Pre-vitrification by viscosity feedback

Anomalous Concentration Dependence of Viscosity: Hidden Role of Cross-Correlations in Aqueous Electrolyte Solutions

The viscosity of aqueous electrolyte solutions exhibits well-known composition-dependent anomalies that show certain definitive trends and universal features. The viscosity of LiCl and NaCl solutions increases with concentration in a monotonic fashion, while solutions of KCl, RbCl, and CsCl exhibit a more complex behavior. Here, the viscosity first decreases and then increases with increasing concentration, with a rather broad minimum at intermediate concentrations (ca. 1-3 m). To unearth the origin of such puzzling behavior, we carried out detailed molecular-level analyses by interrogating the exact Green-Kubo expression of viscosity in terms of the stress-stress time correlation function (SS-TCF). The total SS-TCF can be decomposed into a collection of three self- and three cross-SS-TCFs arising from the three constituent components (water, cations, and anions). Mode coupling theory (MCT) analysis for the friction on ions and the viscosity of the solution suggests the possible importance of two-particle static and time-dependent cross-correlations between water and the ions. We calculate the viscosity and other dynamical properties for all five electrolyte (LiCl, NaCl, KCl, RbCl, and CsCl) solutions over a range of concentrations, using two models of water (SPC/E and TIP4P/2005). The total viscosity derives non-negligible contributions from all of the terms. The cross-correlations are found to be surprisingly large and seen to play a hidden role in the concentration dependence. However, the importance of cross-correlations is often not discussed. Our study leads to a theoretical understanding of the microscopic origin of the observed anomalies in the composition dependence of viscosity across all five electrolytes.

Relationship between the Relaxation of Ionic Liquid Structural Motifs and That of the Shear Viscosity

In a set of recent articles, we have highlighted that friction is highly inhomogeneous in a typical ionic liquid (IL) with charge networks that are stiff and charge-depleted regions that are soft. This has consequences not only for the dynamics of ILs but also for the transport properties of solutes dissolved in them. In this article, we explore whether the family of alkylimidazolium ILs coupled with bis(trifluoromethylsulfonyl)imide (with similar Coulombic interactions but different alkyl tails), when dynamically “equalized” by having a similar shear viscosity, display q-dependent structural relaxation time scales that are the same across the family. Our results show that this is not the case, and in fact, the relaxation of in-network charge alternation appears to be significantly affected by the presence of separate polar and apolar domains. However, we also find that if one was to assign weight factors to the relaxation of the structural motifs, charge alternation always contributes about the same amount (between 62.1 and 66.3%) across systems to the running integral of the stress tensor correlation function from which the shear viscosity is derived. Adjacency correlations between positive and negative moieties also contribute an identical amount if a prepeak is not present (about 38%) and a slightly smaller amount (about 28%) when intermediate range order exists. The prepeak only contributes about 6% to viscoelastic relaxation, highlighting that the dynamics of the smaller scale motifs is the most important.

Microscopic origin of breakdown of Stokes-Einstein relation in binary mixtures: Inherent structure analysis

Aqueous binary mixtures often exhibit dramatic departure from the predicted hydrodynamic behavior when transport properties are plotted against composition. We show by inherent structure (IS) analysis that this sharp composition dependent breakdown of the Stokes-Einstein relation can be attributed to the non-monotonic variation in the average inherent structure energy of these mixtures. Further IS analysis reveals the existence of a unique ground state, stabilized by both the formation of an optimum number of H-bonds and a favorable hydrophobic interaction at this composition. The surprisingly sharp turnaround behavior observed in the effective hydrodynamic radius also owes its origin to the same combination of these two factors. Interestingly, the temperature dependence of isothermal compressibility shows a minimum at the particular composition. Extensive studies on water-dimethyl sulfoxide and water-ethanol mixtures using two different force-fields of water reveal many features that are nearly universal. A justification of this quasi-universal behavior is provided in terms of a mode-coupling theory (MCT) of viscosity, which can serve as the starting point of a remarkable correlation observed with the nearest neighbor structure, as captured by the first peaks of the radial distribution function, and the slowdown in the intermediate scattering function at intermediate wavenumbers. Therefore, the formation of the local structure captured through IS analysis can be correlated with the MCT.

