Dynamics of supercooled liquids and glassy solids

Hybrid Particle-Field Molecular Dynamics Simulations of Charged Amphiphiles in an Aqueous Environment.

We develop and test specific coarse-grained models for charged amphiphilic systems such as palmitoyloleoylphosphatidylglycerol (POPG) lipid bilayer and sodium dodecyl sulfate (SDS) surfactant in an aqueous environment, to verify the ability of the hybrid particle-field method to provide a realistic description of polyelectrolytes. According to the hybrid approach, the intramolecular interactions are treated by a standard molecular Hamiltonian, and the nonelectrostatic intermolecular forces are described by density fields. Electrostatics is introduced as an additional external field obtained by a modified particle-mesh Ewald procedure, as recently proposed [Zhu et al. Phys. Chem. Chem. Phys.…

Dynamic force spectroscopy: analysis of reversible bond-breaking dynamics

The problem of diffusive bond-dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e. under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach …

Performance of Different Force Fields in Force Probe Simulations

We present detailed force probe molecular dynamic simulations of mechanically interlocked dimeric calix[4]arene-catenanes, comparing the results obtained using three different commonly used force fields (GROMOS G53a5, OPLS-AA, and AMBER GAFF). The model system is well characterized as a two-state system consisting of a closed compact and an elongated structure. Both states are stabilized by a different hydrogen-bond network, and complete separation of the dimer is prevented by the mechanical lock of the entangled aliphatic loops. The system shows fully reversible rebinding meaning that after bond rupture the system rejoins when the external force is relaxed. We present a detailed study of q…

Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The result…

Aging in a free-energy landscape model for glassy relaxation

The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the re-equilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for re-equilibration is determined by that of the primary relaxation as an intrinsic property of the model.

Response-theory for nonresonant hole burning: Stochastic dynamics

Using non-linear response theory the time signals relevant for nonresonant spectral hole burning are calculated. The step-reponse function following the application of a high amplitude ac field (pump) and an intermediate waiting period is shown to be the sum of the equilibrium integrated response and a modification due to the preparation via ac irradiation. Both components are calculated for a class of stochastic dipole reorientation models. The results indicate that the method can be used for a clearcut distinction of homogeneously and heterogeneously broadened susceptibilities as they occur in the relaxation of supercooled liquids or other disordered materials. This is because only in the…

Mechanically interlocked calix[4]arene dimers display reversible bond breakage under force.

The physics of nanoscopic systems is strongly governed by thermal fluctuations that produce significant deviations from the behaviour of large ensembles1,2. Stretching experiments of single molecules offer a unique way to study fundamental theories of statistical mechanics, as recently shown for the unzipping of RNA hairpins3. Here, we report a molecular design based on oligo calix[4]arene catenanes—calixarene dimers held together by 16 hydrogen bridges—in which loops within the molecules limit how far the calixarene nanocapsules can be separated. This mechanically locked structure tunes the energy landscape of dimers, thus permitting the reversible rupture and rejoining of the individual n…

Spin lattice relaxation rates of tunnelling CD3 groups

The spin lattice relaxation rates of deuterated methyl groups are calculated for threefold and sixfold potentials. It is shown that it should be possible to determine the symmetry of the potential hindering the methyl groups from deuteron spin lattice relaxation experiments. The temperature dependence of the spin lattice relaxation rates is discussed using a simple model. The similarities and the differences between proton NMR and deuteron NMR are pointed out. The main difference is thatEa↔Eb transitions are forbidden by spin selection rules in case of CH3, but not for CD3. Therefore, and due to the fact that the quadrupolar interaction is a single particle interaction, deuteron NMR allows …

Propagation and localisation of vibrational modes in 3–dimensional disordered systems: the binary force constant model

We consider a system of coupled harmonic oscillators on a cubic lattice. The force constants are supposed to take two distinct values at random according to a bond concentration x. The density of states (DOS) is evaluated both by numerical diagonalisation and in coherent-potential approximation (CPA). There is excellent agreement between the results of the two methods. Near the concentration, where the bonds with the larger force constants percolate, the DOS differs appreciably from the crystalline one and is anomalously enhanced at low frequencies as compared to Debye's ω2 law (“boson peak”). These features are shared with models with continuous distributions of force constants. The mean f…

