Landau theory description of observed isotropic to anisotropic phase transition in mixed clay gels

A characteristic new cooperative dehydration transition, in 1:1 Laponite-MMT cogel, was observed at T(c) ≈ 60 °C, a temperature at which the storage modulus (G(')) and depolarization ratio (D(p)) showed sharp increase, and the isotropic cogel turned into an anisotropic one. The dehydration dynamics could be described through power-law relations: G(') ～ (T(c)-T)(-γ) and D(p) ～ (T(c)-T)(-β) with γ ≈ β = 0.40 ± 0.05. The x-ray diffraction data revealed that the crystallite size decreased from 17 nm (at 20 °C) to 10 nm (at 80 °C) implying loss of free and inter-planar water. When this cogel was spontaneously cooled below T(c), it exhibited much larger storage modulii values which implied the existence of several metastable states in this system. This phase transition could be modeled through Landau theory, where the depolarization ratio was used as experimental order parameter (ψ). This parameter was found to scale with temperature, as ψ ～ (T(c)-T)(-α), with power-law exponent α = 0.40 ± 0.05; interestingly, we found α ≈ β ≈ γ.     

Molecular dynamics simulations of nanoparticles in dense isotropic nematogens: the role of matrix-induced long-range repulsive interactions

We have carried out molecular dynamics simulation studies of binary mixtures of spherical nanoparticles (NPs) in a matrix of dense isotropic rod-shaped nematogens, with the size of the nematogen length being similar to that of the NP diameter. NPs at even low concentrations were found to shift the isotropic-nematic (I-N) transition significantly to higher pressure at a given temperature, indicative of long-range perturbation of the nematogenic matrix by the NPs. The NPs were found to be dispersed in the dense isotropic nematogenic matrix over a wide range of NP concentrations due to long-range (compared with the molecular size of the nematogens) repulsion caused by NP-induced local order fluctuations and reduced local orientational correlation in the isotropic nematogenic matrix, in contrast to the phase separation predicted and observed in other studies where the particles were much larger or smaller than the nematogens. Furthermore, since the repulsion observed in the NP-nematogen mixtures is only microscopically long range (on the order of about ten molecular lengths of the nematogens), globally ordered clustering observed in mixtures of colloidal particles in nematic matrices resulting from macroscopically long-range interaction is not observed in our simulations.     

Subdiffusive dynamics of a liquid crystal in the isotropic phase

The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330 K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the beta-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1 ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures Tc are 244+/-6 and 258+/-6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of Tc we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320 K to a few nanoseconds at 275 K.     

Density functional theory predictions of isotropic hyperfine coupling constants

The reliability of density functional theory (DFT) in the determination of the isotropic hyperfine coupling constants (hfccs) of the ground electronic states of organic and inorganic radicals is examined. Predictions using several DFT methods and 6-31G, TZVP, EPR-III and cc-pVQZ basis sets are made and compared to experimental values. The set of 75 radicals here studied was selected using a wide range of criteria. The systems studied are neutral, cationic, anionic; doublet, triplet, quartet; localized, and conjugated radicals, containing 1H, 9Be, 11B, 13C, 14N, 17O, 19F, 23Na, 25Mg, 27Al, 29Si, 31P, 33S, and 35Cl nuclei. The considered radicals provide 241 theoretical hfcc values, which are compared with 174 available experimental ones. The geometries of the studied systems are obtained by theoretical optimization using the same functional and basis set with which the hfccs were calculated. Regression analysis is used as a basic and appropriate methodology for this kind of comparative study. From this analysis, we conclude that DFT predictions of the hfccs are reliable for B3LYP/TZVP and B3LYP/EPR-III combinations. Both functional/basis set scheme are the more useful theoretical tools for predicting hfccs if compared to other much more expensive methods.     

Characteristics of relaxational dynamics and the structure of nematogens

Abstract

Dielectric relaxation of two esters, 4-cyanophenyl-4-n-butyl-(n-pentyl-)cyclohex-1-enecarboxylates, in the frequency range 0-5 to 100 MHz, has been investigated for nematic and isotropic phases. Bifurcation of the loss peak for the nematic phase is observed. For the n-pentyl compound, we conclude that molecular dimerization could play an essential role in mesophase formation.     

