Table of contents

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.

Protein–DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein–DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.

A temperature gradient induces different driving forces on the components of a mixture which translates into their segregation. We show that these driving forces constitute the physical picture behind the thermodiffusion effect, and provide an alternative expression of the Soret coefficient which can be applied to both colloidal suspensions and molecular mixtures. To verify the validity of the formalism, we quantify the related forces in an Eulerian reference frame by non-equilibrium molecular simulations. Furthermore, we present an analytical argument to show that the hydrodynamic interactions need to be accounted for to obtain the proper scaling of the thermophoretic force. This result combined with the presented expression satisfactorily explains the experimentally known size dependence of the thermodiffusion coefficient in dilute polymer solutions.

The symmetry breaking Fréedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of a nematic liquid crystal in the presence of a magnetic field above the Fréedericksz threshold. We identify the bifurcation point when the localized soliton-like state is linearly unstable with respect to the perturbations of the wavevector in the direction perpendicular to the initial plane of the soliton. This instability occurs only if the ratio of the saddle-splay elastic constant to the elastic modulus of nematics in the one-constant approximation is above the critical value $\vert {K}_{2 4}/K\vert ⩾ 0.7 0 7$.

Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.

Two special dynamical transitions of universal character have recently been observed in macromolecules (lysozyme, myoglobin, bacteriorhodopsin, DNA and RNA) at T* ∼ 100–150 K and T_D ∼ 180–220 K. The underlying mechanisms governing these transitions have been the subject of debate. In the present work, a survey is reported on the temperature dependence of structural, vibrational and thermodynamical properties of a nearly anhydrous amino acid (orthorhombic polymorph of the amino acid l-cysteine at a hydration level of 3.5%). The temperature dependence of x-ray powder diffraction patterns, Raman spectra and specific heat revealed these two transitions at T* = 70 K and T_D = 230 K for this sample. The data were analyzed considering amino acid–amino acid, amino acid–water, water–water phonon–phonon interactions and molecular rotor activation. Our results indicated that the two referred temperatures define the triggering of very simple and particular events that govern all the interactions of the biomolecular: activation of CH₂ rigid rotors (T < T* ), phonon–phonon interactions between specific amino acid and water dimer vibrational modes (T* < T < T_D), and water rotational barriers surpassing (T > T_D).

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length $\ell =\sqrt{\frac{\hbar c}{B e}}$, probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/ℓ < 1 inter-Landau level mixing is strong and probability densities with energy less than the potential height are non-chiral and localized inside antidot potentials. However, in the strong magnetic field limit R/ℓ ≫ 1, where inter-Landau level mixing is small, they are delocalized outside antidot potentials, and are chiral for N = 0 Landau level (LL) states while non-chiral for N = 1. In the non-trivial crossover regime R/ℓ ∼ 1 localized and delocalized probability densities coexist. States that are delocalized outside antidots when R/ℓ > 1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/ℓ < 1.

The effect of electron–phonon scattering processes on the thermoelectric properties of extrinsic graphene was studied. Electrical and thermal resistivity, as well as the thermopower, were calculated within the Bloch theory approximations. Analytical expressions for the different transport coefficients were obtained from a variational solution of the Boltzmann equation. The phonon-limited electrical resistivity ρ_e−ph shows a linear dependence at high temperatures and follows ρ_e−ph ∼ T⁴ at low temperatures, in agreement with experiments and theory previously reported in the literature. The phonon-limited thermal resistivity at low temperatures exhibits a ∼T dependence and achieves a nearly constant value at high temperatures. The predicted Seebeck coefficient at very low temperatures is $Q(T)\sim -{\pi }^{2}{k}_{\mathrm{B}}^{2}T/(3 e{E}_{\mathrm{F}})$, which shows a n^−1/2 dependence with the density of carriers, in agreement with experimental evidence. Our results suggest that thermoelectric properties can be controlled by adjusting the Bloch–Grüneisen temperature through its dependence on the extrinsic carrier density in graphene.

The changes in crystal structure of LiFeSi₂O₆ induced by the phase transition between the high-temperature C2/c and low-temperature P2₁/c phase are studied using the density functional theory. For both monoclinic phases, the phonon dispersion curves and phonon density of states are calculated. The infrared absorption coefficients are obtained and analyzed in both structural phases of LiFeSi₂O₆. The soft mode inducing the phase transition is revealed at the Z point of the Brillouin zone of the high-symmetry C2/c phase. The pressure dependence of the soft mode is studied and the mechanism of the structural phase transition in LiFeSi₂O₆ is discussed.

The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second- to fourth-order elastic constants. The second-,third- and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P ≈ 69 GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.

