Metastable liquid clusters in super- and undersaturated protein solutions

Dense liquid phases, metastable with respect to a solid phase, but stable with respect to the solution, have been known to form in solutions of proteins and small-molecule substances. Here, with the protein lumazine synthase as a test system, using dynamic and static light scattering and atomic force microscopy, we demonstrate submicron size clusters of dense liquid. In contrast to the macroscopic dense liquid, these clusters are metastable not only with respect to the crystals, but also with respect to the low-concentration solution: the characteristic cluster lifetime is limited to approximately 10 s, after which they decay. The cluster population is detectable only if they occupy >10(-6) of the solution volume and have a number density >105 cm-3 for 3 to 11% of the monitored time. The cluster volume fraction varies within wide limits and reaches up to 10(-3). Increasing protein concentration increases the frequency of cluster detection but does not affect the ranges of the cluster sizes, suggesting that a preferred cluster size exists. A simple Monte Carlo model with protein-like potentials reproduces the metastable clusters of dense liquid with limited lifetimes and variable sizes and suggests that the mean cluster size is determined by the kinetics of growth and decay and not by thermodynamics.     

How does a transient amorphous precursor template crystallization

Crystallization through metastable phases, such as polymorphism, plays an important role in chemical manufacture, biomineralization, and protein crystallization. However, the kinetics creating the final stable crystalline phase from metastable phases has so far remained unclear. In this study, crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), is studied quantitatively in a colloidal model system. In MSC, amorphous dense droplets are first nucleated from the mother phase. Subsequently, a few unstable subcrystalline nuclei can be created simultaneously by fluctuation from the tiny dense droplets, which is different from previous theoretical predictions. It is necessary for these crystalline nuclei to reach a critical size N*(crys) to become stable. However, in contrast to subcrystalline nuclei, a stable mature crystalline nucleus is not created by fluctuation but by coalescence of subcrystalline nuclei, which is unexpected. To accommodate a mature crystalline nucleus larger than the critical size N*(crys), the dense droplets have to first acquire a critical size N*. This implies that only a fraction of amorphous dense droplets can serve as a precursor of crystal nucleation. As an outcome, the overall nucleation rate of the crystalline phase is, to a large extent, determined by the nucleation rate of crystals in the dense droplets, which is much lower than the previous theoretical expectation. Furthermore, it is surprising to see that MSC will promote the production of defect-free crystals. The knowledge acquired in this study will also significantly advance our understandings in polymorphism related processes.     

Nucleation of ordered solid phases of proteins via a disordered high-density state: phenomenological approach

Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.     

Formation of supercooled liquid solutions from nanoscale amorphous solid films of methanol and ethanol

Molecular beam techniques are used to create layered nanoscale composite films of amorphous methanol and ethanol at 20 K. The films are then heated, and temperature programed desorption and infrared spectroscopy are used to observe the mixing, desorption, and crystallization behavior from the initially unmixed amorphous layers. We find that the initially unmixed amorphous layers completely intermix to form a deeply supercooled liquid solution after heating above T(g). Modeling of the desorption kinetics shows that the supercooled liquid films behave as ideal solutions. The desorption rates from the supercooled and crystalline phases are then used to derive the binary solid-liquid phase diagram. Deviations from ideal solution desorption behavior are observed when the metastable supercooled solution remains for longer times in regions of the phase diagram when thermodynamically favored crystallization occurs. In those cases, the finite lifetime of the metastable solutions results in the precipitation of crystalline solids. Finally, in very thick films at temperatures and compositions where a stable liquid should exist, we unexpectedly observe deviations from ideal solution behavior. Visual inspection of the sample indicates that these apparent departures from ideality arise from dewetting of the liquid film from the substrate. We conclude that compositionally tailored nanoscale amorphous films provide a useful means for preparing and examining deeply supercooled solutions in metastable regions of the phase diagram.     