Orientational dynamics in the isotropic phase of a calamitic liquid-crystal model

We report a molecular dynamics simulation study on the isotropic phase of an idealized calamitic liquid crystal model with a length-to-width ratio of approximately 5-6. The study focuses on the characterization of single-particle and collective orientational dynamics on approaching the phase transition to the nematic phase. Recent experimental and simulation works have suggested that a power law behavior exists at relatively short times in the decay of the time derivative of the orientational correlation functions. Qualitatively, our simulation data are consistent with these findings. Both single-particle and collective time correlation function derivatives possess, in their respective log-log plots, a linear region at very short times, whose slope is essentially independent from the thermodynamic state. Nevertheless, the single-particle orientational correlation functions are better described by a function which is the sum of a fast exponential, an intermediate stretched-exponential and a slow exponential, while the collective orientational correlation functions are satisfactorily described by a sum of two exponentials, at higher density, or by just one exponential, at lower density.     

Chaotic dynamics and vibrational mode coupling in small argon clusters

We have computed the local Kolmogorov entropy of molecular dynamics trajectory segments near the potential energy saddles of model Ar₃ and Ar₅ clusters. In the case of Ar₃ clusters bound with a Lennard-Jones potential, the local Kolmogorov entropy of the cluster is significantly smaller in the saddle region than in other areas of the potential surface. This behavior indicates an increase in the degree of nearly quasiperiodic motion near the Ar₃ saddle due to the partial decoupling of the cluster's vibrational modes there. Lennard-Jones Ar₅ clusters do not exhibit similar behavior, but Ar₅ clusters bound with a short-range Morse potential do. This suggests that the “regularizing” effect of saddle regions is strongly dependent on the shape of the energy surface near the saddle. From these observations, we can determine which features of the saddle are most important in this respect; the flatness of the saddle region seems to be one such feature.     

A description of phase equilibria in nonideal systems with the use of integral equation theory

Integral equation theory for partial distribution functions was used to consider a method for calculations of vapor-liquid phase equilibrium conditions in binary Lennard-Jones systems with substantial deviations from the Berthelot-Lorentz mixing rules. Possible sources of errors in pressure and chemical potential values and methods for refining the results were analyzed. The required accuracy of calculations can be reached using two parameters only, one in the closure to the Ornstein-Zernike equation and the other in the equation for the chemical potential. These parameters are determined independently from two thermodynamic equations.     

Nonlinear coupling in the quantum statistical theory of proton transfer dynamics

The possible role of the nonlinear coupling on the character of the dynamics of particle transfer process is investigated. The analysis and solutions of the kinetic equation indicate that nonlinear coupling causes symmetry breaking of particle transfer potential and determines possible equilibrium structure of the system. Dissipative coupling characterizes the rate of the system to reach thermodynamic equilibrium and along with nonlinear coupling and parameters of the system determines in a unique way the resulting equilibrium structure of the system.     

From caging to Rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT), we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question, provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This disagreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.     

Experimental study of short- and long-time diffusion regimes of spherical particles in carboxymethylcellulose solutions

The behavior of latex particles in carboxymethylcellulose (CMC) solutions with different probe radii and solution concentrations is investigated. The diffusion processes of probe particles are studied by means of dynamic light scattering experiments. The existence of two diffusion regimes (a short-time regime and a long-time regime) is established for concentrations higher than the threshold value which changes for each probe dimension. Information is also provided about the relative weight of the probe population undergoing the two diffusion processes. This experimental evidence is discussed in connection with the existence of a defined volume (cage) in which short-time diffusion is the characteristic motion, while the long-time diffusion process dominates the motion over all the cages. Furthermore, there was found to be some deviation from Stokes-Einstein behavior.     

Dynamics in supercooled ionic organic liquids and mode coupling theory analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sj?gren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.     

The dynamics of the CH3CN molecule in the isotropic phase and in a nematic solution

Abstract

NMR lineshape studies of acelonitrile in the isotropic and the liquid-crystalline nematic phase of PCH have been performed. The scalar relaxation of the second kind due to the presence of the ¹⁴N quadrupolar nucleus has been confirmed as the most important relaxation mechanism for this molecule in both the isotropic and the anisotropic phase. It has been found largely responsible for the selective broadening on ¹³C and ¹H transitions. A minor contribution arising from intramolecular dipolar relaxation mechanism has also been investigated. Linewidth analysis of the NMR spectra allowed us to determine the quadrupolar relaxation time T _IN of the ¹⁴N nucleus. This is connected to the correlation time for rotational diffusion perpendicular to the molecular symmetry axis. A possible explanation of a residual selective broadeining which effects the ¹³C and ¹H NMR transitions and is not taken into account by this mechanism, is also given.     