Low-temperature methyl group dynamics of hexamethylbenzene in crystalline and glassy matrices as studied by 2H NMR

Abstract 2 H NMR spectra of hexamethylbenzene (HMB) in protonated crystalline and amorphous matrices at low temperatures are presented. All spectra reveal lineshape changes which can be attributed to methyl group tunnelling. Compared to neat HMB, a drastic increase of the tunnelling frequency is found for all systems. This indicates that the hindering potential originates predominantly from intermolecular forces. We studied the temperature dependence of these spectra and the spin-lattice relaxation in order to exclude a distribution of motional correlation times describing a thermally activated process. In addition, we find a distortion of the methyl tetrahedron.

Temperature dependent mechanical unfolding of calixarene nanocapsules studied by molecular dynamics simulations.

Using atomistic molecular dynamics simulations, we study the temperature dependence of the mechanical unfolding of a model supramolecular complex, a dimer of interlocked calixarene capsules. This system shows reversible transitions between two conformations that are stabilized by different networks of hydrogen bonds. We study the forced dissociation and formation of these networks as a function of temperature and find a strong impact of the nonequilibrium conditions imposed by pulling the system mechanically. The kinetics of the transition between the two conformations is ideally suited to investigate the range of validity of the stochastic models employed in the analysis of force dependent…

Reorientational dynamics in simple supercooled liquids

Abstract The geometry of the reorientational dynamics in the van der Waals liquid, toluene, and the hydrogen bond network, glycerol, are compared. Both systems have contributions from small angle fluctuations. In glycerol the fraction of these small angle fluctuations is much larger than in toluene, due to the stronger anisotropic interactions in the former substance. The average reorientational angle in both systems is similar and on the order of 10 ∘ . In addition we analyze the stretching of the rotational correlation functions of rank one and two. In both cases we find that the second rank correlation function has a more pronounced stretching than the corresponding first rank correlatio…

Reversible hydrogen bond network dynamics: molecular dynamics simulations of calix[4]arene-catenanes.

We present detailed molecular dynamics (MD) simulations of mechanically interlocked calix[4]arene-catenanes under external force. Single-molecule force spectroscopy experiments revealed that the separation of dimers with two aliphatic loops results in reversible hydrogen bond breakage through an intermediate in a triple-well potential, while the tetra-loop species separates in a one-step manner (Janke, M.; et al. Nat. Nanotechnol. 2009, 4, 225). MD simulations show that calix[4]arenes interlocked by four loops (1) display a complete restructuring of the hydrogen bond network under mechanical force. All hydrogen bonds of the closed structure open, and new ones are formed in the extended stru…

Force-dependent folding pathways in mechanically interlocked calixarene dimers via atomistic force quench simulations

Single-molecule force spectroscopy and molecular simulations are well-established techniques to study the mechanical unfolding of supramolecular complexes in various fields of biomolecular physics....

Experimental Determination of Four-Time Stimulated Echoes in Liquids, Colloidal Suspensions, and Crystals

Four-time stimulated echo experiments have been used to monitor the temporal evolution of the reorientation rates of deuterated molecules or colloidal suspensions. We present extended phase cycles for this seven-pulse experiment. In order to test its performance three vastly different materials are chosen. These include a crystal in which the molecules carry out well-defined 180 degrees flips and a supercooled liquid characterized by a distribution of jump angles centered around 10 degrees. As an example for rotational diffusion, data on a concentrated suspension of polystyrene spheres in a viscous medium are presented. Copyright 1998 Academic Press.

The temperature dependence of vibronic lineshapes: linear electron-phonon coupling.

