Equilibrium polymerization models of re-entrant self-assembly

On the mechanism behind the inverse melting in systems with competing interactions

The competition between a short range attractive interaction and a nonlocal repulsive interaction promote the appearance of modulated phases. In this work we present the microscopic mechanisms leading to the emergence of inverse transitions in such systems by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. We identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors in the phase diagram. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we observe that the degree of reentrance decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. These mean-field results are confronted with Langevin simulations of an effective coarse grained model, confirming the expected extension of the reentrance in the phase diagram. These results shed new light on many systems undergoing inverse melting transitions by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points.

Reentrant Phase Transitions and Non-Equilibrium Dynamics in Membraneless Organelles

Compartmentalization of biochemical components, interactions, and reactions is critical for the function of cells. While intracellular partitioning of molecules via membranes has been extensively studied, there has been an expanding focus in recent years on the critical cellular roles and biophysical mechanisms of action of membraneless organelles (MLOs) such as the nucleolus. In this context, a substantial body of recent work has demonstrated that liquid-liquid phase separation plays a key role in MLO formation. However, less is known about MLO dissociation, with phosphorylation being the primary mechanism demonstrated thus far. In this Perspective, we focus on another mechanism for MLO dissociation that has been described in recent work, namely a reentrant phase transition (RPT). This concept, which emerges from the polymer physics field, provides a mechanistic basis for both formation and dissolution of MLOs by monotonic tuning of RNA concentration, which is an outcome of cellular processes such as transcription. Furthermore, the RPT model also predicts the formation of dynamic substructures (vacuoles) of the kind that have been observed in cellular MLOs. We end with a discussion of future directions in terms of open questions and methods that can be used to answer them, including further exploration of RPTs in vitro, in cells, and in vivo using ensemble and single-molecule methods as well as theory and computation. We anticipate that continued studies will further illuminate the important roles of reentrant phase transitions and associated non-equilibrium dynamics in the spatial patterning of the biochemistry and biology of the cell.

Mixtures of two self- and mutually-associating liquids: Phase behavior, second virial coefficients, and entropy-enthalpy compensation in the free energy of mixing

The theoretical description of the phase behavior of polymers dissolved in binary mixtures of water and other miscible solvents is greatly complicated by the self- and mutual-association of the solvent molecules. As a first step in treating these complex and widely encountered solutions, we have developed an extension of Flory-Huggins theory to describe mixtures of two self- and mutually-associating fluids comprised of small molecules. Analytic expressions are derived here for basic thermodynamic properties of these fluid mixtures, including the spinodal phase boundaries, the second osmotic virial coefficients, and the enthalpy and entropy of mixing these associating solvents. Mixtures of this kind are found to exhibit characteristic closed loop phase boundaries and entropy-enthalpy compensation for the free energy of mixing in the low temperature regime where the liquid components are miscible. As discussed by Widom et al. [Phys. Chem. Chem. Phys. 5, 3085 (2003)], these basic miscibility trends, quite distinct from those observed in non-associating solvents, are defining phenomenological characteristics of the "hydrophobic effect." We find that our theory of mixtures of associating fluids captures at least some of the thermodynamic features of real aqueous mixtures.

Re-entrant DNA gels

DNA is acquiring a primary role in material development, self-assembling by design into complex supramolecular aggregates, the building block of a new-materials world. Using DNA nanoconstructs to translate sophisticated theoretical intuitions into experimental realizations by closely matching idealized models of colloidal particles is a much less explored avenue. Here we experimentally show that an appropriate selection of competing interactions enciphered in multiple DNA sequences results into the successful design of a one-pot DNA hydrogel that melts both on heating and on cooling. The relaxation time, measured by light scattering, slows down dramatically in a limited window of temperatures. The phase diagram displays a peculiar re-entrant shape, the hallmark of the competition between different bonding patterns. Our study shows that it is possible to rationally design biocompatible bulk materials with unconventional phase diagrams and tuneable properties by encoding into DNA sequences both the particle shape and the physics of the collective response.

