A mode coupling theory description of the short- and long-time dynamics of nematogens in the isotropic phase

Dynamics of Acrylamide Hydrogels, Polymers, and Monomers in Water Measured with Optical Heterodyne-Detected Optical Kerr Effect Spectroscopy

The ultrafast dynamics of acrylamide monomers (AAm), polyacrylamide (PAAm), and polyacrylamide hydrogels (PAAm-HG) in water were studied using optical heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy. Previous ultrafast infrared (IR) measurements of the water dynamics showed that at the same concentration of the acrylamide moiety, AAm, PAAm, and PAAm-HG exhibited identical water dynamics and that these dynamics slowed with increasing concentration. In contrast to the IR measurements, OHD-OKE experiments measure the dynamics of both the water and the acrylamide species, which occur on different time scales. In this study, the dynamics of all the acrylamide systems slowed with increasing concentration. We found that AAm exhibits tetraexponential decays, the longest component of which followed Debye-Stokes-Einstein behavior except for the highest concentration, 40% (w/v). Low concentrations of PAAm followed a single power law decay, while high concentrations of PAAm and all concentrations of PAAm-HG decayed with two power laws. The highest concentrations, 25% and 40%, of PAAm and PAAm-HG showed nearly identical dynamics. We interpreted this result as reflecting a similar extent of chain-chain interactions. At low concentrations, PAAm displays non-Markovian, single-chain dynamics (single power law), but PAAm displays entangled chain-chain interactions at high concentrations (two power laws). PAAm-HG has chain-chain interactions at all concentrations that arise from the cross-linking. At high concentrations, the dynamics of the entangled of PAAm become identical within error as those of the cross-linked PAAm-HG.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

The inherent dynamics of isotropic- and nematic-phase liquid crystals

The geodesic (shortest) pathways through the potential energy landscape of a liquid can be thought of as defining what its dynamics would be if thermal noise were removed, revealing what we have called the "inherent dynamics" of the liquid. We show how these inherent paths can be located for a model liquid crystal former, showing, in the process, how the molecular mechanisms of translation and reorientation compare in the isotropic and nematic phases of these systems. These mechanisms turn out to favor the preservation of local orientational order even under macroscopically isotropic conditions (a finding consistent with the experimental observation of pseudonematic domains in these cases), but disfavor the maintenance of macroscopic orientational order, even in the nematic phase. While the most efficient nematic pathways that maintain nematic order are indeed shorter than those that do not, it is apparently difficult for the system to locate these paths, suggesting that molecular motion in liquid-crystal formers is dynamically frustrated, and reinforcing the sense that there are strong analogies between liquid crystals and supercooled liquids.

The inherent dynamics of a molecular liquid: geodesic pathways through the potential energy landscape of a liquid of linear molecules

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation-molecules largely thread their way through narrow channels available in the potential energy landscape.

Studies of dispersed liquid crystals in binary mixtures with ionic liquid and their excitation by electric signals

Morphological changes observed in the binary mixtures of nematic liquid crystal and ionic liquid with externally applied electric signals.

Dynamics in the isotropic phase of nematogens using 2D IR vibrational echo measurements on natural-abundance 13CN and extended lifetime probes

