The Effect of Conductive Heat Transfer on the Morphology Formation in Polymer Solutions Undergoing Thermally Induced Phase Separation

Abstract

Owing to the fact that heat transfer during the thermally induced phase separation process is limited, a quench rate is inevitably entailed, which leads to the existence of temporal and spatial variations in temperature. Hence, it is of great importance to take into account the nonisothermality during the phase separation process, especially in high viscosity polymer solutions. In this study, the influence of conductive heat transfer on the morphology formation during the thermally induced phase separation process was investigated theoretically in terms of quench depth, boundary conditions, and enthalpy of demixing to elucidate the interaction between temperature and concentration through incorporating the nonlinear Cahn-Hilliard equation and the Fourier heat transfer equation in two dimensions. The Flory-Huggins free energy theory for the thermodynamics of phase separation, slow mode theory, and Rouse law for polymer diffusion without entanglements were taken into account in the model development. The simulation results indicated a strong interaction between heat transfer and phase separation, which impacted the morphology formation significantly. Results confirmed that quench depth had an indispensable impact on phase separation in terms of higher characteristic frequency by increasing the driving force for heat transfer. Applying quench from various boundaries led to a difference in the quench rate due to the high viscosity of the polymer solution. This led to a gradation in pore size and anisotropic morphology formation. The degree and direction of anisotropy depended on quench depth and rate, quench time, heat conduction rate inside the solution, solution viscosity, temperature evolution, and the enthalpy of demixing. It was also verified that the influence of enthalpy of demixing on phase separation could not be neglected as it increased the solution temperature and led to phase separation being accomplished at a higher temperature than the initial quench temperature.

Morphology formation during the nonisothermal thermally‐induced phase separation (TIPS) process

“…In our previous study, the influence of the heat of demixing on phase separation and morphology formation was investigated comprehensively, and it was verified that when one side of the medium is quenched while keeping the other sides insulated, and also when all four sides of the medium are quenched to the same temperature, the heat that is released during phase separation increases the quench temperature to some extent but does not change the direction of the heat transfer rate as there is no difference in the quench rate between different sides of the sample. [42] At time equal to t* = 1 Â 10 À5 , phase separation has not yet started, and both dimensionless concentration profiles are the same as presented in Figure 2A, depicting the infinitesimal thermal concentration fluctuations that are present in the homogenous system, and as a result, there is no difference between the two concentration profiles. As time proceeds to t* = 2 Â 10 À4 as shown in Figure 2B, phase separation begins in the entire sample homogenously.…”

“…Next, the Cahn-Hilliard equation is coupled with the Fourier heat transfer equation in order to investigate the competition between heat and mass transfer when the two sides of the medium are quenched to two different temperatures and the resultant morphology. [42] Morphology is the key factor in defining the applications of porous polymeric materials in terms of their thermal, mechanical, and insulation properties. [43] It is of the utmost importance to take the nonisothermality during phase separation into account due to the fact that there is always a cooling rate associated with phase separation as a result of the limited heat transfer.…”

The Influence of Physical Properties on the Membrane Morphology Formation during the Nonisothermal Thermally Induced Phase Separation Process

“…The characteristics of the porous polymeric membranes, such as pore shape and size, strongly depend on the operating parameters, system properties, kinetics, dynamics, and thermodynamics of the phase separation process [ 1 , 2 , 3 , 4 , 5 , 6 ]. When investigating spinodal decomposition, it is important to consider the effect of heat transfer on the phase separation process due to the nonisothermal nature of the process [ 7 , 8 , 9 , 10 , 11 , 12 ]. Heat transfer can have a significant impact on the cooling rate and, therefore, on the morphology formation [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ].…”

“…When investigating spinodal decomposition, it is important to consider the effect of heat transfer on the phase separation process due to the nonisothermal nature of the process [ 7 , 8 , 9 , 10 , 11 , 12 ]. Heat transfer can have a significant impact on the cooling rate and, therefore, on the morphology formation [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. Additionally, the physical properties of the polymeric system, such as viscosity, density, heat conductivity, heat capacity, etc., can also impact the morphology formation in terms of the variations in temperature and concentration during phase separation [ 18 , 19 , 20 , 21 , 22 ].…”

“…In our previous studies, we coupled the nonlinear Cahn–Hilliard equation with the Fourier heat transfer equation and a transient heat equation with the aim of investigating the impact of heat transfer on phase separation during the thermally-induced phase separation process in terms of applying various boundary conditions and initial solvent volume fractions. It was observed that heat transfer impacted the phase separation dramatically, and it was concluded that the effect of heat transfer and the heat of demixing could not be ignored during phase separation [ 8 , 9 ].…”