Bifurcational analysis of the isotropic-nematic phase transition of rigid rod polymers subjected to biaxial stretching flow

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non-equlibrium isotropic-nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic-biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15 , 1272 (1982)], which are based on a version of the Onsager theory of isotropic-nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.     

Bifurcational analysis of the isotropic-discotic nematic phase transition in the presence of extensional flow

A bifurcational analysis is performed on a version of Doi's equation of nematodynamics that describes the non-equilibrium isotropic-discotic nematic phase transition in the presence of steady uniaxial extensional flow. The disc-like molecular geometry and the degenerate extensional flow-induced orientation are shown to be the source of a complex bifurcation and multistability behaviour involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. Depending on the temperature and the extension rate, the isotropic-discotic nematic transition, involving the two biaxial nematic phases and the uniaxial paranematic phase, may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. A validation procedure on the validity of the predictions is implemented. The predictions presented here find practical applications in the industrial spinning of mesophase carbon fibres, and also provide new results that increase the present fundamental understanding of the rheology of discotic nematic liquid crystals.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

Landau theory for uniaxial nematic,biaxial nematic,uniaxial smectic-A,and biaxial smectic-A phases

We use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes continuous. The four phases meet at a tetracritical point.     

On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs) has been successfully applied by Rey to study extensional flow-induced, homogeneous phase transitions both for rod-like and disc-like molecular geometry. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic concentration vs. flow rate) for rod-like nematics by analysing all tensor degrees of freedom, i.e. by coupling the three director (eigenvector) degrees of freedom. Here we record and discuss subtleties of the corresponding diagram for discotic LCs in uniaxial extension and uniaxial compression. We focus here on the induced stable orientation configurations. Uniaxial extension (an idealization of fibre flow) yields a low concentration region of unique oblate uniaxial states at every flow rate; a very small finite region of bi-stable oblate and biaxial states; and the predominant region, encompassing all concentrations above the pure I-N transition and all flow rates, where the only stable steady state is a biaxial pattern. Furthermore, whereas uniaxial states are 'unique', all biaxial states occur in a continuous family, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an idealization of film stretching flow) of discotic LCs exclusively yields stable prolate uniaxial patterns.     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.     

Study of phase transitions in 4-n-alkoxybenzilidene-4′-n-alkylanilines by one and two dimensional 13C NMR

Abstract

The phase transition of a series of homologous liquid-crystalline compounds, nO.m (4-n-alkoxybenzilidene-4′-n-alkylanilines), from the nematic phase to the smectic A phase has been studied by ¹³C NMR. The order parameters, determined by a two dimensional technique called separated local field spectroscopy combined with off-magic angle spinning, of different molecular segments of these compounds are related linearly to the ¹³C chemical shifts. Changes in the order parameters of the phenyl rings as well as those of the chains during the S_A–N transition depend on the nature of the phase transition. These changes are quantitatively related to the McMillan ratio, which is defined as the ratio between the S_A–N transition temperature (T _SAN) and the nematic to isotropic transition temperature (T _NI), i.e. M = T _SAN/T _NI. The S_A–N transition is first order for M > M _TCP, and second order for M < M _TCP, where TCP is the tricritical point. The value of M _TCP was found to be 0·958 ± 0·004, in excellent agreement with that obtained from spin probe studies (0·959 ± 0·005) reported by Freed and co-workers [1].     

Optically Biaxial,Re‐entrant and Frustrated Mesophases in Chiral,Non‐symmetric Liquid Crystal Dimers and Binary Mixtures