We calculate the effect of a linear electron-phonon coupling on vibronic transitions of dye molecules of arbitrary complexity. With the assumption of known vibronic frequencies (for instance from quantum-chemical calculations), we give expressions for the absorption or emission lineshapes in a second-order cumulant expansion. We show that the results coincide with those obtained from generalized Redfield theory if one uses the time-local version of the theory and applies the secular approximation. Furthermore, the theory allows to go beyond the Huang-Rhys approximation and can be used to incorporate Dushinsky effects in the treatment of the temperature dependence of optical spectra. We cons…

Four-time rotational correlation functions

A scheme to analyze four-time rotational correlation functions of any rank is developed and details for rank L = 1 and 2 are given. The scheme provides a transparent way for identifying deviations from simple Markovian dynamics as observed, e.g., in complex liquids close to the glass transition. The method should be applicable to NMR and optical multiple-pulse techniques as well as to photon correlation spectroscopy. Results are given for 2H-NMR multiple-pulse data in supercooled glycerol. We identify and analyze the dynamical heterogeneity of molecular reorientation in a range of 205 − 215 K close to the glass temperature Tg = 190 K.

Flexibility of phenylene oligomers revealed by single molecule spectroscopy

The rigidity of a p-phenylene oligomer (p-terphenyl) has been investigated by single molecule confocal fluorescence microscopy. Two different rylene diimide dyes attached to the terminal positions of the oligomer allowed for wavelength selective excitation of the two chromophores. In combination with polarization modulation the spatial orientation of the transition dipoles of both end groups could be determined independently. We have analyzed 597 single molecules in two different polymer hosts, polymethylmethacrylate and Zeonex. On average we find a 22 degrees deviation from the linear gas phase geometry (T = 0 K), indicating a rather high flexibility of the p-phenylene oligomer independent…

Stochastic Models of Higher Order Dielectric Responses

The nonlinear response for systems exhibiting Markovian stochastic dynamics is calculated using time-dependent perturbation theory for the Green’s function, the conditional probability to find the system in a given configuration at a certain time given it was in another configuration at an earlier time. In general, the Green’s function obeys a so-called master-equation for the balance of the gain and loss of probability in the various configurations of the system. Using various models for the reorientational motion of molecules it is found that the scaled modulus of the third-order response, \(X_3\), shows a hump-like behavior for random rotational motion in some cases and it exhibits “triv…

A fundamental catalytic difference between zinc and manganese dependent enzymes revealed in a bacterial isatin hydrolase

Scientific reports 8(1), 13104 (2018). doi:10.1038/s41598-018-31259-y

Structural Origin of Metal Specificity in Isatin Hydrolase from Labrenzia aggregata Investigated by Computer Simulations.

We performed quantum-chemical calculations, ab initio molecular dynamics, hybrid quantum mechanics/molecular mechanics (QM/MM) and enhanced sampling metadynamics simulations to investigate the origin of metal specificity in isatin hydrolase from Labrenzia aggregata. The peculiar octahedral binding geometry of the Mn2+ ion in the Michaelis complex includes both the isatin substrate and the catalytic water within the first coordination shell of the cation. Our calculations show that the same arrangement of the ligands cannot be efficiently achieved in the presence of other small divalent metal cations such as Zn2+ or Cu2+ . On the contrary, bulkier alkaline-earth cations such as Mg2+ , which …

Comparative Study of the Mechanical Unfolding Pathways of α- and β-Peptides

Using molecular simulations, we analyze the unfolding pathways of various peptides. We compare the mechanical unfolding of a β-alanine's octamer (β-HAla8) and an α-alanine's decamer (α-Ala10). Using force-probe molecular-dynamics simulations, to induce unfolding, we show that the 3(14)-helix formed by β-HAla8 is mechanically more stable than the α-helix formed by α-Ala10, although both structures are stabilized by six hydrogen bonds. Additionally, computations of the potential of mean force validate this result and show that also the thermal stability of the 3(14)-helix is higher. It is demonstrated that β-HAla8 unfolds in a two-step fashion with a stable intermediate. This is contrasted wi…

Nonlinear response functions in an exponential trap model

The nonlinear response to an oscillating field is calculated for a kinetic trap model with an exponential density of states and the results are compared to those for the model with a Gaussian density of states. The calculations are limited to the high temperature phase of the model. It is found that the results are qualitatively different only in a temperature range near the glass transition temperature $T_0$ of the exponential model. While for the Gaussian model the choice of the dynamical variable that couples to the field has no impact on the shape of the linear response, this is different for the exponential model. Here, it is found that also the relaxation time strongly depends on the …

Magnetic Resonance Studies of the Heterogeneous Rotational and Translational dynamics in Disordered Materials

Higher-order correlation functions and nonlinear response functions in a gaussian trap model.

