The 3D numerical model for ternary system is established

1. Polymer 1 Polymer 2 Solvent Polymer 1 Polymer 2 Solvent t*=1024 t*=2048 t*=4096 (b) (a) (a)‏ (b)‏ (c)‏ (d)‏ t*=1024, C3=0.088 t*=2048, C3=0.018 t*=4096, C3=0 Numerical Simulation of the Phase Separation of a Ternary Systems on a Heterogeneously Functionalized Substrate Yingrui Shang, David Kazmer, Ming Wei, Joey Mead, and Carol Barry University of Massachusetts Lowell RESULTS BACKGROUND MATERIALS/PROCESSES The Cahn-Hilliar equation for a ternary system can be read as following, F: total free energy f: local free energy : the composition gradient energy coefficient Ci: the composition of component i The system then can be described as a function of the compositions. Considering C1+C2+C3=1. The evolution equation can then be written as a function of only C1 and C2, i,j: represent components 1 and component 2. Mij: mobility of component i through j And M should be a function of the compositions of polymer 1 and polymer 2. The free energy of ternary system can be plotted in a 3D view. The spinodal line can also be calculated. 128 64 Elements 16 Experimental results Simulation results The compatibility of the surface pattern to the substrate, Cs, evolutionwith time. The surface pattern tends to phase separate randomly in a condensed solvent. Cs=0.5 represents a random phase separation. The higher the value, the better the replication of the morphology according to the substrate • The self-assembly of polymer blends directed by a patterned substrate has attracted interests for recent decades. • The numerical simulation of this process can be used to investigate the mechanism of the evolution and to estimate the optimized parameters. A numerical model for ternary phase separation has been studied in this work. The depth composition profile with the existance of the patterned substrate. The composition wave propagates in the early stage and the more condensed system evolves faster than the diluted systems. But in the late stage the difference from the attracting surface to the bulk shrinks in the condensed system, since the polymer blends tend to phase separate into a random pattern. In the later stage the evapurationmodel is too thin to show any profile in depth. The morphology evolution of a polymer-polymer-solvent ternary phase separation with random distribution initial condition, where Cpolymer 1=Cpolymer 2 (a).Csolvent=60%;(b).Csolvent=30%. The concentration of the solven on the interface of the two polymer domains is obvious. APPROACH The evolution of the domain size, R(t)~t, which fits therule that R(t)∝t1/3 And it can be see that the less the solvent, the faster the agglomeration of the domains. • A numerical model for a polymer-polymer-solvent ternary system has be established • The free energy profile of the domain is described by the Cahn-Hilliard equation • The discrete cosine transform method is used to to solve the evolution equation with numerical stability and efficiency. • The functionalization of the template is implemented numerically. And the relation of the domain size and the time are investigated. CONCLUSIONS Comparison of the result pattern of phase separation of different polymer compositions: (a).Csolvent=60%; (b).Csolvent=50%; (c). Csolvent=40%; (d).Csolvent=30%, where Cpolymer 1=Cpolymer 2, t*=4096 The more condensed the blends, the higher surface attraction needed for a refined pattern. This may be due to the stronger intermolecular force of the polymers. • The 3D numerical model for ternary system is established • The evolution mechanism is investigated. The R(t)∝t1/3 rule is fitted. • The condensed system has a faster agglomeration pace. • In the situation with patterned substrate the condensed solution patterns evolute faster in the early stage but in the late stage the surface pattern tends to phase separate randomly. • The evaporation of the solvent can benefit the replication of the patterned substrate when the solution becomes more condensed • The modeling will be verified by the experimentdata in the spin coating of polymer solvent SIGNIFICANCE • The numerical model can be used to investigate the evolution mechanism of the phase separation • The optimized parameters can be optimized from the numerical studies. • The parameters which are difficult to measure can also be evaluated via the simulation. • A commercialized software can be designed to assist the experiments and practical production. The phase separation during solventevaporation. The thickness of the polymer file is controlled to shrinkwith time. The evaporation rate of the solvent is in the manner of h=exp(-a*t), where t is the time, a is a constant, and h is the thicknessof the film. Free energy of ternary mixture Starting point of phase separation Spinodal line Ternary phase diagram Nanoscale Science and Engineering Center for High-rate Nanomanufacturing EEC-0425826