Pattern formation in thin films of polymer solutions: Theory and simulations

Harnessing Polar Interactions Tunes the Stability of Ultrathin Polymer Solution Films

The stability of ultrathin (<100 nm) polymer films is essential in applications like protective coatings. On the contrary, their instability may actually be desirable for the emergence of self-assembled nanoscale patterns utilized in the fabrication of functional devices. Polymer solution films exhibit two distinct kinds of instabilities, viz., dewetting (long-wave) and decomposition (short-wave). Dewetting refers to the rupture of the continuous film to form isolated domains, while decomposition leads to phase separation within the polymer solution. The focus of this work is on leveraging polar interactions between the solute and solvent molecules to tune the stability of the film. A gradient dynamics-based thin film model is developed to investigate pattern formation in a thin polar polymer solution film. The Flory-Huggins theory is suitably modified by introducing a polar interaction parameter that depends upon the concentration of the polymer and the dipole moments of monomer (μ1) and solvent molecules (μ0). A linear stability analysis is performed to determine the characteristic length scale and growth rate of the instabilities. It is shown that the range of concentration space for the occurrence of the decomposition mode is directly affected by the Flory interaction parameter (χ0), μ0, and μ1, thereby serving as control parameters to tune the width of the concentration range. It is further shown that ignoring polar interactions may lead to incorrect predictions of the instability mode, including a complete loss of the decomposition mode. In addition, the long-wave dewetting length scale is found to decrease due to bulk dipolar interactions at higher polymer concentrations. Finally, numerical simulations are carried out to track the nonlinear evolution of the interface and concentration field for both the decomposition and dewetting modes of instability.

Pattern Formation in Evaporating Polymer Solutions-Interplay between Dewetting and Decomposition

Pattern formation during solution evaporation is common in several industrial settings and involves a complex interplay of multiple processes, including wetting/dewetting, diffusion, and rheological characteristics of the solution. Monitoring the emergence of patterns during evaporation under controlled conditions may allow deconvolution of different processes and, in turn, improve our understanding of this common yet complex phenomenon. Here, we probe the importance of initial conditions, defined by the solution concentration c 0, on the pattern formation in evaporating polymer solutions on the air-water interface. Intriguingly, the initial decrease in the lateral length scale (ξ), characterizing the patterns, takes an upturn at higher concentrations, revealing reentrant behavior. We employ a gradient dynamics model consisting of coupled evolution equations for the film height and the polymer fraction in the solution. Our simulations capture two different length scales revealing the reasons underlying the re-entrant behavior of ξ(c 0). While the long-range destabilizing interactions between suspension and water result in the dewetting of thin film solutions, the phase separation between the polymer and solvent occurs at shorter length scales. Our results demonstrate the importance of initial concentration on pattern formation and, thereby, on the resultant properties of thin polymer films.

Simultaneous Decomposition and Dewetting of Nanoscale Alloys: A Comparison of Experiment and Theory

We consider the coupled process of phase separation and dewetting of metal alloys of nanoscale thickness deposited on solid substrates. The experiments involve applying nanosecond laser pulses that melt the Ag₄₀Ni₆₀ alloy films in two setups: either on thin supporting membranes or on bulk substrates. These two setups allow for extracting both temporal and spatial scales on which the considered processes occur. The theoretical model involves a longwave version of the Cahn-Hilliard formulation used to describe spinodal decomposition, coupled with an asymptotically consistent longwave-based description of dewetting that occurs due to destabilizing interactions between the alloy and the substrate, modeled using the disjoining pressure approach. Careful modeling, combined with linear stability analysis and fully nonlinear simulations, leads to results consistent with the experiments. In particular, we find that the two instability mechanisms occur concurrently, with the phase separation occurring faster and on shorter temporal scales. The modeling results show a strong influence of the temperature dependence of relevant material properties, implying that such a dependence is crucial for the understanding of the experimental findings. The agreement between theory and experiment suggests the utility of the proposed theoretical approach in helping to develop further experiments directed toward formation of metallic alloy nanoparticles of desired properties.

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other.

Coarsening Dynamics of True Morphological Phase Separation in Unstable Thin Films

Unstable thin films can spontaneously phase separate into two equilibrium flat-film morphologies of different thicknesses under the influence of gravity or favorable combinations of apolar and polar excess intermolecular forces. Two distinct pathways and associated dynamics of this morphological phase separation are presented based on numerical simulations of the 2-D thin film equation. The two pathways are (1) the "direct pathway" whereby the thicker phase forms directly and concurrently with the thinner phase and (2) the "defect pathway" whereby the thicker phase forms by the coarsening of defects of intermediate thickness and appears much later than the thinner phase. The defect pathway is favored by films whose initial thickness lies closer to the thickness of the thinner phase. Both pathways show an initial power law decay with exponent -1/4 in time followed by a plateau in the number density of domains/defects. Thereafter, the defect pathway shows another universal power law decay with exponent -1/3 and ends with a logarithmic decay, which is specific to the d = 2 case as there is no interfacial curvature in d = 2. The direct pathway skips the second power law decay and goes directly to the logarithmic decay.