Phase Transitions In Binary Mixtures Research Articles

Exploring the nematic to twist-bend nematic phase transition: calorimetric and optical measurements

ABSTRACT We investigate the nematic (N) to twist-bend nematic (NTB) phase transition in binary mixtures of a symmetric liquid crystal dimer (CB7CB) and a calamitic bi-phenyl mesogen (7OCB). As the molar concentration of 7OCB increases, both the Iso–N and N–NTB transition temperatures decrease gradually, consequently, the width of the nematic phase above the NTB phase can suitably be varied from ~12 K to 46 K. Notably, as the nematic range expands, there is a remarkable reduction in transitional entropy, eventually approaching negligible or zero values. Additionally, the heat capacity peak and the phase shift disappear when transitional entropy reaches zero. This behaviour diverges from typical N–SmA and N–SmC phase transitions, where transitional entropy decreases near the tricritical point but the heat capacity peak persists. Our findings indicate a finite positive δ(∆n) across all concentrations at the N–NTB phase transition, suggesting a gradually weakening first-order nature. This contrasts with theoretical predictions of a second-order N–NTB phase transition, as our experimental data consistently supports a first-order nature. The self-consistent mean-field Landau Model successfully validates our experimental data, establishing the universal first-order nature of the N–NTB phase transition, with experimental entropy values in good agreement with theoretical prediction.

Tricritical behavior of the smectic-hexatic phase transitions in binary mixtures using the landau mean field theory

ABSTRACT The smectic-hexatic phase transitions are studied by the Landau mean field theory in binary mixtures, particularly, THI-14 + MPR-6 liquid crystalline system. By considering the phase lines of SmA-Hex B, SmC-SmF (Hex F) and SmF-Hex B as the first order; SmA-SmC and SmC-SmF as the second order, in the presence of the two tricritical points (C-F-B and A-C-B), we calculate the T-X phase diagram of the binary mixture studied. The phase line equations obtained from the free energies of the smectic and hexatic phases, are fitted to the experimental data given in the literature. We find that the Landau mean field theory explains satisfactorily the observed T-X phase diagram for the smectic-hexatic transitions in the binary mixture of THI-14 + MPR-6.

Studying of crystal growth and overall crystallization of naproxen from binary mixtures

Broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC) were applied to investigate the molecular dynamics and phase transitions in binary mixtures composed of naproxen (NAP) and acetylated saccharides: maltose (acMAL) and sucrose (acSUC). Moreover, the application of BDS method and optical microscopy enabled us to study both crystallization kinetics and crystal growth of naproxen from the solid dispersions with the highest content of modified carbohydrates (1:5wt ratio). It was found that the activation barriers of crystallization estimated from dielectric measurements are completely different for both studied herein mixtures. Much higher Ea (=205kJ/mol) was obtained for NAP-acMAL solid dispersion. It is probably due to simultaneous crystallization of both components of the mixture. On the other hand, lower value of Ea in the case of NAP-acSUC solid dispersion (81kJ/mol) indicated, that naproxen is the only crystallizing compound. This hypothesis was confirmed by X-ray diffraction studies. We also suggested that specific intermolecular dipole-dipole interactions between active substance and excipient may be an alternative explanation for the difference between activation barrier obtained for NAP-acMAL and NAP-acSUC binary mixtures. Furthermore, optical measurements showed that the activation energy for crystal growth of naproxen increases in binary mixtures. They also revealed that both excipients: acMAL and acSUC move the temperature of the maximum of crystal growth towards lower temperatures. Interestingly, this maximum occurs for nearly the same structural relaxation time, which is a good approximation of viscosity, for all samples. Finally, it was also noticed that although naproxen crystallizes to the same polymorphic form in both systems, there are some differences in morphology of obtained crystals. Thus, the observed behavior may have a significant impact on the bioavailability and dissolution rate of API produced in that way.

Tracking three-phase coexistences in binary mixtures of hard plates and spheres.