Forming self-assembled soft materials with unconventional properties can be useful in many different applications. Here, Sciortino and co-workers have designed and experimentally realized a one-pot DNA hydrogel that melts both on heating and on cooling.

Lattice model of linear telechelic polymer melts. II. Influence of chain stiffness on basic thermodynamic properties

The lattice cluster theory (LCT) for semiflexible linear telechelic melts, developed in Paper I, is applied to examine the influence of chain stiffness on the average degree of self-assembly and the basic thermodynamic properties of linear telechelic polymer melts. Our calculations imply that chain stiffness promotes self-assembly of linear telechelic polymer melts that assemble on cooling when either polymer volume fraction ϕ or temperature T is high, but opposes self-assembly when both ϕ and T are sufficiently low. This allows us to identify a boundary line in the ϕ-T plane that separates two regions of qualitatively different influence of chain stiffness on self-assembly. The enthalpy and entropy of self-assembly are usually treated as adjustable parameters in classical Flory-Huggins type theories for the equilibrium self-assembly of polymers, but they are demonstrated here to strongly depend on chain stiffness. Moreover, illustrative calculations for the dependence of the entropy density of linear telechelic polymer melts on chain stiffness demonstrate the importance of including semiflexibility within the LCT when exploring the nature of glass formation in models of linear telechelic polymer melts.

Phase field method for nonequilibrium dynamics of reversible self-assembly systems

Phase field methods are extended to describe the nonequilibrium dynamics of reversible self-assembly systems, an extension that is complicated by the mutual coupling of many non-conserved order parameters into a set of highly nonlinear partial differential equations. Further complications arise because the sum of all non-conserved order parameters equals a conserved order parameter. The theory is developed for the simplest model of reversible self-assembly in which no additional constraints are imposed on the self-assembly process since the extension to treat more complex self-assembly models is straightforward. Specific calculations focus on the time evolution of the cluster size distribution for a free association system that is rapidly dropped from one ordered state to a more ordered state within the one-phase region. The dynamics proceed as expected, thereby providing validation of the theory which is also capable of treating systems with spatial inhomogeneities.

Lattice cluster theory of associating telechelic polymers. III. Order parameter and average degree of self-assembly, transition temperature, and specific heat

The lattice cluster theory of strongly interacting, structured polymer fluids is applied to determine the thermodynamic properties of solutions of telechelic polymers that may associate through bifunctional end groups. Hence, this model represents a significant albeit natural extension of a diverse array of prior popular equilibrium polymerization models in which structureless "bead" monomers associate into chain-like clusters under equilibrium conditions. In particular, the thermodynamic description of the self-assembly of linear telechelic chains in small molecule solvents (initiated in Paper II) is systematically extended through calculations of the order parameter Φ and average degree <N> of self-assembly, the self-assembly transition temperature T(p), and the specific heat C(V) of solutions of telechelic molecules. Special focus is placed on examining how molecular and thermodynamic parameters, such as the solution composition φ, temperature T, microscopic interaction energies (ε(s) and ε), and length M of individual telechelic chains, influence the computed thermodynamic quantities that are commonly used to characterize self-assembling systems.

Role of stringlike, supramolecular assemblies in reentrant supernematic liquid crystals

Using a combination of isothermal-isobaric Monte Carlo and microcanonical molecular dynamics we investigate the relation between structure and self-diffusion in various phases of a model liquid crystal using the Gay-Berne-Kihara potential. These molecules are confined to a mesoscopic slit pore with atomically smooth substrate surfaces. As reported recently [seeM. G. Mazza et al., Phys. Rev. Lett. 105, 227802 (2010)], a reentrant nematic (RN) phase may form at sufficiently high pressures and densities. This phase is characterized by a high degree of nematic order and a substantially enhanced self-diffusivity in the direction of the director n that exceeds that of the lower-density nematic and an intermittent smectic-A phase by about an order of magnitude. Here we demonstrate that the unique transport behavior in the RN phase may be linked to a confinement-induced packing effect that causes the formation of supramolecular, stringlike conformations. The strings consist of several molecules traveling in the direction of n as individual "trains" consisting of chains of molecular "cars."

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter S≃1. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity, which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.