Nucleation and Growth of Amino Acid and Peptide Supramolecular Polymers through Liquid–Liquid Phase Separation

The transition of peptides and proteins from the solution phase into fibrillar structures is a general phenomenon encountered in functional and aberrant biology and is increasingly exploited in soft materials science. However, the fundamental molecular events underpinning the early stages of their assembly and subsequent growth have remained challenging to elucidate. Here, we show that liquid–liquid phase separation into solute‐rich and solute‐poor phases is a fundamental step leading to the nucleation of supramolecular nanofibrils from molecular building blocks, including peptides and even amphiphilic amino acids. The solute‐rich liquid droplets act as nucleation sites, allowing the formation of thermodynamically favorable nanofibrils following Ostwald's step rule. The transition from solution to liquid droplets is entropy driven while the transition from liquid droplets to nanofibrils is mediated by enthalpic interactions and characterized by structural reorganization. These findings shed light on how the nucleation barrier toward the formation of solid phases can be lowered through a kinetic mechanism which proceeds through a metastable liquid phase.     

Crystal Growth Mechanisms and Morphological Control of the Prototypical Metal–Organic Framework MOF‐5 Revealed by Atomic Force Microscopy

Crystal growth of the metal–organic framework MOF‐5 was studied by atomic force microscopy (AFM) for the first time. Growth under low supersaturation conditions was found to occur by a two‐dimensional or spiral crystal growth mechanism. Observation of developing nuclei during the former reveals growth occurs through a process of nucleation and spreading of metastable and stable sub‐layers revealing that MOFs may be considered as dense phase structures in terms of crystal growth, even though they contain sub‐layers consisting of ordered framework and disordered non‐framework components. These results also support the notion this may be a general mechanism of surface crystal growth at low supersaturation applicable to crystalline nanoporous materials. The crystal growth mechanism at the atomistic level was also seen to vary as a function of the growth solution Zn/H₂bdc ratio producing square terraces with steps parallel to the <100> direction or rhombus‐shaped terraces with steps parallel to the <110> direction when the Zn/H₂bdc ratio was >1 or about 1, respectively. The change in relative growth rates can be explained in terms of changes in the solution species concentrations and their influence on growth at different terrace growth sites. These results were successfully applied to the growth of as‐synthesized cube‐shaped crystals to increase expression of the {111} faces and to grow octahedral crystals of suitable quality to image using AFM. This modulator‐free route to control the crystal morphology of MOF‐5 crystals should be applicable to a wide variety of MOFs to achieve the desired morphological control for performance enhancement in applications.     

Crystal Memory near Discontinuous Triacylglycerol Phase Transitions: Models,Metastable Regimes,and Critical Points

It is proposed that “crystal memory”, observed in a discontinuous solid-liquid phase transition of saturated triacylglycerol (TAG) molecules, is due to the coexistence of solid TAG crystalline phases and a liquid TAG phase, in a superheated metastable regime. Such a coexistence has been detected. Solid crystals can act as heterogeneous nuclei onto which molecules can condense as the temperature is lowered. We outlined a mathematical model, with a single phase transition, that shows how the time-temperature observations can be explained, makes predictions, and relates them to recent experimental data. A modified Vogel-Fulcher-Tammann (VFT) equation is used to predict time-temperature relations for the observation of “crystal memory” and to show boundaries beyond which “crystal memory” is not observed. A plot of the lifetime of a metastable state versus temperature, using the modified VFT equation, agrees with recent time-temperature data. The model can be falsified through its predictions: the model possesses a critical point and we outline a procedure describing how it could be observed by changing the hydrocarbon chain length. We make predictions about how thermodynamic functions will change as the critical point is reached and as the system enters a crossover regime. The model predicts that the phenomenon of “crystal memory” will not be observed unless the system is cooled from a superheated metastable regime associated with a discontinuous phase transition.     