A Pictorial View of Viscosity in Ionic Liquids and the Link to Nanostructural Heterogeneity

Prototypical ionic liquids (ILs) are characterized by three structural motifs associated with (1) vicinal interactions, (2) the formation of positive-negative charge-alternating chains or networks, and (3) the alternation of these networks with apolar domains. In recent articles, we highlighted that the friction and mobility in these systems are nowhere close to being spatially homogeneous. This results in what one could call mechanical heterogeneity, where charge networks are intrinsically stiff and charge-depleted regions are softer, flexible, and mobile. This Letter attempts to provide a clear and visual connection between friction-associated with the dynamics of the structural motifs (in particular, the charge network)-and recent theoretical work by Yamaguchi linking the time-dependent viscosity of ILs to the decay of the charge alternation peak in the dynamic structure function. We propose that charge blurring associated with the loss of memory of where positive and negative charges are within networks is the key mechanism associated with viscosity in ILs. An IL will have low viscosity if a characteristic charge-blurring decorrelation time is low. With this in mind, engineering new low-viscosity ILs is reduced to understanding how to minimize this quantity.

Anomalous viscoelastic response of water-dimethyl sulfoxide solution and a molecular explanation of non-monotonic composition dependence of viscosity

Amphiphilic molecules such as dimethyl sulfoxide (DMSO) and its aqueous binary mixtures exhibit pronounced nonideality in composition dependence of several static and dynamic properties. We carry out detailed molecular dynamics simulations to calculate various properties including viscosity of the mixture and combine the results with a mode coupling theory analysis to show that this nonideality can be attributed to local structures that are stable on a short time scale but transient on a long time scale to maintain the large scale homogeneity of the solution. Although the existence of such quasistable structures has been deciphered from spectroscopy, a detailed characterization does not exist. We calculate stress-stress autocorrelation functions (SACFs) of water-DMSO binary mixtures. We employ two different models of water, SPC/E and TIP4P/2005, to check the consistency of our results. Viscosity shows a pronounced nonmonotonic composition dependence. The calculated values are in good agreement with the experimental results. Fourier transform of SACF provides frequency-dependent viscosity. The frequency-dependent viscosity (that is, viscoelasticity) is also found to be strongly dependent on composition. Viscoelasticity exhibits sharp peaks due to intramolecular vibrational modes of DMSO, which are also seen in the density of states. We evaluate the wavenumber dependent dynamic structure factor and wavenumber dependent relaxation time. The latter also exhibits a sharp nonmonotonic composition dependence. The calculated dynamic structure factor is used in mode coupling theory expression of viscosity to obtain a semiquantitative understanding of anomalous composition dependence of viscosity. Both the self-diffusion coefficients and rotational correlation times of water and DMSO molecules exhibit nonmonotonic composition dependence.

Yielding behavior of thermo-reversible colloidal gels

The breakdown of structure in gelled suspensions due to the application of an external stress results in flow. Here we explore the onset of flow by investigating the onset of nonlinear behavior in the elastic moduli of a widely studied class of thermo-reversible gels over a range of volume fractions. We employ the system composed of octadecyl-coated silica particles (radius = 24 nm) suspended in decalin that displays a transition from a liquid to a gel below a volume-fraction-dependent gel temperature, Tgel. The perturbative yield stress at which the gel modulus drops to 90% of its value in the linear viscoelastic limit is found to increase monotonically with volume fraction and decreasing temperature. The recently proposed activated barrier-hopping theory of Schweizer and co-workers1,2 presents a framework to capture the impact of external forces on the mechanical properties of structurally arrested systems. By characterizing particle interactions with a Yukawa potential and employing the resultant static structure factor as input into the activated barrier-hopping theory, we make predictions for how the elastic modulus evolves with the applied stress. Comparisons of these calculations with experiments reveal that the theory does an excellent job of quantitatively capturing the perturbative yield stresses over the entire range of volume fractions and temperatures explored in the study. The match of predictions with experimental results suggests that the theory not only captures particle localization but also how this localization is modulated in the presence of an external stress.