The long time scale orientational relaxation of nematogens in the isotropic phase is associated with the randomization of pseudonematic domains, which have a correlation length that grows as the isotropic-to-nematic phase transition temperature is approached from above. Here we begin to address the fast dynamics of the nematogen molecules within the domains using two-dimensional infrared (2D IR) vibrational echo experiments. The problems of performing ultrafast IR experiments in pure liquids are discussed, and solutions are presented. In addition, the issue of short vibrational lifetimes, which limit the ability of 2D IR experiments to examine dynamics over a wide range of times, is addressed. The experiments were performed on the nematogen 4-cyano-4'-pentylbiphenyl (5CB), with the CN stretch initially used as the vibrational probe. Although the CN stretch has a small transition dipole, because the sample is a pure liquid it is necessary to use an exceedingly thin sample to perform the experiments. The small sample volume leads to massive heating effects that distort the results. In addition, the high concentration in the pure liquid can result in vibrational excitation transfer that interferes with the measurements of structural dynamics, and the CN vibrational lifetime is very short (3.6 ps). These problems were overcome by performing the experiments on the natural-abundance (13)CN stretch (5(13)CB), which greatly reduced the absorbance, eliminating the heating problems; also, this stretch has a longer lifetime (7.9 ps). Experiments were also performed on benzonitrile, which showed that the heating problems associated with pure liquids are not unique to 5CB. Again, the problems were eliminated by conducting measurements on the (13)CN stretch, which has an even longer lifetime (20.2 ps) compared with the (12)CN stretch (5.6 ps). Finally, to extend the range of the dynamical measurements, 4-pentyl-4'-thiocyanobiphenyl (5SCB) was synthesized and studied as a dilute solute in 5CB. The CN stretch of 5SCB has a vibrational lifetime of 103 ps, which permits dynamical measurements to 200 ps, revealing the full range of fast structural dynamics in the isotropic phase of 5CB. It is shown that the 5SCB probe reports essentially the same dynamics as 5(13)CB on the short time scale that is observable with the 5(13)CB vibrational probe.

Universal pattern for the distribution of relaxation times in the isotropic phase of liquid crystalline n-cyanobiphenyls

A universal pattern emerging from the analysis of the distribution of relaxation times in the isotropic phase of liquid crystalline n-alkylcyanobiphenyls (nCB) from 4CB to 14CB is presented. The increase of the length of nCB molecules causes the high-frequency (short-time) branch of the primary relaxation loss curve to approach the form epsilon(f>fpeak) approximately omega(-n), with n-->1/2 in frequency (omega=2pif) or approximately sqrt[t] in time on cooling toward the isotropic-mesophase "clearing" phase-transition temperature (TC). Recently, such behavior was suggested as a hypothetical universal pattern for diverse glass forming organic liquids on approaching the glass temperature [A. I. Nielsen, T. Christensen, B. Jakobsen, K. Niss, N. B. Olsen, R. Richert, and J. C. Dyre, J. Chem. Phys. 130, 154508 (2009)]. The isotropic phase of rodlike liquid crystalline compounds is considered to be an important experimental model system for studying glassy dynamics since it constitutes a link with the model fluid of hard ellipsoids of revolution.

Intermolecular dynamics, interactions, and solvation in ionic liquids

Ionic liquids can simultaneously assume multiple solvent roles, because they are strongly polar and polarizable solvents and binary solutions and frequently contain very hydrophobic components. When the cation and anion functional groups are tuned appropriately, ionic liquids can be used as designer solvents for a broad range of applications. In this Account, we discuss our spectroscopic studies on the intermolecular interactions, dynamics, solvation, transport, and friction in ionic liquids, as compared with information obtained from macroscopic experiments including viscometry and calorimetry.

Glassiness of Thermotropic Liquid Crystals across the Isotropic−Nematic Transition

The orientational dynamics of thermotropic liquid crystals across the isotropic-nematic phase transition have traditionally been investigated at long times or low frequencies using frequency domain measurements. The situation has now changed significantly with the recent report of a series of interesting transient optical Kerr effect (OKE) experiments that probed orientational relaxation of a number of calamitic liquid crystals (which consist of rod-like molecules) directly in the time domain, over a wide time window ranging from subpicoseconds to tens of microseconds. The most intriguing revelation is that the decay of the OKE signal at short to intermediate times (from a few tens of picoseconds to several hundred nanoseconds) follows multiple temporal power laws. Another remarkable feature that has emerged from these OKE measurements is the similarity in the orientational relaxation behavior between the isotropic phase of calamitic liquid crystals near the isotropic-nematic transition and supercooled molecular liquids, notwithstanding their largely different macroscopic states. In this article, we present an overview of the understanding that has emerged from recent computational and theoretical studies of calamitic liquid crystals across the isotropic-nematic transition. Topics discussed include (a) single-particle as well as collective orientational dynamics at a short-to-intermediate time window, (b) heterogeneous dynamics in orientational degrees of freedom diagnosed by a non-Gaussian parameter, (c) fragility, and (d) temperature-dependent exploration of underlying energy landscapes as calamitic liquid crystals settle into increasingly ordered mesophases upon cooling from the high-temperature isotropic phase. A comparison of our results with those of supercooled molecular liquids reveals an array of analogous features in these two important classes of soft matter systems. We further find that the onset of growth of the orientational order in the parent nematic phase induces translational order, resulting in smectic-like layers in the potential energy minima of calamitic systems if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. We discuss implications of this startling observation. We also discuss recent results on the orientational dynamics of discotic liquid crystals that are found to be rather similar to those of calamitic liquid crystals.

