent t sol ' n The inherent viscosity is defined by <strong>the</strong> ratio: (3.3) sol' n sol' n inh ln rel t with solution rel (3.4) C t solvent where C =concentration <strong>of</strong> polymer in solution (in g/dL) and t =corrected flow time. For most polymer solutions at low concentrations, solution / solvent 1 . Thus, to a very good approximation, <strong>the</strong> relative viscosity is a simple time ratio: t / t . rel solution "Specific viscosity" represents <strong>the</strong> fractional change in viscosity upon addition <strong>of</strong> polymer: sp solution solvent solvent solvent (Unitless) (3.5) Both rel and sp depend on <strong>the</strong> polymer concentration, so to extract <strong>the</strong> “intrinsic” properties <strong>of</strong> <strong>the</strong> polymer chain itself, one must extrapolate to zero concentration. Measuring at zero concentration (C = 0) would be useless, but this concept <strong>of</strong> extrapolating to C = 0 is very important in polymer characterization and in <strong>the</strong>rmodynamics generally. As shown on Figure 3.5, <strong>the</strong> [] intrinsic viscosity corresponds to <strong>the</strong> intercept to C = 0 <strong>of</strong> <strong>the</strong> two quantities: <strong>the</strong> reduced viscosity (sp/C) and <strong>the</strong> inherent viscosity (C -1 .ln rel ). The intrinsic viscosity is given by <strong>the</strong> relation [Russo et al., 1986]: C sp 1 lim limC ln . (3.6) rel C0 C0 - 65 -
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