Convective instabilities in traveling fronts of addition polymerization

Polymer Hydrogels and Frontal Polymerization: A Winning Coupling

Polymer hydrogels are 3D networks consisting of hydrophilic crosslinked macromolecular chains, allowing them to swell and retain water. Since their invention in the 1960s, they have become an outstanding pillar in the design, development, and application of engineered polymer systems suitable for biomedical and pharmaceutical applications (such as drug or cell delivery, the regeneration of hard and soft tissues, wound healing, and bleeding prevention, among others). Despite several well-established synthetic routes for developing polymer hydrogels based on batch polymerization techniques, about fifteen years ago, researchers started to look for alternative methods involving simpler reaction paths, shorter reaction times, and lower energy consumption. In this context, frontal polymerization (FP) has undoubtedly become an alternative and efficient reaction model that allows for the conversion of monomers into polymers via a localized and propagating reaction-by means of exploiting the formation and propagation of a "hot" polymerization front-able to self-sustain and propagate throughout the monomeric mixture. Therefore, the present work aims to summarize the main research outcomes achieved during the last few years concerning the design, preparation, and application of FP-derived polymeric hydrogels, demonstrating the feasibility of this technique for the obtainment of functional 3D networks and providing the reader with some perspectives for the forthcoming years.

Frontal Polymerizations: From Chemical Perspectives to Macroscopic Properties and Applications

The synthesis and processing of most thermoplastics and thermoset polymeric materials rely on energy-inefficient and environmentally burdensome manufacturing methods. Frontal polymerization is an attractive, scalable alternative due to its exploitation of polymerization heat that is generally wasted and unutilized. The only external energy needed for frontal polymerization is an initial thermal (or photo) stimulus that locally ignites the reaction. The subsequent reaction exothermicity provides local heating; the transport of this thermal energy to neighboring monomers in either a liquid or gel-like state results in a self-perpetuating reaction zone that provides fully cured thermosets and thermoplastics. Propagation of this polymerization front continues through the unreacted monomer media until either all reactants are consumed or sufficient heat loss stalls further reaction. Several different polymerization mechanisms support frontal processes, including free-radical, cat- or anionic, amine-cure epoxides, and ring-opening metathesis polymerization. The choice of monomer, initiator/catalyst, and additives dictates how fast the polymer front traverses the reactant medium, as well as the maximum temperature achievable. Numerous applications of frontally generated materials exist, ranging from porous substrate reinforcement to fabrication of patterned composites. In this review, we examine in detail the physical and chemical phenomena that govern frontal polymerization, as well as outline the existing applications.

Buoyancy-Induced Convection Driven by Frontal Polymerization

In this Letter, we study the interaction between a self-sustaining exothermic reaction front propagating in a direction perpendicular to that of gravity and the buoyancy-driven convective flow during frontal polymerization (FP) of a low-viscosity monomer resin. As the polymerization front transforms the liquid monomer into the solid polymer, the large thermal gradients associated with the propagating front sustain a natural convection of the fluid ahead of the front. The fluid convection in turn affects the reaction-diffusion (RD) dynamics and the shape of the front. Detailed multiphysics numerical analyses and particle image velocimetry experiments reveal this coupling between natural convection and frontal polymerization. The frontal Rayleigh (Ra) number affects the magnitude of the velocity field and the inclination of the front. A higher Ra number drives instability during FP, leading to the observation of thermal-chemical patterns with tunable wavelengths and magnitudes.

Influence of Oxygen on Chemoconvective Patterns in the Iodine Clock Reaction

There is increasing interest in using chemical clock reactions to drive material formation; however, these reactions are often subject to chemoconvective effects, and control of such systems remains challenging. Here, we show how the transfer of oxygen at the air-water interface plays a crucial role in the spatiotemporal behavior of the iodine clock reaction with sulfite. A kinetic model was developed to demonstrate how the reaction of oxygen with sulfite can control a switch from a low-iodine to high-iodine state under well-stirred conditions and drive the formation of transient iodine gradients in unstirred solutions. In experiments in thin layers with optimal depths, the reaction couples with convective instability at the air-water interface forming an extended network-like structure of iodine at the surface that develops into a spotted pattern at the base of the layer. Thus, oxygen drives the spatial separation of iodine states essential for patterns in this system and may influence pattern selection in other clock reaction systems with sulfite.