Sixteen optically active, non‐symmetric dimers, in which cyanobiphenyl and salicylaldimine mesogens are interlinked by a flexible spacer, were synthesized and characterized. While the terminal chiral tail, in the form of either (R)‐2‐octyloxy or (S)‐2‐octyloxy chain attached to salicylaldimine core, was held constant, the number of methylene units in the spacer was varied from 3 to 10 affording eight pairs of (R & S) enantiomers. They were probed for their thermal properties with the aid of orthoscopy, conoscopy, differential scanning calorimetry and X‐ray powder diffraction. In addition, the binary mixture study was carried out using chiral and achiral dimers with the intensions of stabilizing optically biaxial phase/s, re‐entrant phases and important phase sequences. Notably, one of the chiral dimers as well as some mixtures exhibited a biaxial smectic A (SmA_b) phase appearing between a uniaxial SmA and a re‐entrant uniaxial SmA phases. The mesophases such as chiral nematic (N*) and frustrated phases viz., blue phases (BPs) and twist grain boundary (TGB) phases, were also found to occur in most of the dimers and mixtures. X‐ray diffraction studies revealed that the dimers possessing oxybutoxy and oxypentoxy spacers show interdigitated (SmA_d) phase where smectic periodicity is over 1.4 times the molecular length; whereas in the intercalated SmA (SmA_c) phase formed by a dimer having oxydecoxy spacer the periodicity was found to be approximately half the molecular length. The handedness of the helical structure of the N* phases formed by two enantiomers was examined with the aid of CD measurements; as expected, these enantiomers showed optical activities of equal magnitudes but with opposite signs. Overall, it appears that the chiral dimers and mixtures presented herein may serve as model systems in design and developing novel materials exhibiting the apolar SmA_b phase possessing D_2h symmetry and nematic‐type biaxiality.     

X‐ray diffraction from the uniaxial and biaxial nematic phases of bent‐core mesogens

X‐ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent‐core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X‐ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X‐ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial–biaxial phase transition, and estimate the order parameters of the nematic phase.     

Biaxial phase and coexistence of the two uniaxial nematic phases in the system sodium dodecyl sulphate–decanol–D2O

The system sodium dodecyl sulphate (SDS)/decanol (DeOH)/water presents, with temperature increase, an unusual phase transition between a stable biaxial phase and a coexistence region of the two uniaxial nematic phases (discotic N_D + cylindrical N_C). This has been detected previously by several methods for a sample with water/SDS molar ratio M_w = 36. Here, this system is investigated changing the ratio M_w to 32, where previously the coexistence region was reported after a discotic N_D phase, without the biaxial phase. We report now the existence of a biaxial N_B in the temperature range of ~2°C, defining for both values of M_w and the phase sequence as N_B – (N_D + N_C) – N_C. The change in temperature is followed by conoscopic and orthoscopic optical techniques and also analysed through the curve obtained by the technique of digital image processing of the textures, which reveals a continuous transition N_D – N_B – (N_D + N_C). While the biaxial phase is stable for at least 10 hours, in a reproducible way, the coexistence region evolves with time, and drops of the discotic phase grow immersed in a N_C matrix. Results are explained in terms of recent theories dealing with stabilisation of mixtures of cylinders and discs.     

The kerr effect in the vicinity of the transition from the isotropic to smectic a phase

The equilibrium electrooptical effect in the isotropic phase of seven liquid crystalline substances (4-n-decyloxy-4′-cyanobiphenyl, carbosilane dendrimer of the fourth generation with cyanobiphenyl terminal fragments, and the fourth, fifth, sixth, seventh, and tenth members of the homologous series of 4-n-acylphenylene 4′-n-alkoxybenzoates) was studied. The smectic A phases were found to exhibit weaker divergence of the Kerr constant in the vicinity of the T _c isotropic melt-liquid crystal phase transition temperature compared with the nematic phases. The difference between T _c and the temperature T* of the virtual second-order phase transition varied from 3.2 to 19.0 K for the smectic A phases, which substantially exceeded the value (T _c-T*) ≤ 1 K for the nematic phases. A theory of the electrooptical properties of isotropic melts in the vicinity of the T _c temperature of the phase transition from the isotropic to smectic A phase is developed. An equation relating the T _c-T* difference to the phenomenological coefficients of the expansion of the Helmholtz energy of an isotropic melt into a series in powers of the coordination and orientational order parameters is obtained.     