The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter σ) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be pre-empted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios (σ/D) and aspect ratios (L/D). At intermediate values of σ/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail in the description of isotropic-isotropic one [M. Chen et al., Soft Matter 11, 5775 (2015)].

Critical wetting, first-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries.

十字形液晶分子混合物系统的相变

A binary mixture of two different cross-like molecules is considered.Supposing a simple interaction model between molecules,and using mean field approximation,phase diagrams in the plane of molecular structure parameter rA(the length ratio of short and long rods of A type molecule)and reduced temperature t are obtained.The results show there exists a Landau point,through which the binary mixture can enter directly from isotropic phase to biaxial nematic phase.The optimal molecular structure at this point depends on the structures,the number ratio of A and B type molecules.Mixing rod-like and plate-like molecules with equal numbers will lead to this optimal structure.When rB,the length ratio of short and long rods of B type molecules increases,the rAvalue at Landau point decreases.Comparing the free energy curves corresponding to mixed system and phase separated system completely,it is found that by increasing the interaction strength between different types of molecules,increasing temperature,decreasing the structural difference between different molecules,the chance of phase separation will be reduced.

Thermal and Optical Properties of Some Hydrogen-Bonded Liquid Crystal Mixtures

Phase transition properties of the mixtures of hydrogen-bonded nematic liquid crystals (HBLC) 4-hexylbenzoic acid (6BA), 4-(octyloxy)benzoic acid (8OBA), and 4-(decyloxy)benzoic acid (10OBA) have been investigated by means of differential scanning calorimetry (DSC) and polarize optic microscope (POM). The DSC and POM results clearly indicate the existence of smectic and nematic phase transitions in binary mixtures. The phase transition temperature values of 6BA/10OBA mixtures have clearly increased with increasing heating rate. The activation energies were calculated for the phase transitions of 6BA/10OBA liquid crystal (LC) mixture. The optical transmittance of these mixed hydrogen-bonded nematic liquid crystals was investigated in terms of temperature variations through electrooptic methods. The electrooptic experiments indicate that, while low in the nematic phase, the optical transmittance is very high at the nematic-isotropic phase transition. The transmitted light intensity values of 6BA/8OBA mixture are somewhat higher than those of other binary mixtures, 6BA/10OBA and 8OBA/10OBA, a result associated with the different alkyloxy chain lengths.

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: an analytical equation of state.

An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.

Tests of the tricritical point in the SmA-to-N phase transition of binary mixtures of butyloxybenzylidene octylaniline and hexyloxybenzylidene octylaniline

The present work arises from the significant difference between the experimental Landau tricritical point (LTCP) in the Sm A-to-N phase transition in binary mixtures of butyloxybenzylidene octylaniline (4O.8) and hexyloxybenzylidene octylaniline (6O.8) predicted by Stine and Garland, and that arising from the thermodynamic assessment using the Oonk's Equal Gibbs Curve method. By use of specific heat measurements the 4O.8 + 6O.8, phase diagram has been determined anew. The results of the subsequent application of Oonk's thermodynamic analysis are discussed and their compatibility with the behaviour universally exhibited by other liquid crystal binary mixtures for which a LTCP in the SmA-to-N phase transition has been experimentally determined are analysed.

Phase Transition in Binary Mixture of Bose Gases

Based on the Cornwall-Jackiw-Tomboulis (CJT) effective action approach a theoretical formalism is established for studying the Bose-Einstein condensation (BEC) in a binary mixture of Bose gases. The effective potential, which preserves the Goldstone theorem, is found in the Hartree-Fock (HF) approximation. This quantity is then used to consider the equation of state (EOS) and the phase transition of the system.

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.