The temperature and polarization dependence of the optical reflectivity  spectra of a quasi-one-dimensional 1/4-filled band system, (DMEDO-EBDT)₂PF₆, have been investigated. We observed clear anisotropy in the electronic structures corresponding to the anisotropic transport properties. The appearance of a charge gap (E_g > 0.1 eV) and transfer of the spectral weight accompanied by the metal–insulator phase transition were clearly observed. In addition, a split of the intramolecular vibrational modes was observed, which strongly suggested the existence of charge disproportionation in the low temperature phase. We also observed a photoinduced reflectivity change, which implied the occurrence of a photoinduced phase transition from the low temperature insulating phase to the high temperature metallic phase.

Structural properties and energetics of Cr-based Z-phases (CrNbN, Cr(Nb,V)N and CrVN) were investigated using the Vienna ab initio simulation package (VASP) code employing the projector augmented wave (PAW) pseudopotentials by means of both local density approximation (LDA) and generalized gradient approximation (GGA) for the exchange and correlation term. The geometry of all studied phases including NbN, VN and elemental constituents (nonmagnetic bcc Nb and V and antiferromagnetic bcc Cr) was fully relaxed, providing the equilibrium structure parameters and total energies. The calculated lattice parameters of Z-phases correspond very well to the experimental data and decrease with increasing molar fraction of vanadium. Enthalpies of formation show that all three Z-phases are stable at T = 0 K. The electronic structures of Z-phases including densities of states and charge densities were analysed. The calculated bulk moduli and elastic constants were used to evaluate stability conditions and elastic anisotropy ratios. It was confirmed that Z-phases are mechanically stable. Additional information on ductility was obtained from Cauchy pressures, Pugh ratios, Young moduli, and Poisson ratios. The ductility evaluated using the Pugh ratio decreases with number of vanadium atoms.

In this study, we present a combined density functional theory and many-body perturbation theory study on the electronic and optical properties of TiO₂ brookite as well as the tetragonal phases rutile and anatase. The electronic structure and linear optical response have been calculated from the Kohn–Sham band structure applying (semi)local as well as nonlocal screened hybrid exchange–correlation density functionals. Single-particle excitations are treated within the GW approximation for independent quasiparticles. For optical response calculations, two-particle excitations have been included by solving the Bethe–Salpeter equation for Coulomb correlated electron–hole pairs. On this methodological basis, gap data and optical spectra for the three major phases of TiO₂ are provided. The common characteristics of brookite with the rutile and anatase phases, which have been discussed more comprehensively in the literature, are highlighted. Furthermore, the comparison of the present calculations with measured optical response data of rutile indicate that discrepancies discussed in numerous earlier studies are due to the measurements rather than related to an insufficient theoretical description.

We report the theoretical prediction of single and paired electron self-trapping in Ge₂Se₃. In finite atomic cluster, density functional calculations, we show that excess single electrons in Ge₂Se₃ are strongly localized around single germanium dimers. We also find that two electrons prefer to trap around the same germanium dimer, rupturing a neighboring Ge–Se bond. Localization is less robust in periodic, density functional calculations. While paired electron self-trapping is present, as shown by wavefunction localization around a distorted Ge–Ge dimer, single-electron trapping is not. This discrepancy appears to depend only on the boundary conditions and not on the exchange–correlation potential or basis set. For single- and paired-electron trapping, we report the adiabatic barriers to motion and we estimate hopping rates and freeze-in temperatures. For the single trapped electron, we also predict the ⁷³Ge and ⁷⁷Se hyperfine coupling constants.

Density functional theory calculations (DFT) are used to investigate the strain-induced changes to the electronic structure of biaxially strained (parallel to the (001), (110) and (111) planes) and uniaxially strained (along the [001], [110] and [111] directions) germanium (Ge). It is calculated that a moderate uniaxial strain parallel to the [111] direction can efficiently transform Ge to a direct bandgap material with a bandgap energy useful for technological applications.

Phase transitions in a system of indirect excitons in semiconductor double quantum wells are studied for a set-up when one of the electrodes is of finite size and, in particular, has the shape of a disc. At voltage a region under the rim of the disc is created where excitons have lower energy, thus providing a macroscopic trap attractive for excitons while being repulsive for charged particles. The theory of the formation of patterns of the excitonic condensed phase under the disc is built based on the assumption of the existence of the inter-exciton range where the interaction between them is attractive. The finite value of the exciton lifetime is taken into account serving as a limiting factor for the size of the islands of the condensed phase. The calculations reveal complex restructuring of the patterns of the spatial distribution of exciton density with increasing pumping intensity: from the structureless gaseous phase to separate islands of the condensed phase within the gaseous phase, then to islands of the gaseous phase in the bulk of the condensed phase and finally to the continuous condensed phase.