Mass dependence of shear viscosity in a binary fluid mixture: mode-coupling theory

An expression for the shear viscosity of a binary fluid mixture is derived using mode-coupling theory in order to study the mass dependence. The calculated results on shear viscosity for a binary isotopic Lennard-Jones fluid mixture show good agreement with results from molecular dynamics simulation carried out over a wide range of mass ratio at different composition. Also proposed is a new generalized Stokes-Einstein relation connecting the individual diffusivities to shear viscosity.

Scaling law of shear viscosity in atomic liquid and liquid mixtures

A scaling law relating the shear viscosity of one and two component liquid mixtures to their excess thermodynamic entropies defined through pair correlation functions is derived by approximating the mode coupling theory expressions of frictions and then combining with the Stokes-Einstein relation. Molecular dynamics simulation has been performed to generate the data of shear viscosity for one and two component liquid mixtures to test the derived scaling law. The derived scaling laws yield numerical results of shear viscosity for one component and two component liquid mixtures, which are in excellent agreement with the molecular dynamics simulation results for a wide range of density and interaction potential.

Bridging the gap between the mode coupling and the random first order transition theories of structural relaxation in liquids

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating, in a self-consistent way, the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated hopping events called instantons. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event. In the vertex, the probability is proportional to exp(-A/s(c)) where s(c) is the configurational entropy. Close to the glass transition temperature, Tg, since s(c) is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor, phi(t), in deeply supercooled liquid fairly well. We show that below the mode coupling transition temperature, T(c), phi(t) not only decays via the hopping channel but the otherwise frozen MCT part of phi(t) also shows a hopping induced decay. This decay is primarily due to the relaxation of the longitudinal viscosity which is otherwise divergent in the idealized MCT. We further show that although hopping motion induces a decay in the MCT part of phi(t), due to the self-consistent calculation, this effect is nonlinear in nature.

Nonmonotonic composition dependence of vibrational phase relaxation rate in binary mixtures

We present here isothermal-isobaric N-P-T ensemble molecular dynamics simulations of vibrational phase relaxation in a model system to explore the unusual features arising due to concentration fluctuations which are absent in one component systems. The model studied consider strong attractive interaction between the dissimilar species to discourage phase separation. The model reproduces the experimentally observed nonmonotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time tau(c) at mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of mean square frequency modulation [<Delta omega(2)(0)>] with tau(c) indicates that the present model is in the intermediate regime of inhomogeneous broadening. The nonmonotonic composition chi(A) dependence of the dephasing time tau(v) is found to be primarily due to the nonmonotonic chi dependence of tau(c), rather than due to a similar dependence in the amplitude of Delta omega(2)(0). The probability distribution of Delta omega shows a markedly non-Gaussian behavior at intermediate composition (chi(A) approximately =0.5). We have also calculated the composition dependence of the viscosity in order to explore the correlation between the composition dependence of viscosity eta(*) with that of tau(v) and tau(c). It is found that both the correlation time essentially follow the composition dependence of the viscosity. A mode coupling theory is presented to include the effects of composition fluctuations in binary mixture.

Anomalous viscoelasticity near the isotropic-nematic phase transition in liquid crystals

Recent optical Kerr effect experiments have shown that orientational relaxation of nematogens shows a pronounced slow down of the response function at intermediate times and also a power law decay near the isotropic-nematic (I-N) transition. In many aspects, this behavior appears to be rather similar to the ones observed in the supercooled liquid near-glass transition. We have performed molecular dynamics simulations of model nematogens (Gay-Berne with aspect ratio 3) to explore the viscoelasticity near the I-N transition and also investigated the correlation of viscoelasticity (if any) with orientational relaxation. It is found that although the viscosity indeed undergoes a somewhat sharper than normal change near the I-N transition, it is not characterized by any divergence-like behavior (like the ones observed in the supercooled liquid). The rotational friction, on the other hand, shows a much sharper rise as the I-N transition is approached. Interestingly, the probability distribution of the amplitude of the three components of the stress tensor shows anisotropy near the I-N transition-similar anisotropy has also been seen in the deeply supercooled liquid. Frequency dependence of viscosity shows several unusual behaviors: (a) There is a weak, power law dependence on frequency [eta(')(omega) approximately omega(-alpha)] at low frequencies and (b) there is a rapid increase in the sharp peak observed in eta(')(omega) in the intermediate frequency on approach to the I-N transition density. These features can be explained from the stress-stress time correlation function. The angular velocity correlation function also exhibits a power law decay in time. The reason for this is discussed.