Complete phase behavior of the symmetrical colloidal electrolyte

We computed the complete phase diagram of the symmetrical colloidal electrolyte by means of Monte Carlo simulations. Thermodynamic integration, together with the Einstein-crystal method, and Gibbs-Duhem integration were used to calculate the equilibrium phase behavior. The system was modeled via the linear screening theory, where the electrostatic interactions are screened by the presence of salt in the medium, characterized by the inverse Debye length, kappa (in this work kappasigma=6). Our results show that at high temperature, the hard-sphere picture is recovered, i.e., the liquid crystallizes into a fcc crystal that does not exhibit charge ordering. In the low temperature region, the liquid freezes into a CsCl structure because charge correlations enhance the pairing between oppositely charged colloids, making the liquid-gas transition metastable with respect to crystallization. Upon increasing density, the CsCl solid transforms into a CuAu-like crystal and this one, in turn, transforms into a tetragonal ordered crystal near close packing. Finally, we have studied the ordered-disordered transitions finding three triple points where the phases in coexistence are liquid-CsCl-disordered fcc, CsCl-CuAu-disordered fcc, and CuAu-tetragonal-disordered fcc.     

Ab initio computation of the low-temperature phase diagrams of the alkali metal iodide-bromides: MBr(x)I1-x (0 </= x </= 1), Where M = Li, Na, K, Rb, or Cs

We have studied the low-temperature phase diagrams of the systems MBr-MI (M = Li, Na, K, Rb, or Cs) via global exploration of the enthalpy landscapes for many different compositions, leading to candidates for solid solution-like and ordered crystalline phases. For all of these candidates the free enthalpies are computed at the ab initio level, and the low-temperature phase diagrams of the five chemical systems are derived. We find not only the expected stable solid solution in the rocksalt structure type but also metastable solid solutions based on the CsCl type for the RbBr-RbI and CsCl-CsI systems. Furthermore, additional metastable structure candidates exhibiting ordered crystalline structures exist for several compositions. In the case of the LiBr-LiI system, the metastable solid solution based on the wurtzite type was generated, and the location of the miscibility gap was predicted.     

Liquid Crystal Emulsions

We review recent findings about the behavior of emulsions made of droplets suspended in liquid crystalline materials. By contrast to classical emulsions, which are usually made of isotropic oils and water, liquid crystal emulsions exhibit a variety of structures result in the ordering of the continuous phase. The droplets induce the formation of topological defects and distortions that lead to strong and anisotropic elastic forces between the particles. These elastic forces govern the stability and the ordering of the particles. This is observed in aqueous emulsions as well as in non-aqueous emulsions obtained from phase separation phenomena. It is shown that phase separations in liquid crystals can lead to the formation of highly ordered arrays of uniformly sized droplets. More generally, ordered structures seen in liquid crystal emulsions are of interest as examples of topologicallv-controlled organizations; they are also of potential practical importance as a novel way to control both the stability and the structures of colloidal particles.     

Molecular dynamics studies of the kinetics of phase changes in clusters III: structures, properties, and crystal nucleation of iron nanoparticle Fe331

Molecular dynamics (MD) computer simulations have been carried out to study the structures, properties, and crystal nucleation of iron nanoparticles with 331 Fe atoms or with diameter around 2 nm. Structure information for the nanoparticles was analyzed from the MD simulations. Three crystalline phases and one amorphous phase were obtained by cooling the nanoparticles from their molten droplets at different cooling rates or with different lengths of cooling time periods. Molten droplets froze into three different solid phases and a solid-solid transition from a disordered body-centered cubic (BCC) phase to an ordered BCC phase were observed during the slow cooling and the quenching processes. Properties of nanoparticle Fe₃₃₁, such as melting point, freezing temperature, heat capacity, heat of fusion, heat of crystallization, molar volume, thermal expansion coefficient, and diffusion coefficient, have been estimated. Nucleation rates of crystallization to two solid phases for Fe₃₃₁ at temperatures of 750, 800, and 850 K are presented. Both classical nucleation theory and diffuse interface theory are used to interpret our observed nucleation results. The interfacial free energy and the diffuse interface thickness between the liquid phase and two different solid phases are estimated from these nucleation theories.     

