Crystallization of soft matter under confinement at interfaces and in wedges

Topographic Control of Order in Quasi-2D Granular Phase Transitions

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

Self-assembly of binary solutions to complex structures

Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionalities rise from their internal structure and molecular arrangement. The key microscopic features that control such assemblies remain poorly understood, nevertheless. Using classical density functional theory, we demonstrate how the intrinsic length scales and their interplay in terms of interspecies molecular interactions can be used to tune soft matter self-assembly. We apply our strategy to two different soft binary mixtures to create guidelines for tuning intermolecular interactions that lead to transitions from a fully miscible, liquid-like uniform state to formation of simple and core-shell aggregates and mixed aggregate structures. Furthermore, we demonstrate how the interspecies interactions and system composition can be used to control concentration gradients of component species within these assemblies. The insight generated by this work contributes toward understanding and controlling soft multi-component self-assembly systems. Additionally, our results aid in understanding complex biological assemblies and their function and provide tools to engineer molecular interactions in order to control polymeric and protein-based materials, pharmaceutical formulations, and nanoparticle assemblies.

Surface-Induced Crystallization of Sodium Dodecyl Sulfate (SDS) Micellar Solutions in Confinement

We investigate the role of confinement on the onset of crystallization in subcooled micellar solutions of sodium dodecyl sulfate (SDS), examining the impact of sample volume, substrate surface energy, and surface roughness. Using small angle neutron scattering (SANS) and dynamic light scattering (DLS), we measure the crystallization temperature upon cooling and the metastable zone width (MSZW) for bulk 10-30 wt% SDS solutions. We then introduce a microdroplet approach to quantify the impact of surface free energy (18-65 mN/m) and substrate roughness (R_α ≃ 0-60 μm) on the kinetics of surface-induced crystallization through measurements of induction time (t_i) under isothermal conditions. While t_i is found to decrease exponentially with decreasing temperature (increasing subcooling) for all tested surfaces, increasing the surface energy could cause a significant further reduction of up to ∼40 fold. For substrates with the lowest surface energy and longest t_i, microscale surface roughness is found to enhance crystal nucleation, in particular for R_α ≥ 10 μm. Finally, we demonstrate that tuning the surface energy and microscopic roughness can be effective routes to promote or delay nucleation in bulk-like volumes, thus greatly impacting the stability of surfactant solutions at lower temperatures.

Mesoscopic theory for systems with competing interactions near a confining wall

Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler-Lagrange equations and the boundary conditions (BCs) for the local volume fraction and the correlation function are derived from the density functional theory expression for the grand thermodynamic potential. Various levels of approximation can be considered for the obtained equations. The lowest-order nontrivial approximation [generic model (GM)] resembles the Landau-Brazovskii-type theory for a semi-infinite system. Unlike in the original phenomenological theory, however, all coefficients in our equations and BCs are expressed in terms of the interaction potential and the thermodynamic state. Analytical solutions of the linearized equations in the GM are presented and discussed on a general level and for a particular example of the double-Yukawa potential. We show exponentially damped oscillations of the volume fraction and the correlation function in the direction perpendicular to the confining surface. The correlations show oscillatory decay in directions parallel to this surface too, with the decay length increasing significantly when the system boundary is approached. The framework of our theory allows for a systematic improvement of the accuracy of the results.

Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each. One approximation that is made in standard derivations is to neglect a term of form ∇·[n∇Ln], where n is the scaled density profile and L is a linear operator. We show that this term makes a significant contribution to the stability of the crystal, and that dropping this term from the theory forces another approximation, that of replacing the logarithmic term from the ideal gas contribution to the free energy with its truncated Taylor expansion, to yield a polynomial in n. However, the consequences of doing this are (i) the presence of an additional spinodal in the phase diagram, so the liquid is predicted first to freeze and then to melt again as the density is increased; and (ii) other periodic structures, such as stripes, are erroneously predicted to be thermodynamic equilibrium structures. In general, L consists of a nonlocal convolution involving the pair direct correlation function. A second approximation sometimes made in deriving PFC theory is to replace L with a gradient expansion involving derivatives. We show that this leads to the possibility of the density going to zero, with its logarithm going to -∞ while being balanced by the fourth derivative of the density going to +∞. This subtle singularity leads to solutions failing to exist above a certain value of the average density. We illustrate all of these conclusions with results for a particularly simple model two-dimensional fluid, the generalized exponential model of index 4 (GEM-4), chosen because a DDFT is known to be accurate for this model. The consequences of the subsequent PFC approximations can then be examined. These include the phase diagram being both qualitatively incorrect, in that it has a stripe phase, and quantitatively incorrect (by orders of magnitude) regarding the properties of the crystal phase. Thus, although PFC models are very successful as phenomenological models of crystallization, we find it impossible to derive the PFC as a theory for the (scaled) density distribution when starting from an accurate DDFT, without introducing spurious artifacts. However, we find that making a simple one-mode approximation for the logarithm of the density distribution lnρ(x) rather than for ρ(x) is surprisingly accurate. This approach gives a tantalizing hint that accurate PFC-type theories may instead be derived as theories for the field lnρ(x), rather than for the density profile itself.

Phenomenological Theory of First-Order Prefreezing

Prefreezing is the prewetting of the crystalline phase at the interface of a melt to a solid substrate via a first-order phase transition. We present a phenomenological theory of prefreezing and analyze thermodynamic properties of the prefrozen crystalline layer. The theory enables a clear thermodynamic explanation of the abrupt formation of a mesoscopically thick crystalline layer during cooling and defines the corresponding transition temperature as a function of the interfacial free energies. It is shown that the interfacial energy difference γ_sm - ( γ_sc + γ_cm) acts as a driving force for prefreezing. The analytical results are congruent with recent experimental outcomes for poly(ε-caprolactone) crystallized on graphite via prefreezing. The calculated interfacial free energies take reasonable values being close to the experimental estimates.

Density functional approach to the description of the structure of dimer nanoparticles at liquid–liquid interfaces

A density functional approach to the description of the structure of dimer nanoparticles at liquid–liquid interfaces.

Classical density functional theory, unconstrained crystallization, and polymorphic behavior

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into "atoms" but in an amorphous structure having many of the structural characteristics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the fcc structure typical of bulk Lennard-Jones solids. The fcc crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decrease until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.

Flow induced crystallisation of penetrable particles

For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallisation and spatially varying shear flow. For thermodynamic state points within the liquid part of the phase diagram, but close to the crystallisation phase boundary, we observe that imposing a Poiseuille flow can induce nonequilibrium crystalline ordering in regions of low shear gradient. The physical mechanism responsible for this phenomenon is shear-induced particle migration, which causes particles to drift preferentially towards the center of the flow channel, thus increasing the local density in the channel center. The method employed is classical dynamical density functional theory.

Dynamical density functional theory analysis of the laning instability in sheared soft matter

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by nonaffine particle motion arising from interparticle interactions. Starting from a DDFT which incorporates the nonaffine motion, we perform a linear stability analysis that enables identification of the regions of parameter space where lanes form. We illustrate our general approach by applying it to a simple one-component fluid of soft penetrable particles.

Structural Changes in Acetophenone Fluid Films as a Function of Nanoscale Thickness

We report experimental observations of a developing fluid/solid interface by examining acetophenone films of varying thicknesses, supported on solid silver substrates. A dynamic wetting technique provides experimental control of fluid film thickness, as a function of rotational velocity. Ellipsometry and infrared reflection absorption spectroscopy data are analyzed to provide absolute film thickness and details of the changing chemical environment for varying film thickness. These data are compared to theoretical models that predict fluid film thicknesses, based on physical-chemical properties of the acetophenone/silver pair. As the velocity of the substrate is varied from 0.003 cm s^-1 to 1.872 cm s^-1, the fluid film's thickness changes from a ca. 200 nm to 2 μm. This increase in film thickness with increasing velocity follows a Landau trend, which is linear with respect to velocity^2/3. Our data also show clear evidence of molecular orientation changes, as a function of film thickness, which occur as the thinner films are increasingly comprised of acetophenone molecules within a confined, interfacial environment. The spectral changes for the thinnest fluid films (<100 nm) are shown to exhibit features similar to transmission Fourier transform infrared (FTIR) data of frozen acetophenone, suggesting that these films are highly ordered, as a result of their nanometer-scale confinement.