Homogeneous nucleation of a non-critical phase near a continuous phase transition

Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is nucleating. Mean-field calculations show that as the continuous transition is approached, the size of the nucleus varies as the response function of the order parameter of the continuous transition. This response function diverges at the continuous transition, as does the temperature derivative of the free energy barrier to nucleation. This rapid drop of the barrier as the continuous transition is approached means that the continuous transition acts to reduce the barrier to nucleation at the first-order transition. This may be useful in the crystallisation of globular proteins.Comment: 6 pages, 1 figur

Sonocrystallisation of ZIF-8 in water with high excess of ligand: Effects of frequency, power and sonication time

A systematic study on the sonocrystallisation of ZIF-8 (zeolitic imidazolate framework-8) in a water-based system was investigated under different mixing speeds, ultrasound frequencies, calorimetric powers and sonication time. Regardless of the synthesis technique, pure crystals of ZIF-8 with high BET (Brunauer, Emmett and Teller) specific surface area (SSA) can be obtained in water after only 5 s. Furthermore, 5 s sonication produced even smaller crystals (~0.08 µm). The type of technique applied for producing the ZIF-8 crystals did not have any significant impact on crystallinity, purity and yield. Crystal morphology and size were affected by the use of ultrasound and mixing, obtaining nanoparticles with a more spherical shape than in silent condition (no ultrasound and mixing). However, no specific trends were observed with varying frequency, calorimetric power and mixing speed. Ultrasound and mixing may have an effect on the nucleation step, causing the fast production of nucleation centres. Furthermore, the BET SSA increased with increasing mixing speed. With ultrasound, the BET SSA is between the values obtained under silent condition and with mixing. A competition between micromixing and shockwaves has been proposed when sonication is used for ZIF-8 production. The former increases the BET SSA, while the latter could be responsible for porosity damage, causing a decrease of the surface area. © 2021 The Author(s

Long Cycles in a Perturbed Mean Field Model of a Boson Gas

In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density $\rho=\rho_{{\rm short}}+\rho_{{\rm long}}$ into the number density of particles belonging to cycles of finite length ($\rho_{{\rm short}}$) and to infinitely long cycles ($\rho_{{\rm long}}$) in the thermodynamic limit. For this model we prove that when there is Bose condensation, $\rho_{{\rm long}}$ is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of $\rho_{{\rm long}}\neq 0$ with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas.Comment: 10 page

Interactions between proteins bound to biomembranes

We study a physical model for the interaction between general inclusions bound to fluid membranes that possess finite tension, as well as the usual bending rigidity. We are motivated by an interest in proteins bound to cell membranes that apply forces to these membranes, due to either entropic or direct chemical interactions. We find an exact analytic solution for the repulsive interaction between two similar circularly symmetric inclusions. This repulsion extends over length scales of order tens of nanometers, and contrasts with the membrane-mediated contact attraction for similar inclusions on tensionless membranes. For non circularly symmetric inclusions we study the small, algebraically long-ranged, attractive contribution to the force that arises. We discuss the relevance of our results to biological phenomena, such as the budding of caveolae from cell membranes and the striations that are observed on their coats.Comment: 22 pages, 2 figure

Density functional theory and demixing of binary hard rod-polymer mixtures

A density functional theory for a mixture of hard rods and polymers modeled as chains built of hard tangent spheres is proposed by combining the functional due to Yu and Wu for the polymer mixtures [J. Chem. Phys. {\bf 117}, 2368 (2002)] with the Schmidt's functional [Phys. Rev. E {\bf 63}, 50201 (2001)] for rod-sphere mixtures. As a simple application of the functional, the demixing transition into polymer-rich and rod-rich phases is examined. When the chain length increases, the phase boundary broadens and the critical packing fraction decreases. The shift of the critical point of a demixing transition is most noticeable for short chains.Comment: 4 pages,2 figures, in press, PR

Clustering transitions in vibro-fluidized magnetized granular materials

We study the effects of long range interactions on the phases observed in cohesive granular materials. At high vibration amplitudes, a gas of magnetized particles is observed with velocity distributions similar to non-magnetized particles. Below a transition temperature compact clusters are observed to form and coexist with single particles. The cluster growth rate is consistent with a classical nucleation process. However, the temperature of the particles in the clusters is significantly lower than the surrounding gas, indicating a breakdown of equipartition. If the system is quenched to low temperatures, a meta-stable network of connected chains self-assemble due to the anisotropic nature of magnetic interactions between particles.Comment: 4 pages, 5 figure

Criticality in confined ionic fluids

A theory of a confined two dimensional electrolyte is presented. The positive and negative ions, interacting by a $1/r$ potential, are constrained to move on an interface separating two solvents with dielectric constants $\epsilon_1$ and $\epsilon_2$. It is shown that the Debye-H\"uckel type of theory predicts that the this 2d Coulomb fluid should undergo a phase separation into a coexisting liquid (high density) and gas (low density) phases. We argue, however, that the formation of polymer-like chains of alternating positive and negative ions can prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Simulation study of Non-ergodicity Transitions: Gelation in Colloidal Systems with Short Range Attractions

Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the results for other systems (hard spheres and Lennard Jones). The self-intermediate scattering function and the mean squared displacement were used as the main dynamical quantities. Two different colloid packing fractions have been studied. For the lower packing fraction, $\alpha$-scaling holds and the wave-vector analysis of the correlation function shows that gelation is a regular non-ergodicity transition within MCT. The leading mechanism for this novel non-ergodicity transition is identified as bond formation caused by the short range attraction. The time scale and diffusion coefficient also show qualitatively the expected behaviour, although different exponents are found for the power-law divergences of these two quantities. The non-Gaussian parameter was also studied and very large correction to Gaussian behaviour found. The system with higher colloid packing fraction shows indications of a nearby high-order singularity, causing $\alpha$-scaling to fail, but the general expectations for non-ergodicity transitions still hold.Comment: 13 pages, 15 figure

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure