Statistical description of the sol-gel transition in systems with thermoreversible chemical bonds

A general statistical model is proposed for describing network-forming systems. The model is based on the representation of the partition function for all possible configurations of a thermoreversible network in the form of a functional integral over a scalar field. According to this model, two types of first-order phase transitions can occur in the systems under consideration: macroscopic phase separation with the structural phase transition due to the change in the configuration of the spatial network and the sol-gel transition due to the formation of a thermoreversible percolation cluster consisting of bound structural units. A detailed analysis is performed of the thermodynamic and structural properties of a solution of monomers that have f functional groups and can form thermoreversible chemical bonds. The influence of specific features of the chemical and volume interactions on the phase diagram of the system is investigated. The mutual position of the sol-gel transition line and the phase diagram is determined for different model parameters. It is revealed that two substantially different regimes of the behavior of the sol-gel transition line in the “temperature-volume fraction of structural units” plane are observed with a change in the rigidity of chemical bonds.     

Separation and gelation in associated systems with thermoreversible chemical bonds

Possible types of separation curves for a binary solution of chemically interacting molecules in a neutral solvent have been analyzed within the statistical model. It has been shown that the variation of the model parameters characterizing the energy and entropy of chemical bonds makes it possible to describe most of the possible types of solubility curves within the unified formalism. It has been demonstrated that the sol-gel transition for the case where the reactivity of molecules depends on the number of bonds can occur as a first-order phase transition; in the opposite case, gelation is a purely geometrical percolation transition.     

Mesodroplet Heterogeneity of Low-Concentration Aqueous Solutions of Polar Organic Compounds

It is found experimentally that a mesoscopic droplet phase is formed in low-concentration aqueous solutions of various polar organic compounds, which are considered in the chemical literature as infinitely soluble in water. The content of dissolved organic molecules in droplets is much higher than in the ambient solution. The droplet size increases with temperature. Theory can explain the mesodroplet formation by the phase separation of a binary mixture affected by the dichotomous noise of twinkling hydrogen bonds between molecules of organic compound and water. The Snyder polarity index, which is used by chemists as a miscibility criterion for molecular compounds, depends in the model on the dipole moments of mixed molecules and the energy and number of hydrogen bonds. With this refinement, it can be used as an estimation criterion for the existence and intensity (i.e., the number of droplets per unit volume of organic aqueous solution) of mesodroplet separation.

     

Janus Particles: Metallic Janus and Patchy Particles (Part. Part. Syst. Charact. 1/2013)

The concepts of Janus and patchy particles are relatively new in nanoscience. Much effort has been made during recent years to devise and fabricate asymmetric particles with multiple compositions and functionalities due to their interesting properties and potential applications in a variety of fields such as catalysis, optical imaging, or drug delivery. Here, recent advances in the field of Janus particles are highlighted, focusing on nanoparticles comprising (at least) one metallic component, which is responsible for the most interesting properties of the particles. First, the main synthetic approaches are summarized, i.e., phase separation, masking, and self‐assembly techniques, and then the special properties, applications, and future prospects of metallic Janus particles are described.     

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice ? ^d . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate λ>0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density ζ and the sleeping rate λ. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small λ) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (β=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density.     

Motility-induced phase separation and coarsening in active matter

Active systems, or active matter, are self-driven systems that live, or function, far from equilibrium – a paradigmatic example that we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The non-equilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one, which has recently been the subject of intense interest among biological and soft matter physicists, is that of the so-called “motility-induced phase separation”, whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions – we will briefly discuss at the end their role, which is not currently fully understood in this context.     

Tricritical Directed Percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations. PACS numbers: 05.70.Ln, 05.50.+q, 05.65.+b     

Charting the invisible in phase space (Abstract only)

One challenge in particle physics is that not all the momenta relevant to many processes are observable. Some particles are nearly invisible (neutrinos and hypothetical neutralinos), others escape undetected down the beam pipes of colliders. One faces the task of extracting the maximum information (e.g. on the mass of the unobserved particles) from a set of more unknowns than constraining energy?Cmomentum conservation equations. We study the simplest realistic case of current interest: single-W production at a hadron collider, followed by its leptonic decay. We derive and discuss the statistically-optimal ??singularity variable?? relevant to the measurement of the W mass. In spite of its simplicity, this process is fairly non-trivial and constitutes a good ??training?? example for the scrutiny of phenomena involving invisible objects. Our graphical analysis of the phase space is akin to that of a Dalitz plot, extended to such processes.     

Doubly Periodic Propagating Wave Patterns of （2＋1）-Dimensional Maccari System

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.     

Phase transition properties of polyethylene glycol-cellulose blends and their miscibility in mixed solvents

The phase transition properties of blends of polyethylene glycol (PEG) with cellulose (CELL) prepared from solution in N,N-dimethylacetamide/lithium chloride (DMAC/LiCI) and those from solution in dimethylsulfoxide/paraform- aldehyde (DMSO/PF) were found to be completely different. The differences of the phase transition properties were probably related to the different miscibilities of these two polymers in the two solvent systems. In DMAC/LiCl, the miscibility of CELL and PEG was limited; the composite obtained exhibited a solid- liquid phase transition and had a small phase transition enthalpy. However, in DMSO/PF, these two polymers had a high level of miscibility; the composite obtained exhibited a solid-solid phase transition and had a large phase enthalpy. It is suggested that the differences of miscibility and the phase transition properties were caused by the different dissolving mechanisms of CELL and the different interactions in these two solutions.     

Macroscopic alignment of nanoparticle arrays in soft crystals of cubic and cylindrical polymer micelles

We describe a method to organize nanometer-sized hydrophilic particles into ordered arrays by templating them in the soft, micelle-crystal phases (spherical and cylindrical) of a thermoreversible block copolymer. Small-angle neutron scattering (SANS) with contrast variation is used to show that the dispersed particles (in this case, proteins or silica) form structured arrays by being constrained in the interstitial cavities between the polymer micelles in the ordered micelle crystal. Simple shear is used to macroscopically align both phases of the nanocomposites (micelles and particles) into macro-domains. The temperature-induced order-order transition between templates of spherical and cylindrical micelles is demonstrated as a reversible technique to modify the structure of the templated nanoparticle arrays.     

A Study on Properties of Poly(vinyl chloride)/Poly(α-methylstyrene-acrylonitrile) Binary Blends

Blends of poly(vinyl chloride) (PVC) and poly(α-methylstyrene-acrylonitrile) (α-MSAN) with variable composition of 0 to 100 wt% were prepared by melt mixing. Properties of binary blends were extensively studied by differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR), heat distortion temperature (HDT), mechanical properties, melt flow rate (MFR), and scanning electron microscope (SEM). A single glass transition temperature (T_g ) was observed by DSC and DMTA, indicating miscibility between PVC and α-MSAN. The results of ATR-FTIR indicated that specific strong interactions were not present in the blends and the miscibility was due to interaction between –CN and PVC. With increasing amount of α-MSAN, considerable increase occurred in HDT, flexural strength, and flexural modulus compared with reverse s-shaped decrease in impact strength and elongation at break. Synergism was observed in tensile strength and MFR. No phase separation was observed in SEM photographs, indicating miscibility between PVC and α-MSAN. In addition, morphology of the impact-fractured surfaces, including roughness and non-fused particles, correlated well with the mechanical properties and MFR.     

Thermal stability of high concentration Fe-Ag and Fe-Cu alloys produced by vapor quenching

Mössbauer effect measurements were carried out for sputtered fcc Fe-Ag and Fe-Cu alloys annealed at various temperatures. At temperatures higher than 300 °C, the metastable fcc phases decompose by removing saturated Fe atoms. During the phase separation processes, the ejected Fe atoms form clusters, which initially have a fcc structure and transform to bcc particles as their sizes grow beyond a critical value.     

Maccari系统的椭圆函数传播波

基于多线性分离变量法所得(2＋1)维Maccari非线性系统的精确解，在分离变量函数中引入雅克比椭圆函数，获得两类双周期传播波模式. 椭圆函数波在不同模量取值下，具有不同的性状特点，特别是在模量极限情形下，可以约化为dromion和peakon激发形态.利用图示法对椭圆函数波的相互作用进行了探讨，发现其相互作用是非弹性的. 关键词： Maccari系统 多线性分离变量法 雅克比椭圆函数 周期波     

Preparation and Characterization of New Biodegradable Films Made from Poly(L-Lactic Acid) and Chitosan Blends Using a Common Solvent

Poly-(L-lactic acid) (PLLA) has been widely used for various biomedical applications due to its interesting properties such as its mechanical behavior, processability, biocompatibility, and biodegradability. Blending this polymer with chitosan that, besides being biodegradable and hydrophilic, can interact with anionic glycosaminoglycans, proteoglycans, and other negatively charged molecules of the extracellular matrix, could constitute an excellent way to improve the biological performance of PLLA in these kinds of applications. Such blends could also be used in environmental applications. In this work a new and simple method of preparing biodegradable blends of chitosan and PLLA at room temperature was developed. To the best of our knowledge, this is the first time that a common solvent for the two polymers has been used, hexafluor-2-propanol (HFIP), to produce a homogeneous solution containing both PLLA and chitosan. We also anticipate that this solvent can also be used to compatibilize other combinations of natural and synthetic polymers. Membranes were then obtained by solvent casting. Films with different fractions of each component were successfully prepared and didn't show visible phase separation. The prepared films were characterized by differential scanning calorimetry (DSC) in order to analyze the miscibility of the two components as a function of the composition of the film.     

Doubly Periodic Propagating Wave for （2d-1）-Dimensional Breaking Soliton Equation

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.     

Statistical description of glass-forming alloys with chemical interaction: Application to Al-R systems

The statistical model for describing network-forming systems, developed in our previous works, is applied to study of metallic alloys with chemical bonding. The model is based on the representation of the sum of statistical weights over all possible configurations for a thermoreversible network in the form of a functional integral over a scalar field. The mean-field solution of the model is derived, and for particular case of a binary alloy having single element of chemical short-range order A₂B-type, thermodynamic and structural properties have been analyzed. This analysis allows to plot the temperature-concentration phase diagram of the model representing two immiscibility gap meeting in the distectic point. It is shown that at some temperatures and concentrations, geometry percolation of the network of chemical bonds and thus a sol-gel transition may take place. The critical percolation line was plotted in common with phase diagram. Then, the structural transitions, glass-forming ability and magnetic properties of Al-R alloys are discussed in the frames of this conception. It is proposed that the range of easy glass formation is confined on the left by the minimal concentration for the sol-gel transition and on the right by the concentration corresponding to the fractal-to-Euclidian crossover in the structure of percolation cluster. Finally, the abnormal growth of Al-REM magnetic susceptibility occurring above melting point of Al₂R compound is also explained.     

Stabilization of Solutions to a FitzHugh-Nagumo Type System

We consider a bistable reaction-diffusion system arising in the theory of phase transitions; it appears in several physical contexts such as thin magnetic films and the microphase separation in diblock copolymer melts. Mathematically it takes the form of an Allen-Cahn equation coupled to an elliptic equation. This system possesses a Lyapunov functional which represents the Gibbs free energy of the phase separation problem. We study the large time behavior of the solution orbits, and use the fact that the problem has a gradient structure to prove their stabilization by means of a version of ?ojasiewicz inequality.     

Tunable miscibility in a dual-species Bose-Einstein condensate

We report on the observation of controllable phase separation in a dual-species Bose-Einstein condensate with 85Rb and 87Rb. Interatomic interactions between the different components determine the miscibility of the two quantum fluids. In our experiments, we can clearly observe immiscible behavior via a dramatic spatial separation of the two species. Furthermore, a magnetic-field Feshbach resonance is used to change them between miscible and immiscible by tuning the 85Rb scattering length. The spatial density pattern of the immiscible quantum fluids exhibits complex alternating-domain structures that are uncharacteristic of its stationary ground state.