Kinetics Of Phase Separation

We employ a unique experimental system that has been developed in our laboratory to document the kinetics of pressure-induce phase separation and make assessment on the metastable gap through verification of the crossover from the nucleation and growth to spinodal type phase separation mechanism.1216-19 The technique combines the notion of multiple repetitive pressure-drop (MRPD) with time-and angle resolved light scattering. Figure 7 illustrates the basic methodology and the essential components of the system. At any given polymer concentration, the system pressure is reduced from a point A in the homogenous one-phase region to a point B while the time evolution of the angular variation of the (Is) is monitored. The solution is then homogenized and brought back to the initial condition A. Now a second pressure quench is imposed, this time to a lower end-pressure such as the point C while again monitoring the time-evolution of the scattered light intensities. The process is repeated by bringing the solution to its homogenous condition A, and then subjecting the solution to deeper quenches to with end-pressures at points D, E or lower. Depending upon the depth of penetration into the region of immicibility, the timeevolution of the angular variation of the scattered light intensities show characteristic differences when the spinodal boundary is crossed. In the nucleation and growth (NG) regime scattered light intensties show a continual decrease with increasing angle 9 (or the wave vector q) while in the spinodal regime (SD) the angular variation of the scattered light intensities display a maximum. These type of experiments are repeated for solutions of different concentrations that span concentrations below and above the critical polymer concentrations to permit generation of the complete pressure-composition phase diagrams with experimentally accessible spinodal boundaries.

The light-scattering cell that is shown in Figure 7 is designed to have a short path length with two flat sapphire windows (SW) that are separated by 250 microns. The cell geometry permits monitoring the scattered light intensities over a range of angles. The cell body has a built-in piston that is moved by a pressurizing fluid (PF) with the aid of a pressure generator, a movable air-actuated rod (PR), and a dedicated valve stem (V) that can be used to impose pressure quenches of different depths and rates. The solution is first homogenized and filly circulated through the scattering cell with a circulation loop (not shown in the figure). Then, the cell is isolated and the internal pressure is changed either by the movement of the piston (for small or large pressure changes at a slow rate), or the valve stem (for small and rapid pressure changes), or the air-actuated rod (for large and rapid pressure changes). The actual temperature and the pressure in the solution as well as the transmitted and the scattered light intensities over an angle range from 0 to 13 degrees are monitored in real time during pressure quench. All angles are scanned every 3.2 ms to generate information of the time evolution of the scattered light intensities at all angles.

Figure 7. Experimental system and the methodology to study kinetics of phase separation. Controlled pressure quenches are imposed to bring the system from a homogeneous one-phase state into metastable and unstable regions while changes in pressure, temperature, transmitted light and scattered light at a range of angles are monitored in real time. The angular variation of the scattered light intensities during phase separation shows characteristic fingerprint patterns depending upon the mode of phase separation. Nucleation growth (NG) lead to continual decay, but spinodal decomposition (SD) lead to a maximum in the scattered light intensity profiles.

Figure 7. Experimental system and the methodology to study kinetics of phase separation. Controlled pressure quenches are imposed to bring the system from a homogeneous one-phase state into metastable and unstable regions while changes in pressure, temperature, transmitted light and scattered light at a range of angles are monitored in real time. The angular variation of the scattered light intensities during phase separation shows characteristic fingerprint patterns depending upon the mode of phase separation. Nucleation growth (NG) lead to continual decay, but spinodal decomposition (SD) lead to a maximum in the scattered light intensity profiles.

Using this system we have already investigated the kinetics of pressure-induced phase separation in several polymer-solvent systems including "polystyrene + methyl cyclohexane" 17, "poly (dimethylsiloxane) + supercritical carbon dioxide" 18,and "polyethylene + n-pentane"." Figure 8 shows the time-evolution of the scattered light intensities for a 5.5 wt % PDMS (Mw= 94,300, Mw/M„ = 2.99) solution in supercritical carbon dioxide in two different quench experiments. The angular variation is expressed in terms of the wave number which is given by q = (4n IX) Sin(0/2) where X is the wave length of the He-Ne laser (X = 632.8 nm) and 9 is the scattering angle. From an initial pressure of Pi, s 33 MPa, for a shallow quench of 0.16 MPa the system enters the metastable region. This is reflected by the continual decay of the scattered light intensities with increasing angle. This behavior is retained at different time scans up to 17.6 seconds shown in the figure. With a small increase in the quench depth to 0.25 MPa the system enters the unstable region and undergoes spinodal decomposition. This is reflected by the maximum in the angular variation of the scattered light intensities. In this system the spinodal ring develops immediately after the quench is imposed, and moves into the observable q range within about 40 ms. These type of experiments are conducted at different polymer concentrations for different quench depths to determine the expenmentally accessible spinodal boundary. For some concentrations spinodals are however not experimentally accessible due to the wide metastable gap. Figure 9 shows the binodal and the spinodal boundaries for the PDMS + carbon dioxide system that has been determined by the present technique. Over a concentration range from about 2 to 5.5 % the crossover from nucleation and growth to spinodal decomposition could be experimentally demonstrated by progressive increase in the quench depth. However in the 0.9 wt % solution, even for a quench depth of 2.4 MPa, spinodal boundary could not be crossed.