We report on electronic collective excitations in RMn₂O₅ (R  =Pr, Sm, Gd, Tb) showing condensation starting at and below  ∼ T_N ∼ T_C ∼ 40–50 K. Their origin is understood as partial delocalized e_g electron orbitals in the Jahn–Teller distortion of the pyramid dimer with strong hybridized Mn³⁺–O bonds. Our local probes, Raman, infrared, and x-ray absorption, back the conclusion that there is no structural phase transition at T_N ∼ T_C. Ferroelectricity is magnetically assisted by electron localization triggering lattice polarizability by unscreening. We have also found phonon hardening as the rare earth is sequentially replaced. This is understood as a consequence of lanthanide contraction. It is suggested that partially f-electron screened rare earth nuclei might be introducing a perturbation to e_g electrons prone to delocalize as the superexchange interaction takes place.

Lattice dynamics calculations and temperature-dependent Raman scattering experiments were performed on RbNbWO₆ and CsTaWO₆ pyrochlore oxides. The observed bands were assigned to the respective motions of atoms in the unit cell. The spectra showed the presence of additional Raman bands not allowed for by the $F d\bar {3}m$ cubic structure. We have shown that these bands appear due to both substitutional disorder in the 16c sites and displacive disorder of the A ions. Raman studies also revealed the presence of an additional 80 cm⁻¹ band at room temperature for RbNbWO₆, not observed for CsTaWO₆. The presence of this band has been attributed to off-center displacement of the Nb and W ions due to structural phase transition into a tetragonal ferroelectric phase. The temperature evolution of the 80 cm⁻¹ band intensity revealed that it disappeared at a much higher temperature (about 650 K) than the reported phase transition temperature (about 360 K). This behavior is reminiscent of chemically disordered perovskite ferroelectrics, including relaxor ferroelectrics, and was attributed to the presence of small polar regions with local tetragonal distortion embedded in the paraelectric matrix of the $F d\bar {3}m$ structure.

We report on the growth of c-axis oriented thin films of NbFe₂ prepared by pulsed laser deposition. Variation of the deposition conditions results in variation of the composition of the Nb_1−yFe_2+y films in the range from Nb rich to Fe rich films. Films near the stoichiometric composition (y ≈ 0) are the most interesting. However, microstructural investigations of these films reveal two kinds of grain, which exhibit different shape, epitaxial relation and chemical composition. The different chemical compositions of opposing doping character result in two magnetic phases confirmed by means of magnetization and Hall measurements. This investigation demonstrates the possibility of NbFe₂ thin film growth and discusses the microstructural inhomogeneities occurring.

High-resolution polarized broadband (1800–23 000 cm⁻¹) optical absorption spectra of Tb³⁺ in TbFe₃(BO₃)₄ single crystals are studied between room temperature and 4.2 K. The spectral signatures of the structural (R32–P3₁21, T_S  = 192 K) and magnetic (T_N  = 41 K) phase transitions are found and analyzed. Energies and symmetries of the Tb³⁺ crystal-field (CF) levels were determined for both the high-temperature R32 and the low-temperature P3₁21 structures of TbFe₃(BO₃)₄ and compared with the calculated ones. It follows unambiguously from the spectral data that the ground state is the Γ₁ + Γ₂ quasi-doublet of the local D₃ point symmetry group for Tb³⁺ in the R32 high-temperature structure. The CF calculations revealed the CF parameters and wavefunctions for Tb³⁺ in TbFe₃(BO₃)₄. The value of the Tb–Fe exchange integral and of the effective magnetic field created by the ordered Fe subsystem were estimated as J_fd = 0.26 K and B_eff = 3.92 T, using the observed splitting Δ = 32 cm⁻¹ of the Tb³⁺ ground quasi-doublet at the temperature 5 K. The reliability of the obtained parameters was proven by modeling the literature data on the magnetic susceptibility of TbFe₃(BO₃)₄. Lattice distortions below T_S were evidenced by the observed changes of probabilities of the forced electric dipole transitions of Tb³⁺.

Microcrystals of orthorhombic nickel (II) oxalate dihydrate were synthesized through a precipitation reaction of aqueous solutions of nickel chloride and oxalic acid. Magnetic susceptibility exhibits a sharp peak at 3.3 K and a broad rounded maximum near 43 K. We associated the lower maximum with a metamagnetic transition that occurs when the magnetic field is about  ≥ 3.5 T. The maximum at 43 K is typical of 1D antiferromagnets, whereas weak ferromagnetism behavior was observed in the range of 3.3–43 K.