The heat conductivity of liquid crystal phases of a soft ellipsoid string-fluid evaluated by molecular dynamics simulation

We have applied a nonequilibrium molecular dynamics heat flow algorithm to calculate the heat conductivity of a molecular model system, which forms uniaxial and biaxial nematic liquid crystals. The model system consists of a soft ellipsoid string-fluid where the ellipsoids interact according to a repulsive version of the Gay-Berne potential. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the discotic nematic phase, the heat conductivity has two components, one parallel and one perpendicular to the director, where the last mentioned component is the largest one. This order of magnitudes is reversed in the calamitic nematic phase. In the biaxial nematic phase there are three components of the heat conductivity, one in the direction around which the long axes of the molecules are oriented, this is the largest component, another one in the direction around which the normals of the broadsides of the molecules are oriented, this is the smallest component, and one in the direction perpendicular to these two directions with a magnitude in between those of the first mentioned components. The relative magnitudes of the components of the heat conductivity span a fairly wide interval so it should be possible to use the model to parameterise experimental data.     

Stress–strain relations of crosslinked rubbers under different types of strain

Experimental data for the stresses and the deformations for crosslinked rubbers at uniaxial and symmetrical and asymmetrical biaxial extension and pure shear are given. Stressed states up to 100% extension are described by a single parameter, the highly elastic potential of Bartenev and Khazanovich. The classical statistical potential of Kuhn-James-Guth-Treloar is not in agreement with experimental data, as shear modulus G has different values for different types of stressed states.     

Thermotropic biaxial nematic liquid crystals: spontaneous or field stabilized?

An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematic liquid crystals. The phase is macroscopically uniaxial but has microscopic biaxial, and possibly polar, domains. Under the action of an electric field, the phase acquires macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.     

On the Uniaxial–Biaxial Nematic Phase Transition in Liquid‐Crystalline Polymers and Elastomers

We study how the uniaxial–biaxial nematic phase transition changes its nature when going from a low‐molecular‐weight liquid crystal to a liquid‐crystalline elastomer or polymer (the latter above the Maxwell frequency) and find a qualitative change due to the presence of a coupling to the strain field in these materials. While this phase transition can be of second‐order in low‐molecular‐weight materials, as is also experimentally observed, we show here that the order of this phase transition is changed generically to no phase transition at all or to a first‐order phase transition in mean‐field approximation. We analyze the influence of an external mechanical stress field above the uniaxial–biaxial nematic phase transition and find that either biaxial nematic order is induced, which is linear or quadratic in the stress intensity, or no response to an external stress results at all, depending on the relative orientation of the applied shear with respect to the director of the uniaxial nematic phase.     

Thermophysical properties of azomethine ether main-chain liquid crystalline polymers at pressures to 200 MPa

This article reports on an experimental investigation of the equation of state and the transition behavior of main-chain thermotropic liquid crystalline polymers over a wide temperature range, and at pressures to 200 MPa. The materials studied were a series of azomethine ether polymers. A varying number n (= 4, 7, 8, 9, 10 and 11) of methylene spacer units in the backbone provided systematic variation of the structure. Experimental techniques used included high-pressure dilatometry (PVT measurements) to 200 MPa, high-pressure differential thermal analysis, also to 200 MPa, and conventional (atmospheric-pressure) differential scanning calorimetry (DSC). The equation of state of the materials can be well represented by the Tait equation in distinct regions, separated by a glass transition, T_g(P), a first-order transition to a nematic state, T_k-n(P), and a first-order transition to an isotropic melt state T_c(P). The atmospheric pressure values of T_k-n and T_c decreased with increasing number of spacer units and showed a clear odd-even effect. T_g and T_k-n both increased with pressure. The pressure dependence of T_c could not be observed due to the onset of degradation in the same temperature region. On isobaric cooling at 3°C/min, the crystallization from the nematic state occurred a few tens of degrees below T_k-n. This supercooling was independent of pressure for some materials, while for others it increased with increasing pressure. The values of the enthalpy and entropy associated with the first-order transition into the nematic state were lower than those of typical isotropic polymers at their melting transitions. The transition enthalpy did not have any systematic variation with increasing number of spacer units. Values of the transition enthalpy calculated from the Ciapeyron equation did not always agree with the values measured by DSC. This may be due to the two-phase nature of the low-temperature state. At the transition to the isotropic state, the transition enthalpy at P = 0 decreased with n and showed an odd-even effect. © 1994 John Wiley & Sons, Inc.     