Glassy orientational dynamics of rodlike molecules near the isotropic-nematic transition

We investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including nonexponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dynamics in line with the established methods in supercooled liquids, we construct a relaxation time versus scaled inverse temperature plot and demonstrate that one can indeed define a "fragility index" for thermotropic liquid crystals that depends on density and aspect ratio. The values of the fragility parameter are surprisingly in the range observed for glass-forming liquids. A plausible correlation between the energy landscape features and the observed fragility is discussed.

Depolarized light scattering versus optical Kerr effect. II. Insight into the dynamic susceptibility of molecular liquids

We have previously discussed [J. Chem. Phys. 125, 114502 (2006)] that optical Kerr effect (OKE) and depolarized light scattering (DLS) data of molecular liquids reveal, each in their native domain, the same characteristic signatures of the glass transition dynamics; in particular, the intermediate power law of OKE is equivalent with the excess wing of the frequency-domain data, long since known in dielectric spectroscopy. We now extend the discussion to show that the excess wing is an equally common feature in DLS. We further discuss the time-temperature superposition property of OKE data in relation to our DLS and literature dielectric-spectroscopic results, and the merits of their mode coupling theory analyses. Spectroscopic signatures of a liquid-crystal-forming system (nematogen) are discussed in the same frame.

Anomalous Diffusion and Cage Effects in the Isotropic Phase of a Liquid Crystal

The translational motion of 4-n-hexyl-4'-cyanobiphenyl (6CB) in its isotropic phase has been studied by atomistic molecular dynamics simulation from 280 to 330 K. The mean square displacement shows evidence of a subdiffusive dynamics, with a plateau that becomes very apparent at the lowest temperatures. A three-time self-intermediate scattering function reveals that this plateau is connected with a homogeneous dynamics that, at longer times, becomes heterogeneous and finally exponential. These features are shared by, for example, a high-density system of hard spheres, which supports the universal character of the translational dynamics of liquids in their supercooled condition. As predicted by the idealized version of the mode-coupling theory (MCT), the diffusion coefficient dependence upon temperature is well described by a power law, with a critical temperature very close to that obtained by experimental measurements on orientational relaxation. This agreement might indicate a complete freezing of both rotational and translational intradomain dynamics. The time-temperature superposition principle also holds. The shape of the cage that surrounds a 6CB molecule has been reconstructed, and this analysis suggests a preferential side-by-side arrangement of molecules, which locally tend to align their long axes even in the isotropic phase.

Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystal and in a model supercooled liquid

Recent optical Kerr effect experiments have revealed a power law decay of the measured signal with a temperature independent exponent at short-to-intermediate times for a number of liquid crystals in the isotropic phase near the isotropic-nematic transition and supercooled molecular liquids above the mode coupling theory critical temperature. In this work, the authors investigate the temperature dependence of short-to-intermediate time orientational relaxation in a model thermotropic liquid crystal across the isotropic-nematic transition and in a binary mixture across the supercooled liquid regime in molecular dynamics simulations. The measure of the experimentally observable optical Kerr effect signal is found to follow a power law decay at short-to-intermediate times for both systems in agreement with recent experiments. In addition, the temperature dependence of the power law exponent is found to be rather weak. As the model liquid crystalline system settles into the nematic phase upon cooling, the decay of the single-particle second-rank orientational time correlation function exhibits a pattern that is similar to what has been observed for supercooled liquids.