The four-time correlation function of a general dynamical variable obeying Gaussian statistics is calculated for the trap model with a Gaussian density of states. It is argued that for energy-independent variables this function is reminiscent of the four-time functions that have been discussed earlier in the interpretation of the results of four-dimensional NMR experiments on supercooled liquids. Using an approximative relation between the four-time correlation function and the cubic response function the nonlinear susceptibility is calculated and the results are compared with the corresponding ones resulting from an exact calculation. It is found that the results of the approximation chang…

Determining Factors for the Unfolding Pathway of Peptides, Peptoids, and Peptidic Foldamers.

We present a study of the mechanical unfolding pathway of five different oligomers (α-peptide, β-peptide, δ-aromatic-peptides, α/γ-peptides, and β-peptoids), adopting stable helix conformations. Using force-probe molecular dynamics, we identify the determining structural factors for the unfolding pathways and reveal the interplay between the hydrogen bond strength and the backbone rigidity in the stabilization of their helix conformations. On the basis of their behavior, we classify the oligomers in four groups and deduce a set of rules for the prediction of the unfolding pathways of small foldamers.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles

Abstract The shape and size of self‐assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long‐range interactions. Combining small‐angle X‐ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry br…

Mechanical unfolding pathway of a model β-peptide foldamer.

Foldamers constructed from oligomers of β-peptides form stable secondary helix structures already for small chain lengths, which makes them ideal candidates for the investigation of the (un)folding of polypeptides. Here, the results of molecular simulations of the mechanical unfolding of a β-heptapeptide in methanol solvent revealing the detailed unfolding pathway are reported. The unfolding process is shown to proceed via a stable intermediate even for such a small system. This result is arrived at performing non-equilibrium force ramp simulations employing different pulling velocities and also using standard calculations of the potential of mean force, i.e., the free energy as a function …

Correlation of primary relaxations and high-frequency modes in supercooled liquids. I. Theoretical background of a nuclear magnetic resonance experiment

The question regarding a possible correlation of the time scales of primary and secondary relaxations in supercooled liquids is formulated quantitatively. It is shown how this question can be answered using spin-lattice relaxation weighted stimulated-echo experiments, which are presented in an accompanying paper [A. Nowaczyk, B. Geil, G. Hinze, and R. Böhmer, Phys. Rev. E 74, 041505 (2006)]. General theoretical expressions relevant for the description of such experiments in the presence of correlation effects are derived. These expressions are analyzed by Monte Carlo integration for various correlation scenarios also including exchange processes, which are the hallmark of dynamical heteroge…

Aging effects in simple models for glassy relaxation

Aging effects in the two-time correlation function and the response function after a quench from a high temperature to some low temperature are considered for a simple kinetic random energy model exhibiting stretched exponential relaxation. Because the system reaches thermal equilibrium for long times after the quench, all aging effect are of a transient nature. In particular, the violations of the fluctuation-dissipation theorem are considered and it is found that the relation between the response and the two-time correlation function depends on another function, the so-called asymmetry. This asymmetry vanishes in equilibrium but cannot be neglected in the aging regime. It is found that pl…

Heterogeneity at the glass transition: what do we know?

We critically discuss the information that can be obtained from experiments with respect to the existence, the life time, and the length scale of dynamical heterogeneity in glass-forming liquids. The ability to select a dynamically distinguishable subensemble and observe its return to the full equilibrium ensemble is illustrated by examples from multi-dimensional NMR. We also discuss non-resonant hole burning spectroscopy as an example for which two separate time scales are involved.

Comment on “Hole-Burning Experiments within Glassy Models with Infinite Range Interactions”

Comment on: L.F. Cugliandolo and J.L. Iguain; Phys. Rev. Lett. {\bf 85} 3448 (2000)

Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle

The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.