Spinodal for the solution-to-crystal phase transformation

The formation of crystalline nuclei from solution has been shown for many systems to occur in two steps: the formation of quasidroplets of a disordered intermediate, followed by the nucleation of ordered crystalline embryos within these droplets. The rate of each step depends on a respective free-energy barrier and on the growth rate of its near-critical clusters. We address experimentally the relative significance of the free-energy barriers and the kinetic factors for the nucleation of crystals from solution using a model protein system. We show that crystal nucleation is 8-10 orders of magnitude slower than the nucleation of dense liquid droplets, i.e., the second step is rate determining. We show that at supersaturations of three or four k(B)T units, crystal nuclei of five, four, or three molecules transform into single-molecule nuclei, i.e., the significant nucleation barrier vanishes below the thermal energy of the molecules. We show that the main factor, which determines the rate of crystal nucleation, is the slow growth of the near-critical ordered clusters within the quasidroplets of the disordered intermediate. Analogous to the spinodal in supersaturated fluids, we define a solution-to-crystal spinodal from the transition to single-molecule crystalline nuclei. We show that heterogeneous nucleation centers accelerate nucleation not only because of the wettinglike effects that lower the nucleation barrier, as envisioned by classical theory, but by helping the kinetics of growth of the ordered crystalline embryos.     

液晶聚芳醚酮的结构与性能研究

以联苯二酚、取代对苯二酚及含氟酮单体为原料 ,通过亲核取代反应 ,合成了系列具有液晶性的新型聚芳醚酮 .研究了聚合物分子结构与性能之间的关系 .由于结晶相是从有序的液晶相转化形成的 ,故侧基含量的增加对液晶聚合物的融熔转变温度无显著影响 .聚合物的液晶稳定性受侧基影响较大 ,含极性侧基的氯取代聚合物的液晶温区比含大空阻侧基的聚合物的液晶温区小得多 ,说明空间几何因素比极性因素对液晶稳定性的影响大 .不同分子量聚合物有不同的液晶有序结构 ,低分子量聚合物具有高有序液晶结构 ,而高分子量聚合物只有低有序的向列相结构 .     

Exploring bovine pancreatic trypsin inhibitor phase transitions

This paper presents an investigation of the phase diagram of BPTI (bovine pancreatic trypsin inhibitor)/350 mM KSCN at pH 4.9 by direct observation and numerical simulations. We report optical microscopy and light and X-ray scattering experiments coupled with theoretical data analysis using numerical tools. The phase diagram is thoroughly determined, as a function of temperature. Two polymorphs are observed by video microscopy and their solubility measured. In this phase diagram, the liquid-liquid phase separation (LLPS) is metastable with respect to the solid-liquid phase separation. Above the T(L-L) boundary curve, solutions are composed of a mixture of BPTI monomers and decamers. Attractive interactions are stronger between decamers than between monomers. Below the T(L-L) boundary curve, the dense phase is highly concentrated in protein and composed of BPTI decamers alone. Thus, the driving force for liquid-liquid or liquid-solid phase separation is the attraction between decamers at low pH. The structure factors of the dense phases are characteristic of repulsive dense phases because of a hard sphere repulsion core, meaning that in the dense phase proteins are actually in contact (interparticle distance of 53 A). In agreement with the Oswald rule of stages, LLPS occurs prior to and impedes the solid nucleation.     

Equilibrium and non-equilibrium phase transitions studied by adiabatic calorimetry

An adiabatic calorimetry was used for some investigations of equilibrium and non-equilibrium phase transitions. For one of the substances studied (4,4′-di-n-heptyloxyazoxybenzene) it was possible to determine temperature dependence of an order parameter and number of clusters of high temperature phase in a region of a phase transition. For another substance (liquid 3,4 dimethylpiridine) an anomaly on the specific heat curves was interpreted as being responsible for a decay of molecules’ clusters. Non-equilibrium phase transitions were investigated for some liquid crystal substances. The process of transformation between metastable and stable phases was described quantitatively. The conclusions obtained concern the stability of metastable phases.     