Thermotropic uniaxial and biaxial nematic and smectic phases in bent-core mesogens

Two azo substituted achiral bent-core mesogens have been synthesized. Optical polarizing microscopy and synchrotron X-ray scattering studies of both compounds reveal the existence of the thermotropic uniaxial and biaxial nematic and three smectic phases at different temperatures in these single component small molecule systems. The transition from the uniaxial to biaxial nematic phase is confirmed to be second order. The transitions from the biaxial nematic to the underlying smectic phase and between the smectic phases have barely discernible heat capacity signatures and thus are also second order.     

The van der Waals equation: analytical and approximate solutions

The thermodynamic properties, enthalpy of vaporization, entropy, Helmholtz function, Gibbs function, but especially the heat capacity at constant volume of a van der Waals gas (and liquid) at the phase transition are examined in two different limit approximations. The first limit approximation is at the near-critical temperatures, i.e., for T/T _c → 1, where T _c is the critical temperature, the other limit approximation is at the near-zero temperatures, T→ 0. In these limits, the analytical equations for liquid and gas concentrations at saturated conditions were obtained. Although the heat capacities at constant volume of a van der Waals gas and liquid do not depend on the volume, they have different values and their change during the phase transition was calculated. It should be noticed that for real substances the equations obtained at the near-zero temperature are only valid for T > T _{triple point} and T ≪ T _c , which means that found equations can be used only for substances with T _{triple point} ≪ T _c .     

Charge transfer interaction between the nematogen 5CB and non-liquid crystal

In general, when a non-nematic solute is added to a nematic, the nematic-isotropic phase transition temperature (T _NI) decreases with increase in non-nematic concentration. But when there are hydrogen bonded complexes or π-complexes of suitable strength formed between the nematic and the solute molecules, the T _NI can rise. Mixing of p-terphenyl or anthracene with 5CB (4-cyano-4'-pentylbiphenyl) results in a T _NI rise. On the other hand, in a binary system consisting of a substance with strong acceptor properties (e.g. tetracyanoethylene; TCNE) and nematic 5CB, T _NI fell remarkably. We have now studied the effect of intermolecular interactions on the T _NI of 5CB by using various acceptor molecules and donor molecules as solutes. We have found that for binary systems in which 5CB and a solute molecule form distinct one-to-one complexes, T _NI falls rather rapidly. When the solute molecules have a strong acceptor power, the rate of T _NI fall with solute concentration is found to be correlated well with the electonegativity of the solute molecules.     

Molecular Dynamics Simulations of Polymers of Unsubstituted and Substituted Poly(p‐phenylene terephthalate)s in the Bulk State

A molecular dynamics simulation has been carried out on polymers of p‐phenylene terephthalate (PPT) and 1,4‐phenylene‐2‐octyloxy terephthalate (PTA8) at six different temperatures: 300 K, 375 K, 450 K, 575 K, 600 K, and 625 K. The periodic simulation boxes consisted of 18 (PPT) or 16 (PTA8) chains with 9 monomer units. The Compass force field was used in the simulations. The crystallographic data and density obtained from the NPT simulation at room temperature agreed well with the experimental data of PPT. Our simulations showed that, in the case of PTA8, the crystal → layered nematics phase transition temperature (T_m) is close to the experimental value for the polymer similar to PTA8. The average initial structure was obtained from X‐ray scattering data. The simulated X‐ray data indicated the existence of a biaxial nematic phase, in accordance with experimental findings.