Statistics of reversible transitions in two-state trajectories in force-ramp spectroscopy

A possible way to extract information about the reversible dissociation of a molecular adhesion bond from force fluctuations observed in force ramp experiments is discussed. For small loading rates the system undergoes a limited number of unbinding and rebinding transitions observable in the so-called force versus extension (FE) curves. The statistics of these transient fluctuations can be utilized to estimate the parameters for the rebinding rate. This is relevant in the experimentally important situation where the direct observation of the reversed FE-curves is hampered, e.g. due to the presence of soft linkers. I generalize the stochastic theory of the kinetics in two-state models to the…

On the nature of slow β-relaxation in supercooled liquids

We propose a model for reorientational motions of molecules associated with secondary beta-relaxation in supercooled liquids. The secondary relaxation is attributed to relaxation within a given local minimum, while the primary relaxation is attributed to transitions between distinct free-energy minima. We find that (i) at the temperature where the peak frequency of the extrapolated beta-relaxation intersects the alpha-relaxation, the actual and the extrapolated spectra differ in their time constants by approximately one decade; (ii) there is no clear division between the imaginary part of the dielectric susceptibility for the alpha- and the beta-relaxation for temperatures larger than 1.1 T…

Force-clamp spectroscopy of reversible bond breakage.

We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple two-state models. In the calculations, we exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Environmental fluctuation models are used to describe deviations from Markovian behavior. The second moment of the event-number distribution is found to be very sensitive to possible exchange processes and can thus be used to identify temporal fluctuations of th…

Force probe simulations of a reversibly rebinding system: Impact of pulling device stiffness.

We present a detailed study of the parameter dependence of force probe molecular dynamics (FPMD) simulations. Using a well studied calix[4]arene catenane dimer as a model system, we systematically vary the pulling velocity and the stiffness of the applied external potential. This allows us to investigate how the results of pulling simulations operating in the constant velocity mode (force-ramp mode) depend on the details of the simulation setup. The system studied has the further advantage of showing reversible rebinding meaning that we can monitor the opening and the rebinding transition. Many models designed to extract kinetic information from rupture force distributions work in the limit…

Nonlinear response theory for Markov processes II: Fifth-order response functions

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012)). For sinusoidal fields the $5\om$-component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurence of such a hump as compared to a …

Self-diffusion coefficients in plastic crystals by multiple-pulse NMR in large static field gradients.

Measurements of self-diffusion coefficients in solids with the gradient spin echo technique have until now been limited due to short spin-spin relaxation times. Here we make use of multiple-pulse sequences, which average out the nuclear dipole interaction, to expand the measurable range for macroscopic self-diffusion coefficients by 2 orders of magnitude. By combining multiple-pulse NMR, in our case using the MREV-8 sequence, with a high static gradient we measured the self-diffusion coefficient in a molecular crystal of camphene down to a value of $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{m}}^{2}{\mathrm{s}}^{\en…

Symmetry-species conversion in CD3systems

The rates for symmetry-species conversion of CD3 groups are calculated using a model in which the interaction between the quadrupolar moment of the deuterons with electric-field gradient at the site of the nucleus causes symmetry-changing transitions. Just the same phonons are considered for energy conservation as are used to describe the temperature dependence of inelastic neutron scattering experiments. For the conversion rate, a similar temperature dependence is found as has already been obtained for CH3. For temperatures around the tunnelling energy, a behaviour is predicted for CD3 that is different from the behaviour in protonated systems according to all theories known to the authors…

Far-off-resonance averaging of dipolar interactions in solids

Abstract The far-off-resonance performance of several line-narrowing sequences is investigated. Both theoretically and experimentally, it is found that transverse relaxation times, dominated by dipole–dipole interactions, are most effectively prolonged not only on-resonance but also for certain, generally large, resonance offsets. These correspond to a situation when, during the basic pulse separation, the frequency offset rotates the toggling-frame Hamiltonian by multiples of 180°. The implications of these results for the study of macroscopic translational diffusion using static-field-gradient NMR are discussed.