In search of temporal power laws in the orientational relaxation near isotropic–nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Microscopic theory of gelation and elasticity in polymer–particle suspensions

A simplified mode-coupling theory (MCT) of ergodic-nonergodic transitions, in conjunction with an accurate two-component polymer reference interaction site model (PRISM) theory for equilibrium structural correlations, has been systematically applied to investigate gelation, localization, and elasticity of flexible polymer-hard particle suspensions. The particle volume fraction at the fluid-gel transition is predicted to depend exponentially on reduced polymer concentration and size asymmetry ratio at relatively high colloid concentrations. In contrast, at lower particle volume fractions, a power-law dependence on polymer concentration is found with effective exponents and prefactors that depend systematically on the polymer/particle size ratio. Remarkable power-law and near universal scaling behavior is found for the localization length and elastic shear modulus. Multiple experiments for gel boundaries and shear moduli are in good agreement with the no adjustable parameter theory. The one exception is the absolute magnitude of the shear modulus which is strongly overpredicted, apparently due to nonequilibrium dense cluster formation. The simplified MCT-PRISM theory also captures the qualitative aspects of the weak depletion-driven "glass melting" phenomenon at high particle volume fractions. Calculations based on an effective one-component model of structure within a low particle volume fraction framework yield qualitatively different features than the two-component approach and are apparently all in disagreement with experiments. This suggests that volume fraction and size asymmetry dependent many-body screening of polymer-mediated depletion attractions at finite particle concentrations are important.

Self-consistent mode-coupling theory for the viscosity of rodlike polyelectrolyte solutions

A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rodlike polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-Huckel approximation is inadequate even at low concentrations. The theory predicts a nonmonotonic dependence of the reduced excess viscosity eta(R) on concentration from the behavior of the static structure factor in polyelectrolyte solutions. The theory predicts that the peak in eta(R) occurs at concentrations slightly lower than the overlap threshold concentration, c*. The peak height increases dramatically with increasing molecular weight and decreases with increased concentrations of added salt. The position of the peak, as a function of concentration divided by c*, is independent of salt concentration or molecular weight. The predictions can be tested experimentally.

Reentrant behavior of relaxation time with viscosity at varying composition in binary mixtures

In order to understand the long known anomalies in the composition dependence of diffusion and viscosity of binary mixtures, we introduce here two new models and carry out extensive molecular dynamics simulations. In these models, the two molecular species (A and B) have the same diameter and mass. In model I the interspecies interaction is more attractive than that between the pure components, while the reverse is true for model II. Simulations and mode coupling theory calculations reveal that the models can capture a wide variety of behavior observed in experiments, including the reentrant viscosity dependence of relaxation time.

Mode-coupling theory of the fifth-order Raman spectrum of an atomic liquid

A fully microscopic molecular hydrodynamic theory for the two-dimensional (fifth-order) Raman spectrum of an atomic liquid (Xe) is presented. The spectrum is obtained from a simple mode-coupling theory by projecting the dynamics onto bilinear pairs of fluctuating density variables. Good agreement is obtained in comparison with recently reported molecular dynamics simulation results. The microscopic theory provides an understanding of the timescales and molecular motions that govern the two-dimensional signal. Predictions are made for the behavior of the spectrum as a function of temperature and density. The theory shows that novel signatures in the two-dimensional Raman spectrum of supercritical and supercooled liquids are expected.

Supercooled liquids and the glass transition

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.