INDUSTRIA 1.2.1 Origen
5.1.2. Cristalización fraccionada
the diffusion measurements. It consisted of a 4.0 mm ID copper r.f. coil and an un screened planar gradient coil (Cy ) . The maximum field gradient possible was
48.7 T m -1 A-I .
The velocity data were collected on the Bruker (AMX) spectrometer operating at 60 MHz when used in conjunction with the electromagnet described above and at 300 MHz when used in conjunction with the vertical bore, super-conducting magnet. Both the cylindrical-Couette and capillary measurements were completed in their respective magnets at a temperature of 28 Q C . Because the capillary flow experiments in the vertical bore magnet were carried out using a 1.5 mm ID tube, a standard Bruker imaging probe was used with the smallest (5.0 mm ID
)
r.f. insert in order to optimise the signal-to-noise ratio. Two of the three screened gradient coils (Gx, Gy ) offered a maximum gradient of 0.35 T m-I , while Gz gave a larger field variation of 1 .06 T m-I . The solutions were pumped through the capillary by pressurised nitrogen, fed from an industrial gas cylinder with an adjustable pressure regulator(
see Fig. 4.1). Thus a change in the flow rate could be easily achieved by changing the pressure in the reservoir. Due to the non-cyclic pumping system, a relatively large amount of the PEO / H20 solution was required. This criterion was met by a one litre reservoir filled almost to capacity.Figure 4. 1 : A maximum of 20 atm . pressure, provided from an industrial nitrogen
cylinder, allowed a maximum flow rate of 5.8 ml min- 1 through the 1 .5 mm capillary
tube. Care was taken to ensure line feeds were free from air bubbles which would cause serious anomalies in both position and velocity of the image.
Details of the cylindrical-Couette rheometer are given in section 3.4.2. The cell comprise of an inner rod of outside diameter 5.0 mm and an outer cylinder of
CHAPTER 4. SHEAR THINNING OF SEMI-DIL UTE PEO SOL UTIONS 53
inner diameter 9.0 mm. The rheometer was housed inside a home-built imaging probe which used two quadrupole coils and a planar coil. The quadrupole (refer Sec. 8.2. 1 ) coils, Gy and Gz, could generate a maximum gradient of around 7.12
T m-I . The planar coil, Gx, offered a smaller linear field variation of 2.80 T m-I . As well as rf synthesis, gradient switching was also controlled by the AMX spectrometer in conjunction with a Bruker B-AFPA 30 power amplifier. With a typical gradient coil resistance of around 2
n,
a peak power of 1 800 W is available. Depending upon the relevant pulse sequence used, the corresponding duty cycle may give a continuous power of up to 50 W.Both the diffusion and velocity measurements utilised the pulsed gradient spin echo ( PGSE) pulse sequence described in section 3.2.3. The diffusion data was cal culated from the decrease of the echo amplitude as the magnitude of the gradients were increased ( Eqn. (3.40)). The echo amplitude is proportional to the area of its corresponding Fourier spectrum, allowing an estimate with reduced noise because of the bandpass filtering effect of setting a narrow frequency window. Gradient du rations in the range 0 . 1 - 1 .0 ms were used, with separation between gradient pulses ranging from 10- 100 ms. To ensure an accurate measurement of echo magnitude decay, at least 80 % attenuation was achieved in all measurements.
The velocity data was calculated by using the offset of the motional propaga tor with results from the ordered motion. An FFT with respect to the stepped gradient g, for each pixel in the q images, will reveal the shifted motion spectrum.
A detailed description of this process is given in section 3.2.4.
4 . 1 . 2 Results
A sample echo attenuation plot for 930 000 da P EO in D2 0 is shown in figure 4.2
along with a straight line fit based on Eqn. (3.40). The initial rapid decay is prob ably due to the proton signal arising from non-deuterated or partially deuterated water. This signal decays rapidly leaving the signal from the polymer protons un contaminated at larger values of q. Hence the diffusion coefficients obtained from the higher q data are not affected by this anomaly. Figure 4.3 shows the polymer
diffusion coefficients as a function of the w Iv concentration of PE�. There exists a clear change in the slope around a concentration of 1-2 %, indicating the crit ical concentration, c* , for the onset of polymer entanglements. The dependence of diffusion on concentration above c* is consistent with the scaling exponent of around - 1 .7.
To illustrate the velocity data obtained from the cylindrical-Couette rheometer, a normalised velocity plot of a water sample is shown in figure 4.4. A central diametral slice was taken from a 128 X 128 velocity image with a 15.0 mm field of
CHAPTER 4. SHEAR THINNING OF SEMI-DIL UTE PEO SOL UTIONS 54 -0.2 Y = - 0. 1 1 557 - 2.2456e-1 3x RI\2 = 0.976 -0.6 • '0 w W -1.0 • C -l -1 .4 • - 1 .8 • -2.2
Oe+O 2e+ 1 2 4e+ 1 2 6e+12 8e+1 2 1 e+1 3 1 e+1 3 2 2
4 q Tt t:J.
Figure 4.2: The echo attenuation associated with application of the increasing q gra dient is a result of non-refocussed magnetisation. This is caused by the random motion associated with diffusion . The logarithmic plot of the signal versus q2 reveals a straight line, the slope of which is the diffusion coefficient. Note q = ,og/27r.
view (FOV ) . The positive and negative lobes can be seen on the normalised plot, corresponding to the velocity measured perpendicular to the inner rod's direction.
A rotational speed of both 0.4 and 0.8 Hz shows no change in the shape of the velocity profile typical of a Newtonian fluid, such as water. A power law fit (refer Sec. 3.4.4), with an exponent of n = 1 .0, agrees well with the velocity distribution for this geometry.
The shape of the velocity profile obtained using 5 % monodisperse P EO / H20 ( Fig. 4.5) is quite different from that of water. In the polymer solution, shear thinning effects lead to a velocity profile which exhibited a high shear region close to the inner rod . A comparison of this region expanded (Fig. 4.6), as the inner rod's rotational frequency is increased, shows a subtle increase in the local shear rate. The difference in gradient is more pronounced closer to the inner rod where the local stress is larger (see Eqn. (3.5 1 ) . A power law exponent of around 0.4 shows a good agreement for the smallest rotational speed of 0.4 Hz (see Fig. 4.7).
A smaller exponent of around 0 .35 best described the largest angular velocity profile. This tendency to lower power law exponent with increasing shear rate is also apparent in mechanical measurements using a cone-and-plate rheometer ( Fig. 4.6) and is entirely consistent with both the Doi-Edwards and Graessley[78] models for entangled polymer non-linear viscosity.
CHAPTER 4. SHEAR THINNING OF SEMI-DIL UTE PEO SOL UTIONS 55
Slope = ·1.7
.1 1
Concentration (% (w/v)) 1 0
Figure 4.3: Double logarithmic plot of diffusion versus concentration for 930 000 d a PEO in D20. The change in the slope at around 1 % concentration suggests a c* transition to
an entangled state.
Figure 4.8 shows comparative data for the same solution flowing in a capillary tube. Again a diametral slice is shown with a corresponding FOV of 2.5 mm. A comparison can be made between the velocity distribution of the 5 % PEO / H2 0
and a power law fit of n = 0.4. Although the velocity contrast is poor, a reasonable agreement is found. The maximum velocity of approx. 1 1 .0 mm
S- 1
determines that the shear rate is 30S- 1
at the tube walls.CHAPTER 4. SHEAR THINNING OF SEMI-DIL UTE PEO SOL UTIONS 56