High-field nuclear spin relaxation in liquids and solids

The authors generalise the standard theory of nuclear spin relaxation to situations in which the Markovian approximation is not applicable. Expressions for generalised frequency-dependent spin relaxation functions are presented. They show that under high-field conditions the relaxation of longitudinal magnetisation is exponential independent of the particular time dependence of the correlation functions.

Memory effects in the relaxation of the Gaussian trap model

We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model thermal equilibrium is reached at all finite temperatures and therefore we can consider jumps from low to high temperatures in addition to the quenches usually considered in aging studies. We show that the evolution of the energy following the Kovacs-protocol can approximately be expressed as a difference of two monotonously decaying functions and thus show the existence of a so-called Kovacs hump whenever these functions are not single exponentials. It is well established that the Kovacs effect also occurs in the linear response regime and we show that mos…

Mechanical Properties of Single Molecules and Polymer Aggregates

This chapter deals with the mechanical properties of single polymer chains, aggregates, and supramolecular complexes. The topics discussed cover a broad range from fundamental statistical mechanics of the equilibrium elastic properties of single polymer chains to details of the behavior of binding pockets in biomolecular assemblies as observed by force spectroscopy. The first section treats the equilibrium mechanical properties of single polymer chains in various environments, investigated via extensive simulations employing coarse-grained models that have proven extremely successful in many branches of polymer physics, namely the bond-fluctuation model and the self-avoiding walk model. Apa…

Spatial heterogeneity in glassy polystyrene detected by deuteron NMR relaxation

Using deuteron NMR, the dynamics of supercooled polystyrene-d 3 was investigated near the calorimetric glass transition. At these temperatures non-exponential spin lattice relaxation is found, indicating the presence of spatial heterogeneity. With increasing temperature, structural relaxation becomes fast enough to average efficiently over different spatial environments, leading to exponential magnetization decays. A qualitative comparison with toluene as a representative of a low molecular weight glass former is carried out. Indications are found that in polystyrene the observed averaging process is more effective at T g than it is in toluene.

Dynamic heterogeneity in supercooled ortho-terphenyl studied by multidimensional deuteron NMR

Using deuteron NMR, we have studied molecular reorientation rates and rate exchange processes in supercooled ortho-terphenyl. We monitor the re-equilibration of differently selected subensembles through four-time stimulated echo experiments. A comparison of the two-time with the four-time echoes suggests that the characteristic time scales for reorientation and dynamical exchange are relatively similar. The four-time correlation functions were described using various multi-state rate exchange models.

Nonlinear response theory for Markov processes: simple models for glassy relaxation.

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature $T_0$ determined by the value of the asymmetry. In a narrow temperature range around $T_0$, the modulus of the frequency-dependent cubic response shows a peak at a frequency …

Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependency of the respective rates. We discuss two different kinds of counting statistics, the event-counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle-counting. While in the former case all transitions are counted, cycle-counting means that we focus on one type of transitions. This might be advantageous in p…

Aging effects manifested in the potential-energy landscape of a model glass former

We present molecular dynamics simulations of a model glass-forming liquid (the binary Kob-Anderson Lennard-Jones model) and consider the distributions of inherent energies and metabasins during aging. In addition to the typical protocol of performing a temperature jump from a high temperature to a low destination temperature, we consider the temporal evolution of the distributions after an 'up-jump', i.e. from a low to a high temperature. In this case the distribution of megabasin energies exhibits a transient two-peak structure. Our results can qualitatively be rationalized in terms of a trap model with a Gaussian distribution of trap energies. The analysis is performed for different syste…

Correlation of primary and secondary relaxations in a supercooled liquid

The widespread assumption that primary and secondary relaxations in glass-forming materials are independent processes is scrutinized using spin-lattice relaxation weighted stimulated-echo spectroscopy. This nuclear magnetic resonance (NMR) technique is simultaneously sensitive to the dynamics on well-separated time scales. For the deeply supercooled liquid sorbitol, which exhibits a strong secondary relaxation, the primary relaxation (that is observable using NMR) can be modified by suppressing the contributions of those subensembles which are characterized by relatively slow secondary relaxations. This is clear evidence for a correlation between primary and secondary relaxation times. In t…

Kerr effect as a tool for the investigation of dynamic heterogeneities

We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxation in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of non-inertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show that exchange between relatively 'slow' and 'fast' environments does not affect the possibility of …

Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin models.