Dynamics of a discotic liquid crystal in the isotropic phase

Optically heterodyne-detected optical Kerr effect (OHD-OKE) experiments are conducted to study the orientational dynamics of a discotic liquid crystal 2,3,6,7,10,11-hexakis(pentyloxy)triphenylene (HPT) in the isotropic phase near the columnar-isotropic (C-I) phase transition. The OHD-OKE signal of HPT is characterized by an intermediate power law t(-0.76+/-0.02) at short times (a few picoseconds), a von Schweidler power law t(-0.26+/-0.01) at intermediate times (hundreds of picoseconds), and an exponential decay at long times (tens of nanoseconds). The exponential decay has Arrhenius temperature dependence. The functional form of the total time dependent decay is identical to the one observed previously for a large number of molecular supercooled liquids. The mode coupling theory schematic model based on the Sjogren [Phys. Rev. A 33, 1254 (1986)] model is able to reproduce the HPT data over a wide range of times from <1 ps to tens of nanoseconds. The studies indicate that the HPT C-I phase transition is a strong first order transition, and the dynamics in the isotropic phase display a complex time dependent profile that is common to other molecular liquids that lack mesoscopic structure.

Structural relaxation in complex liquids: Non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with <x(0)x(t)> of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.

Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.

Orientational ordering of a banana-shaped solute molecule in a nematic calamitic solvent by 2H-NMR spectroscopy: an indication of glasslike behavior

The Saupe ordering matrix of a banana-shaped mesogenic molecule as a solute in a common nematic calamitic solvent has been determined by 2H-NMR spectroscopy as a function of temperature. The temperature dependence of the Saupe ordering matrix element associated with the principal molecular axis is consistent with a glassy behavior in the reorientational motion of this particular solute molecule. The Haller expression, appropriately modified, provides a good fit to the experimental data.

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 Sjögren 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.

Molecular dynamics and interactions of aqueous and dichloromethane solutions of polyvinylpyrrolidone

We have investigated the dynamics of polyvinylpyrrolidone solutions (PVP, M(w)=10 000) on time scales from 20 fs to 42 ps using femtosecond optically heterodyne-detected Raman-induced Kerr effect spectroscopy. To compare the dynamics of polymer solutions with those of the analogous monomer, we also characterized solutions of 1-ethyl-2-pyrrolidone (EP). Dynamics of both PVP and EP solutions have been characterized for sample concentrations of 6.4, 12.7, 24.5, 33.3, and 40.7 wt %. The longest time scale relaxations observed in the Kerr transients for these solutions occur on the picosecond time scale and are best fit to triexponential functions. The intermediate and slow relaxation time constants for PVP and EP solutions are concentration dependent. The time constants for the PVP solutions are not consistent with the predictions of hydrodynamic models, while the analogous time constants for the EP solutions do display hydrodynamic scaling. The predominant relaxation of the polymer is assigned to reorientations of the pyrrolidone side group or torsional motions of the constitutional repeat unit, with additional relaxation pathways including hydrogen bond reorganization in aqueous solution and segmental motion of multiple repeat units. The vibrational dynamics of PVP and EP solutions occur on the femtosecond time scale. These dynamics are analyzed with a focus on the additional degrees of freedom experienced by EP relative to PVP that result from the absence of the tether from the pyrrolidone group on the main chain backbone. The intermolecular Kerr spectra of PVP in H(2)O and CH(2)Cl(2) differ because H(2)O can donate a hydrogen bond to the carbonyl acceptor group on the pyrrolidone ring, while CH(2)Cl(2) cannot.

Power law relaxation and glassy dynamics in Lebwohl-Lasher model near the isotropic-nematic phase transition

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.