Figure 8. Time evolution of the scattered light intensities as a function of the wave number q = 4n IX Sin(Q/2) after a pressure quench of 0.16 MPa (left) and 0.25 MPa (right) in a 5.5 % solution ofpoly (dimethylsiloxane) (PDMS, Mw=94,300) in supercritical carbon dioxide at initial condition of 348 K and 33 MPa.

Figure 8. Time evolution of the scattered light intensities as a function of the wave number q = 4n IX Sin(Q/2) after a pressure quench of 0.16 MPa (left) and 0.25 MPa (right) in a 5.5 % solution ofpoly (dimethylsiloxane) (PDMS, Mw=94,300) in supercritical carbon dioxide at initial condition of 348 K and 33 MPa.

Figure 9. Binodal and experimentally accessible spinodal curves for poly (dimethyl siloxane) [Mw= 94,300; Mw/Mn = 2.99] + carbon dioxide.

As a second example, Figure 10A shows the angular variation and the time evolution of the light scattering patterns in a 5.75 % solutions of polyethylene (Mw = 121,000; PDI = 4.43) in n-pentane at 423 K. The figure shows that the system is undergoing spinodal decomposition for this relatively deep quench of 1.1 MPa. In this system for shallower quenches, phase separation was observed to proceed by nucleation and growth.9 Figure 10B is the binodal and spinodal envelopes that were determined for this system at 423 K. As in the case of PDMS + carbon dioxide, unstable domains are relatively easy to enter at certain concentrations. This is the concentration range that includes the critical polymer concentration. Figures 9 and 10 show that for these polymer solutions the spinodal and the binodal merge at concentrations higher than the apex of the binodals. This is a manifestation of the broad molecular weight distribution for these polymers. The selection of broad molecular weight distribution was intentional and helpful to demonstrate the shift in the concentration as an added verification of the power of the technique. (Experiments conducted with narrower molecular weight distribution polyethylenes show that the spinodal and the binodal indeed merge closer to the apex of the binodal).19

Figure 10. A (Lefl) Time evolution of the scattered light intensities as a function of the wave number q = 4 n IX Sin(q2) after a 1.1 MPa quench in 5.75 % solution of polyethylene (Mw, = 121,000; PDI = 4.43) in n-pentane. B (right) Binodal and the experimentally accessible spinodal boundary for the same system.

Figure 10. A (Lefl) Time evolution of the scattered light intensities as a function of the wave number q = 4 n IX Sin(q2) after a 1.1 MPa quench in 5.75 % solution of polyethylene (Mw, = 121,000; PDI = 4.43) in n-pentane. B (right) Binodal and the experimentally accessible spinodal boundary for the same system.

It is important to note significance of these experiments in demonstrating that even at concentrations away from the critical polymer concentration the spinodal decomposition regime may be entered by a rapid pressure quench as long as the metastable gap is not too large. It is also important to note that the time evolution of the scattered light intensities in polymer solutions subjected to a pressure quench display fast kinetics. As can be assessed from Figure 8 and 10, the new phase growth progresses rapidly within seconds.

For quenches leading to spinodal decomposition, the location of the scattered light intensity maximum in these experiments does not remain stationary at a fixed angle, but moves to smaller angles (lower q values) in time within the sampling time intervals of the present experimental system. That the intensity maximum is not stationary suggests that the system passes through the early stage of the spinodal decomposition extremely fast (most likely that within microseconds that we cannot capture in the present system) and enters the intermediate and late stages. The scattered light intensity profiles shown in Figures 8 and 10 correspond to the intermediate or late stage of spinodal decomposition and the maximum of scattered light intensity I, and the peak wave number qmshow power law relationship ofthe type qm = t -a and Im is tb that are typical of later stages of spinodal decomposition.317-19

The maximum value of the wave number qmis related20 to the dominant size scale through L = 2 n/qm. In these systems the characteristic domain size grows rapidly and reaches a size of about 4 microns within about 1 s after the quench is initiated. This is illustrated in Figure 11 for the case of the PDMS and PE solutions undergoing spinodal decomposition as shown in Figues 8 and 10. The domain size grows from about 4 to 10 microns within 5 s after the pressure quench.

Figure 11. Characteristic domain growth in PDMS + CO2 (left) and PE + n-pentane (right) solutions undergoing pressure-induced spinodal decomposition. OP = one-phase; NPG = new phase growth. See Figures 8 and 10.
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