Manipulating Frontal Polymerization and Instabilities with Phase-Changing Microparticles

Recently presented as a rapid and eco-friendly manufacturing method for thermoset polymers and composites, frontal polymerization (FP) experiences thermo-chemical instabilities under certain conditions, leading to visible patterns and spatially dependent material properties. Through numerical analyses and experiments, we demonstrate how the front velocity, temperature, and instability in the frontal polymerization of cyclooctadiene are affected by the presence of poly(caprolactone) microparticles homogeneously mixed with the resin. The phase transformation associated with the melting of the microparticles absorbs some of the exothermic reaction energy generated by the FP, reduces the amplitude and order of the thermal instabilities, and suppresses the front velocity and temperatures. Experimental measurements validate predictions of the dependence of the front velocity and temperature on the microparticle volume fraction provided by the proposed homogenized reaction-diffusion model.

Carbon and carbon composites obtained using deep eutectic solvents and aqueous dilutions thereof

Extending the “all-in-one” features of DESs to DES/H₂O binary mixtures.

Thermally driven directional free-radical polymerization in confined channels

We report on the formation of poly(acrylamide) (PAAm) with a relatively-narrow molecular weight distribution (MWD) by means of thermally-driven directional free-radical polymerization carried out in polymerization chambers featuring two parallel glass walls separated by various distances, ranging from sub-millimeter to a few millimeters.

Convection induced by thermal gradients on thin reaction fronts

We present a thin front model for the propagation of chemical reaction fronts in liquids inside a Hele-Shaw cell or porous media. In this model we take into account density gradients due to thermal and compositional changes across a thin interface. The front separating reacted from unreacted fluids evolves following an eikonal relation between the normal speed and the curvature. We carry out a linear stability analysis of convectionless flat fronts confined in a two-dimensional rectangular domain. We find that all fronts are stable to perturbations of short wavelength, but they become unstable for some wavelengths depending on the values of compositional and thermal gradients. If the effects of these gradients oppose each other, we observe a range of wavelengths that make the flat front unstable. Numerical solutions of the nonlinear model show curved fronts of steady shape with convection propagating faster than flat fronts. Exothermic fronts increase the temperature of the fluid as they propagate through the domain. This increment in temperature decreases with increasing speed.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

Role of heat generation and thermal diffusion during frontal photopolymerization

Frontal photopolymerization (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerization front that propagates into the bath as a planar traveling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerization influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerization, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerization front. This leads to an accumulation of heat behind the polymerization front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth direction.

Controlling frontal photopolymerization with optical attenuation and mass diffusion

Frontal photopolymerization (FPP) is a versatile directional solidification process that can be used to rapidly fabricate polymer network materials by selectively exposing a photosensitive monomer bath to light. A characteristic feature of FPP is that the monomer-to-polymer conversion profiles take on the form of traveling waves that propagate into the unpolymerized bulk from the illuminated surface. Practical implementations of FPP require detailed knowledge about the conversion profile and speed of these traveling waves. The purpose of this theoretical study is to (i) determine the conditions under which FPP occurs and (ii) explore how optical attenuation and mass transport can be used to finely tune the conversion profile and propagation kinetics. Our findings quantify the strong optical attenuation and slow mass transport relative to the rate of polymerization required for FPP. The shape of the traveling wave is primarily controlled by the magnitude of the optical attenuation coefficients of the neat and polymerized material. Unexpectedly, we find that mass diffusion can increase the net extent of polymerization and accelerate the growth of the solid network. The theoretical predictions are found to be in excellent agreement with experimental data acquired for representative systems.

Synthesis and characterization of functionally gradient materials obtained by frontal polymerization

Functionally gradient materials (FGMs) with gradual and continuous changes of their properties in one or more dimensions are useful in a wide range of applications. However, obtaining such materials with accurate control of the gradient, especially when the gradient is nonlinear, is not easy. In this work, frontal polymerization (FP) was exploited to synthesize polymeric FGMs. We demonstrated that the use of ascending FP with continuous feeding of monomers with computer-controlled peristaltic pumps provided an excellent method for the preparation of functionally gradient materials with programmed gradients. To test the effectiveness of the method, copolymers made from triethylene glycol dimethacrylate/hexyl methacrylate with linear and hyperbolic gradient in composition were synthesized. Differential scanning calorimetry (DSC), Shore A hardness measurements, compression tests, and swelling studies were performed along the length of the materials to assess the relationship between the gradients and the material properties. Glass transition temperatures, determined by DSC, showed a linear dependence on the composition and were in agreement with theoretical values. The other properties showed different and specific behaviors as a function of the compositional gradient.