Phase polymorphism of [Ni(DMSO)6](BF4)2 studied by differential scanning calorimetry

The tetrafluoroborate of hexadimethylsulfoxidenickel(II) was synthesized and studied by differential scanning calorimetry. Seven solid phases of [Ni(DMSO)₆](BF₄)₂ were revealed. Specifically, six phase transitions of the first order were detected between the following solid phases: stable KIb → stable KIa at T _C6 = 335 K, metastable KIIb → metastable KIIa at T _C5 = 368 K, metastable KIII → overcooled phase KI at T _C4 = 378 K, metastable KIIa → overcooled phase KI at T _C3 = 396 K, stable KIa → stable KI at T _C2 = 415 K and stable KI → stable K0 at T _C1 = 433 K. [Ni(DMSO)₆](BF₄)₂ begins decomposition at 440 K with loss of one DMSO molecule per formula unit forming [Ni(DMSO)₅](BF₄)₂ (phase L0) which melts next in two steps in the temperature range 550–593 K. From the entropy changes connected both with melting and with phase transitions, it can be concluded that phases KI, overcooled KI and K0 are orientationally dynamically disordered (ODIC) crystals. Stable phases KIb, KIa and metastable phase KIII are ordered solid phases. Metastable phase KIIa and metastable phase KIIb are more or less ordered solid phases.     

Stresses inside critical nuclei

The usual derivation of classical nucleation theory is inappropriate for crystal nucleation. In particular, it leads to a seriously flawed estimate of the pressure inside a critical nucleus. This has consequences for the prediction of possible metastable phases during the nucleation process. In this paper, we reanalyze the theory for crystal nucleation based on the thermodynamics of small crystals suspended in a liquid, due to Mullins (J. Chem. Phys. 1984, 81, 1436). As an illustration of the difference between the classical picture and the present approach, we consider a numerical study of crystal nucleation in binary mixtures of hard spherical colloids with a size ratio of 1:10. The stable crystal phase of this system can be either dense or expanded. We find that, in the vicinity of the solid-solid critical point where the crystallites are highly compressible, small crystal nuclei are less dense than large nuclei. This phenomenon cannot be accounted for by either classical nucleation theory or by the Gibbsian droplet model.     

Copolymerizable initiator for improved polymer dispersed liquid crystal films

The problems of photoinitiator contamination are addressed for the liquid crystal phase in polymer dispersed liquid crystal films formed by photopolymerization induced phase separation of liquid crystal from monomer solutions. Initiator contamination lowers the clearing point of the liquid crystal phase, and decreases the photostability and resistivity of the polymer dispersed liquid crystal. These problems are minimized by replacing the conventional photoinitiators with copolymerizable initiators which become incorporated in the polymer phase as it separates. Copolymerizable photoinitiators are studied and used to form polymer dispersed liquid crystals with higher clearing point liquid crystal phases, higher resistivity, and better photostability than polymer dispersed liquid crystals formed with conventional photoinitiators. These improvements provide very significant advantages for many polymer dispersed liquid crystal applications.     

Emulsion of aqueous-based nonspherical droplets in aqueous solutions by single-chain surfactants: templated assembly by nonamphiphilic lyotropic liquid crystals in water

Single-chain surfactants usually emulsify and stabilize oily substances into droplets in an aqueous solution. Here, we report a coassembly system, in which single types of anionic or non-ionic surfactants emulsify a class of water-soluble nonamphiphilic organic salts with fused aromatic rings in aqueous solutions. The nonamphiphilic organic salts are in turn promoted to form droplets of water-based liquid crystals (chromonic liquid crystals) encapsulated by single-chain surfactants. The droplets, stabilized against coalescence by encapsulated in a layer (or layers) of single chain surfactants, are of both nonspherical tactoid (elongated ellipsoid with pointy ends) and spherical shapes. The tactoids have an average long axis of ～9 μm and a short axis of ～3.5 μm with the liquid crystal aligning parallel to the droplet surface. The spherical droplets are 5-10 μm in diameter and have the liquid crystal aligning perpendicular to the droplet surface and a point defect in the center. Cationic and zwitterionic surfactants studied in this work did not promote the organic salt to form droplets. These results illustrate the complex interplay of self-association and thermodynamic incompatibility of molecules in water, which can cause new assembly behavior, including potential formation of vesicles or other assemblies, from surfactants that usually form only micelles. These unprecedented tactoidal shaped droplets also provide potential for the fabrication of new soft organic microcapsules.     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.