Phase diagrams and kinetics of phase transitions in protein solutions

The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.     

Thermodynamic formalism of phase transitions in solid solutions

A thermodynamic theory of ferroelectric and ferroelectric-semiconductor solid solutions is presented with account of the effect of hydrostatic pressure in the cases of sharp as well as diffuse transitions. A number of analytical relations are obtained which allow to estimate the effect of admixture concentration and hydrostatic pressure on dielectric permeability, transition temperature, Curie-Weiss constant, heat capacity, thermal expansion coefficient and other properties of crystals with a ferroelectric subsystem. The theoretical results are compared with the experimental data.     

Structural phase transitions in barium-titanate-type ferroelectrics

Barium-titanate-type ferroactive crystals are analysed thermodynamically using dimensionless variables. The paper considers the conditions of phase stability, the equation determining polarization, the interval of the possible existence of a phase (or interval of several phases of simultaneous coexistence), constraints on numerical values of thermodynamic potential coefficients. The results obtained have good qualitative agreement with experiment.     

Microevaporators for kinetic exploration of phase diagrams

We use pervaporation-based microfluidic devices to concentrate species in aqueous solutions with spatial and temporal control of the process. Using experiments and modeling, we quantitatively describe the advection-diffusion behavior of the concentration field of various solutions (electrolytes, colloids, etc.) and demonstrate the potential of these devices as universal tools for the kinetic exploration of the phases and textures that form upon concentration.     

Calculation of the susceptibility of an eight-site order-disorder model for ferroelectrics

The contribution of the diffusion of the titanium ion to the dielectric tensor, is estimated for all phases of BaTiO₃ in thermodynamical model; the values obtained for the tetragonal phase are in good agreement with the difference between the phonon contribution and the capacitance measurements, for both directions parallel and perpendicular to the ferroelectric axis.     

Pressure-induced ferroelectric-antiferroelectric phase transitions in lead zirconate-tatanate-based solid solutions

The ferroelectric-antiferroelectric phase transitions induced by hydrostatic pressure in solid solutions based on lead zirconate-titanate (PZT) with introducing 20 at % tin into B sites and composites based on these ceramics have been studied. In the composites with the same composition of solid solution, the transition pressure can be varied within wide ranges depending on the type of binders. The latter is due to the vitrification of the binder and, consequently, the formation of a rigid framework preventing the transmission of pressure to the ceramic matrix.     

Pore formation phase diagrams for lipid membranes

Critical lateral pressure for a pore formation and phase diagram of porous membrane are derived analytically as functions of the microscopic parameters of the lipid chains. The derivation exploits path-integral calculation of the free energy of the ensembles of semi-flexible strings and rigid rods that mimic the hydrophobic tails of lipids in the lipid bilayers and bolalipid membranes respectively. Analytical expressions for the area stretch/compressibility moduli of the membranes are derived in both models.     

Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

Structure and phase transitions of lead zirconate hafnate solid solutions

Solid solutions of two antiferroelectrics, namely, lead zirconate and lead hafnate, i.e., PbZr_{1 − x} Hf _x O₃ (x = 0, 0.3, 0.5, 0.7, 1.0), have been prepared by solid-phase synthesis from simple oxides. The elemental composition of the samples and their structure have been studied using X-ray fluorescence and X-ray diffraction analyses. The phase transformations of the solid solutions have been determined in the temperature range 20°C < T < 300°C.     

Crystalline ferroelectrics with a glassy polarization phase

It is found that, far above the ferroelectric transition temperature, T_c, certain ferroelectric systems show a temperature dependent index of refraction, n(T), that is qualitatively different from ordinary ferroelectrics. We review measurements in these systems and show how some aspects of this n(T) data can be quantitatively understood. This is done by considering the polarization in these materials to arise from very small localized clusters of a few unit cells far above T_c. The strongly broken long range symmetry allows these effects to occur. Furthermore, we find a one-to-one correspondence between ferroelectrics that show this unusual high temperature behavior and those that show glass-like excitations at very low temperatures; this clarifies the ambiguities in the low temperature heat capacity and thermal conductivity results.     

Thermodynamics of diffused phase transitions in dirty ferroelectrics

A thermodynamic approach of ferroelectric transition in which the polarization P goes to zero asymptotically when the temperature T increases is presented. The second derivatives of the free energy: $\text{dP}\text{dT}$, the susceptibility, and the specific heat exhibit maxima, but at different temperatures.     

Evolution of phase transitions in SrTiO3-BiFeO3 solid solutions

The dielectric and acoustic properties of (1 ? x)SrTiO₃?xBiFeO₃ solid solutions (0 ≤ x ≤ 1) have been studied in the temperature range from 4.2 to 850 K. Evolution of the antiferrodistortive transition and its suppression in the concentration range 0.1 < x < 0.2 have been revealed. X-ray diffraction data obtained at room temperature, as well as the observed acoustic anomalies combined with dielectric measurements, have been used to estimate the concentration range of the existence of the relaxor state, as well as of the formation and coexistence of the antiferromagnetic and ferroelectric phases at high BiFeO₃ concentrations.