Deep eutectic solvents in polymerizations: a greener alternative to conventional syntheses

The use of deep eutectic solvents (DESs) that act as all-in-one solvent-template-reactant systems offers an interesting green alternative to conventional syntheses in materials science. This Review aims to provide a comprehensive overview to emphasize the similarities and discrepancies between DES-assisted and conventional syntheses and rationalize certain green features that are common for the three DES-assisted syntheses described herein: one case of radical polymerization and two cases of polycondensations. For instance, DESs contain the precursor itself and some additional components that either provide certain functionality (e.g., drug delivery and controlled release, or electrical conductivity) to the resulting materials or direct their formation with a particular structure (e.g., hierarchical-type). Moreover, DESs provide a reaction medium, so polymerizations are ultimately carried out in a solventless fashion. This means that DES-assisted syntheses match green chemistry principles 2 and 5 because of the economy of reagents and solvents, whereas the functionality incorporated by the second component allows the need for any post-synthesis derivatization to be minimized or even fully avoided (principle 8). DESs also provide new precursors that favor more efficient polymerization (principle 6) by decreasing the energy input required for reaction progress. Finally, the use of mild reaction conditions in combination with the compositional versatility of DESs, which allows low-toxic components to be selected, is also of interest from the viewpoint of green chemistry because it opens up the way to design biocompatible and/or eco-friendly synthetic methods (principle 3).

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated.

Convective mixing induced by acid-base reactions

When two miscible solutions, each containing a reactive species, are put in contact in the gravity field, local variations in the density due to the reaction can induce convective motion and mixing. We characterize here both experimentally and theoretically such buoyancy-driven instabilities induced by the neutralization of a strong acid by a strong base in aqueous solutions. The diverse patterns obtained are shown to depend on the type of reactants used and on their relative concentrations. They have their origin in a combination of classical hydrodynamic instabilities including differential diffusion of the solutes involved while temperature effects only play a marginal role.

Hot spots revealed by simultaneous experimental measurement of the two-dimensional concentration and temperature fields of an exothermic chemical front during finger-pattern formation

A noninvasive optical technique combining digital interferometry in transmission and transparency measurement of concentration is developed to analyze spatiotemporal dynamics of physicochemical systems. This technique allows one to measure simultaneously the two-dimensional (2D) dynamics of concentration and temperature fields in both reactive and nonreactive systems contained inside a transparent cell. When used to experimentally analyze buoyancy-driven fingering of an exothermic autocatalytic chemical front, this method reveals in the 2D temperature field the presence of hot spots where the temperature locally exceeds the adiabatic one.

Exhaustive Analysis of Frontal Copolymerization of Functionalized Monovinyl and Divinyl Monomers

A series of copolymers of 2-hydroxyethyl methacrylate (HEMA)/glycidyl methacrylate (GMA) and ethylene dimethacrylate (EGDM) were synthesized by frontal polymerization (FP). This study was conducted to investigate the effect of crosslink density, type and concentration of initiator, the use of a complex initiator system, porogen, and diluent on the most relevant parameters of FP, such as sustainability of the front, temperature profile, front velocity, and yield. The products were also characterized for intruded pore volume, pore-size distribution, epoxy-functionality number, and surface morphology. Higher crosslink densities (CLDs) and initiator concentration produced higher front velocities, whereas no trend in front temperature was noted. A complex initiation system was effective in stabilizing and increasing the polymerization yield. Relative to suspension polymerization (SP), FP products synthesized without a solvent were microporous, whereas micro-to-macroporous products were obtained in the presence of a solvent (for HEMA-EGDM polymers). We also present, explain, and discuss the exotic patterns observed under a microscope. We observed two basic types of spatial patterns, namely, planar and nonplanar patterns. The type of planar pattern observed under scanning electron microscopy (SEM) has a spatial impulse that appears as a loop followed by regular periodic motion in the radial and axial directions. This behavior gives rise to a repeating pattern that is a few microns thick. Also, nonplanar patterns, namely, layered concentric rings and winding staircase patterns, were observed under SEM.

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Benard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented.

Complex morphology in a simple chemical system

Chemical systems, far from thermodynamic equilibrium, may spontaneously self-construct complex structures mimicking biological structures.