Evolution of the isotropic to nematic phase transition in binary mixtures of octylcyanobiphenyl and n-hexane

High-resolution calorimetry has been performed to study the effect of dilution by a nonmesogenic, low-molecular weight solvent (linear n-hexane) on the isotropic-nematic (I-N) phase transition in the liquid crystal (LC) octylcyanobiphenyl (8CB) as a function of n-hexane concentration. Numerous temperature scans were performed without continuous mixing for pure 8CB and all mixture samples of n-hexane mole fraction ranging from x(hex)=0.02 to 0.12. The I-N specific heat peak remains first-order for all samples and shifts toward lower temperature nonlinearly while the two-phase I+N coexistence width broadens linearly with increasing x(hex). Multiple heating and cooling scans are reproducible and indicate phase separation, if it occurs, must be on very short length scales and is reversible. These results may be a consequence of a competition between random dilution effects and the tendency to phase separate. It is shown that solvent dilution of a LC, if miscible and depending on solvent structure, can lead to a controlled altering of the intermolecular potentials and softening of the LC viscoelastic properties.

Anomalous phase behavior of liquid–vapor phase transition in binary mixtures of DNA-coated particles

We report a Monte Carlo study of a 1 : 1 binary mixture of particles coated with DNA chains with “sticky” ends. The system was modeled using a coarse-grained representation. In order to map out the phase diagram of this model system we combined biased Monte Carlo simulations with histogram reweighting techniques. We find that, at low temperatures (strong hybridization) this system undergoes a phase separation between a dilute vapor-like phase and a dense network-forming liquid-like phase. We observe a surprising non-monotonic dependence of the coexistence pressure on the temperature, or more precisely, on the reduced hybridization free energy (fhyb/kBT). This anomalous behavior can be understood in terms of a cross-over between two distinct regimes for the driving force of the phase transition: a hybridization-free-energy-driven regime and an entropy-driven regime. In the former regime, we observe a “normal” vapor–liquid equilibrium where during condensation, the system gains hybridization free energy but loses entropy. In the entropy-driven regime, the phase transition is driven by the increase in entropy due to the re-arrangement of sticky-end bonds in the liquid phase. Finally, we observe that the system can only undergo phase separation if the valence (i.e., the number of DNA-chains per particle) is larger than two. The coexistence region widens markedly as the valence is increased.

Kinetics of the Isotropic‐Ordered Phase Transition in Binary Mixtures of Mesogenic Monomers and Polymers

Kinetics of the nematic phase growth in the melted liquid crystalline azomethine monomer, siloxane‐azomethine polymer, and their mixtures was studied under a deep cooling using polarizing optical microscopy. The nematic droplets revealed in the optical images across the phase transition were treated statistically and the resulting statistical size distributions were described using principles of irreversible thermodynamics. Analysis of the mean droplet diameter as a function of time allowed recognition of two regimes involved to the nematic phase evolution: (1) nucleation and rapid nucleus growth and (2) nucleus coarsening. Both regimes were quantitatively described with the universal law of the cluster growth.

Cellular Automata Model of Phase Transition in Binary Mixtures

We investigate the dynamical behavior of spinodal decomposition in binary mixtures using a variation on the Rothman−Keller cellular automaton, in which particles of type A(B) move toward domains of greater concentration of A(B). Domain growth and system morphologies are determined via the pair correlation function, revealing that (i) the characteristic domain size grows as R(t) ≈ t1/3 and (ii) the configurations of the mixtures at different times are self-similar. These results did not change when different game rules were adopted, indicating that self-similarity and the 1/3 scaling law constitute fundamental properties of any diffusion-driven phase separation process. The same model also was applied to describe the mixing process, and, as expected, it was determined that the characteristic time was dependent on the square of a characteristic linear dimension of the system.

Pretransitional critical-like behavior of dielectric permittivity in mixtures of mesomorphic and nonmesomorphic compounds

Static dielectric measurements are performed in the temperature range of the isotropic-nematic phase transition of binary mixtures of mesomorphic n-heptylcyanobiphenyl (7CB) and nonmesomorphic: (a) n-heptylcyanophenyl (7CP) and (b) carbon tetrachloride (CCl4) , the solutes of different molecular shape and polarity. In the whole studied range of the solutes mole fraction (x) (x(max) approximately equal to 0.17) , the critical-like temperature behavior of the permittivity in the vicinity of the transition from the isotropic phase to the two-phase (nematic+isotropic) region can be well described with a critical exponent close to 0.5, as in a pure 7CB, indicating the tricritical nature of the transitions. It seems to be important that the fitting-determined temperatures of the virtual second-order transition in the solutions, T*, i.e., the temperature limit of the thermodynamic stability of supercooled isotropic phase, correspond well to the experimentally observed low-temperature limits of the two-phase isotropic+nematic region.