The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning experiment (NHB) for temperatures below the respective critical temperatures. It is shown that it is possible to select dynamic features in the out-of-equilibrium dynamics of both models, one of the hallmarks of dynamic heterogeneities. The behavior of the s-SK model and the s-FM in three dimensions is very similar, showing dynamic heterogeneities in the long time behavior, i.e. in the aging regime. The appearence of dynamic heterogeneities in the s-SK model explicitly demonstr…

Kommentar zu: H. Mustroph, S. Ernst “Das Franck-Condon-Prinzip”

Die Zeitschrift “Chemie in unserer Zeit” wendet sich an ein breites Leserspektrum. Sie will zuverlassig uber neue Entwicklungen in der Chemie und verwandten Gebieten berichten sowie komplexe Sachverhalte auch fur den Nichtfachmann verstandlich aufbereiten. Mit grosem Bedauern kommen wir jedoch zu der Einschatzung, dass der Beitrag “Wer kennt es noch? Das Franck-Condon-Prinzip” von H. Mustroph und S. Ernst (im Folgenden als Ref. 1 bezeichnet) nach unserem Ermessen diesem Anspruch nicht gerecht wird. Der Beitrag enthalt einige erhebliche fachliche Fehler sowie sachlich unbegrundete und zum Teil irrefuhrende Kritik an Lehrbuchinhalten und wissenschaftlichen Arbeiten. Wir sehen es daher geboten…

Intramolecular structural parameters are key modulators of the gel-liquid transition in coarse grained simulations of DPPC and DOPC lipid bilayers

The capability of coarse-grained models based on the MARTINI mapping to reproduce the gel-liquid phase transition in saturated and unsaturated model lipids was investigated. We found that the model is able to reproduce a lower critical temperature for 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) with respect to 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Nonetheless, the appearance of a gel phase for DOPC is strictly dependent on the intramolecular parameters chosen to model its molecular structure. In particular, we show that the bending angle at the coarse-grained bead corresponding to the unsaturated carbon-carbon bond acts as an order parameter determining the temperature of …

Aging in a free-energy landscape model for glassy relaxation. II. Fluctuation-dissipation relations.

Several fluctuation-dissipation relations are investigated for a simple free-energy landscape model designed to describe the primary relaxation in supercooled liquids. The calculations of the response and of the correlation functions are performed for a quench from a high temperature to a low temperature. In the model, all dynamical quantities reach equilibrium after long times, but for times shorter than the re-equilibration time they do not exhibit time-translational invariance and the fluctuation-dissipation theorem is violated. Two measures for these violations are considered. One such measure is given by the slope in a plot of the integrated response versus the correlation function and…

Nature of the non-exponential primary relaxation in structural glass-formers probed by dynamically selective experiments

Several experimental methods feature the potential to distinguish between slow and fast contributions to the non-exponential, ensemble averaged primary response in glass-forming materials. Some of these techniques are based on the selection of subensembles using multi-dimensional nuclear magnetic resonance, optical bleaching, and non-resonant spectral hole burning. Others, such as the time-dependent solvation spectroscopy, measure microscopic responses induced by local perturbations. Using several of these methods it could be demonstrated for various glass-forming materials that the non-exponential relaxation results from a superposition of dynamically distinguishable entities. The experime…

Impact of local compressive stress on the optical transitions of single organic dye molecules

The ability to mechanically control the optical properties of individual molecules is a grand challenge in nanoscience and could enable the manipulation of chemical reactivity at the single-molecule level. In the past, light has been used to alter the emission wavelength of individual molecules or modulate the energy transfer quantum yield between them. Furthermore, tensile stress has been applied to study the force dependence of protein folding/unfolding and of the chemistry and photochemistry of single molecules, although in these mechanical experiments the strength of the weakest bond limits the amount of applicable force. Here, we show that compressive stress modifies the photophysical …

Model calculations for vibrational properties of disordered solids and the “boson peak”