The dynamics of the CH3CN molecule in the isotropic phase and in a nematic solution

NMR lineshape studies of acelonitrile in the isotropic and the liquid-crystalline nematic phase of PCH have been performed. The scalar relaxation of the second kind due to the presence of the ¹⁴N quadrupolar nucleus has been confirmed as the most important relaxation mechanism for this molecule in both the isotropic and the anisotropic phase. It has been found largely responsible for the selective broadening on ¹³C and ¹H transitions. A minor contribution arising from intramolecular dipolar relaxation mechanism has also been investigated. Linewidth analysis of the NMR spectra allowed us to determine the quadrupolar relaxation time T_IN of the ¹⁴N nucleus. This is connected to the correlation time for rotational diffusion perpendicular to the molecular symmetry axis. A possible explanation of a residual selective broadeining which effects the ¹³C and ¹H NMR transitions and is not taken into account by this mechanism, is also given.     

Effective separation of forces in a mode coupling theory of self-diffusion

A mode coupling theory (MCT) expression for the self-diffusion coefficient follows simply when the soft fluctuating intermolecular forces are projected along a collective densitylike variable. The projected forces separate into two parts: from the gradient of the direct correlation function (dcf), and from the short range forces. The time correlation function of the dcf-derived forces is related to the excess entropy, as shown by Ali [J. Chem. Phys. 124, 144504 (2006)], and this relationship is evaluated for two variations of MCT. As for hard spheres, the derivation of an analogous MCT is beset by a number of singularities that kinetic theory could not remove. A justifiable MCT for hard sphere fluids may not exist.     

Evidence for lateral chain conformation change in the solid phase of substituted nematogens

A new homologous series of 4-(4-chlorobenzoyloxy)-2-alkoxy-3-methyl-4'-(4-trans-pentyl-cyclohexanoyloxy) azobenzenes has been synthesized. These compounds contain four rings in the main core, a lateral alkoxy branch and an adjacent lateral methyl group on one inner ring. They present a large nematic range and a solid-solid phase transition for the first members of the series. The crystal structures of two similar compounds containing a lateral butoxy chain have been solved. The HM4 compound (C₃₁H₃₃N₂O₅Cl) is derived from the series, but does not have the terminal pentyl chain while the PM4 compound (C₃₆H₄₃N₂O₅Cl) possesses this terminal chain. HM4 and PM4 crystallize, respectively, in P2₁/c (Z = 4) and P1 (Z = 2) space groups. The final reliability factors are R = 0.138 for HM4 (the terminal cyclohexyl ring is largely disordered) and R = 0.041 for PM4, for 2204 and 1963 observed reflections, respectively. The four ring central core is linear and rigid for both compounds. The conformation of the butyloxy side chain branched on one of the central phenyl rings is very dependent on the terminal substituent, as it is found in a largely bent conformation in HM4 and in an extended conformation in PM4. To monitor the lateral chain conformation in the solid and nematic phase, we have used the -OCH₂- resonance in the ¹³C MAS NMR spectra. The temperature dependence of this resonance has indicated that the solid-solid transition encountered for the first members of the series is associated with a change of the lateral chain conformation within the solid phase. At the solid-nematic transition, the change of the chain conformation involving the first segment of the lateral chain is far less pronounced. When this solid-solid phase transition disappears for the last members of the series, this change in the conformation occurs at the solid-nematic transition.     

Dynamical correlations and long-time tails in chemical reactions. A molecular dynamics study

A simple hard-sphere and disk model of a chemical reaction of the type A + B ⇌ C + D is studied by molecular dynamics (MD). Ensemble and time averages are carried out so that the MD calculation simulates chemical relaxation in a homogeneous system which is in equilibrium with respect to the mechanical degrees of freedom. For large times, the decay of the concentrations of the different species is not given by the expected exponential law but shows a long-time tail instead. A simple explanation of the effect is given in terms of recollision events (dynamical correlations) between pairs of particles. It is argued that non-exponential decay of the kind observed might be a general phenomenon in chemical reactions.