Thermal diffusivity of binary mixture of n-tricosane and n-tetracosane by Fourier transform temperature wave analysis

The phase transitions of binary mixtures of n-tricosane (C 23H 48)/ n-tetracosane (C 24H 50) are investigated by Fourier transform temperature wave analysis (FT-TWA) and differential scanning calorimetry (DSC). The phase diagram determined by both methods gives a good agreement. Thermal diffusivity shows an odd–even effect at the solid state, and the temperature dependence of thermal diffusivity of the mixture is classified into two types, odd-like type and even-like type, depending on the mixing ratio. The increase of thermal diffusivity in the rotator phase RI (orthorhombic rotator phase) prior to the phase transition to α-RII (rhombohedral rotator phase with hexagonal subcell) is found for odd number n-tricosane (C 23H 48). A detailed study of the rotator phase transition is shown by the measurement of thermal diffusivity.

Homogenization of a Phase Field Model for Binary Mixtures

The aim of this article is the derivation of a two-scale model that describes the evolution of equiaxed dendritic microstructure in liquid-solid phase transitions of binary mixtures. The approach i...

Phase Behaviors of Binary Hard-Sphere Mixtures Using Simple Analytical Equations of State

Recently, we have proposed a unified analytical equation of state (EOS) for solid–liquid–vapor states of matter, and have examined the thermodynamic properties of argon, carbon dioxide, and methane, as well as binary mixtures of methane and carbon dioxide. Also it has been demonstrated that the EOS can be applied for the solid–fluid transition of hard spheres, by eliminating the attractive part of the EOS. The present work is an extension of the earlier calculations for identical hard spheres, and here we examine the phase behavior of binary hard-sphere mixtures. The hard-sphere EOS employed in this study is $$P = \frac{{RT}}{{V - b}}\left( {\frac{{V - d}}{{V - c}}} \right)^k ,$$ where k = 1 or 2, and k = 0 [or c = d = 0] as a special case. b, c, and d are proportional to a hard-sphere volume, and their mixing rule is a quadratic form in mole fraction x, with a mixing parameter l ij (l ij = l ji and l ii = 0). The b parameter is given by $$b = \sum\limits_{i,j = 1}^2 {\frac{{\left( {b_i + b_j } \right)}}{2}} \left( {1 - 1_{ij} } \right)x_i x_j .$$ Similar mixing rules are applied to c and d. It is shown that various fundamental phase-transition behaviors can be described: ideal or near ideal, azeotropic (maximum and minimum), eutectic, eutectoid, monotectic, peritectic types, and stable fluid–fluid de-mixings without becoming metastable due to the interference of solid–liquid phase transitions. Rather complicated phase diagrams with a combination of various types are also predicted. The present study is a starting point and is useful for understanding the global topology of solid–liquid–vapor phase transitions of binary mixtures.

Light scattering investigation above the nematic-smectic-A phase transition in binary mixtures of calamitic and bent-core mesogens.

Quasielastic light scattering measurements were performed in the nematic phase of mixtures consisting of the calamitic mesogen 8OCB doped with small concentrations of the bent-core molecule P-7PIMB. It was found that the regular part of the bend elastic constant decreases strongly with dopant concentration X. Close to the nematic-smectic-A phase transition temperature, the divergent part of the bend elastic constant, which is proportional to the bare correlation length xi(0)(||) parallel to the layer normal, also decreases rapidly with X. The effect of the dopant on xi(0)(||) is examined in brief theoretically.