Abstract It is demonstrated that a disordered system of coupled classical harmonic oscillators with a continuous distribution of coupling parameters exhibits generally a low-frequency enhancement (“boson peak”) of the density of states, as compared with the Debye law. This phenomenon is most pronounced if the system is close to an instability. This is shown by means of a scalar model on a simple cubic lattice. The force constants are assumed to fluctuate from bond to bond according to a Gaussian distribution which is truncated at its lower end. The model is solved for the density of states and the one-phonon dynamic structure factor S(q, ω) by applying the two-site coherent potential approx…

Force probe simulations using a hybrid scheme with virtual sites.

Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method an…

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies.

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene un…

Nonresonant holeburning in the Terahertz range: Brownian oscillator model

The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the respon…

Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline β-eucryptite

Abstract Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7 Li and 9 Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I =3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener–Broekaert pulse sequence are derived. Extensions to larger spin systems are also …

Microscopic origin of the nonexponential dynamics in a glassy crystal

The origin of the slow relaxation and of the dynamic heterogeneity is studied for an orientation-ally disordered crystal, orthocarborane, composed of quasi-icosahedrally shaped molecules. Multidimensional deuteron magnetic resonance reveals that large jump angles dominate their complex, anisotropic reorientational motion. It involves a sequence of small-angle tilts about locally preferred axes as well as symmetry adapted threefold jumps. The intrinsic dynamics of this glassy crystal is nonexponential and can be fully accounted for in terms of the tilt and jump motion.

Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules

We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structural details and solvent properties on the mechanical unfolding pathways. The system consists of two calixarene "cups" that form a catenane structure via interlocked aliphatic loops of tunable length. The dimer shows reversible rebinding, and the kinetics of the system can be understood in terms of a two-state model for shorter loops (≤14 CH2 units) and a three-state model for longer loops (≥15 CH2 units). The various conformational states of the dimer are stabilized by networks of hydrogen bonds, the mechanical susceptibility of which can be altered by changi…

Force probe simulations using an adaptive resolution scheme

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute a…

Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding

We present a dynamic coarse-graining technique that allows to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSM), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling we additionally perform steered molecular dynamics simulations and find excellen…

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the anal…

Fluctuation-dissipation relations for Markov processes.

The fluctuation-dissipation relation is calculated for stochastic models obeying a master equation with continuous time. In the general case of a nonstationary process, there appears to be no simple relation between the response and the correlation. Also, if one considers stationary processes, the linear response cannot be expressed via time-derivatives of the correlation function alone. In this case, an additional function, which has rarely been discussed previously, is required. This so-called asymmetry depends on the two times also relevant for the response and the correlation and it vanishes under equilibrium conditions. The asymmetry can be expressed in terms of the propagators and the…

Nonresonant dielectric hole-burning spectroscopy on a titanium-modified lead magnesium niobate ceramic

Nonresonant dielectric hole-burning experiments were performed on the titanium-modified relaxor ferroelectric lead magnesium niobate around the diffuse maximum in the dielectric permittivity. After applying large alternating electric pump fields we monitored the polarization response to small field steps for times between 0.3 ms and 100 s. Depending on the frequency of the pump oscillation a speedup of the polarization response was observed with a maximum located around times corresponding to the inverse pump frequency. The refilling of the dielectric holes was investigated for several temperatures, pump frequencies, and pump field amplitudes. It proceeded always slower than the time scale …

Nonresonant dielectric hole burning spectroscopy of supercooled liquids

The nonexponential response of propylene carbonate and glycerol near their glass transitions could be selectively altered using nonresonant spectral hole burning (NSHB) experiments. This observation provides evidence of the existence of a distribution of relaxation times in these supercooled liquids. NSHB is based on a pump, wait, and probe scheme and uses low-frequency large amplitude electrical fields to modify the dielectric relaxation. The temporal evolution of the polarization of the sample is then measured subsequent to a small voltage step. By variation of a recovery time inserted between pump and probe, the refilling of the spectral features could be monitored and was found to take …

Rotational Correlation Functions of Single Molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict non-exponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.