Dynamics of supercooled liquids and glassy solids

Control of the electronic energy transfer pathway between two single fluorophores by dual pulse excitation.

We report on the control of the energy transfer pathway in individual donor-acceptor dyads by proper timing of light pulses matching the donor and acceptor transition frequencies, respectively. Excitation of both chromophores at virtually the same time induces efficient singlet-singlet annihilation, whereby excitation energy effectively flows from the acceptor to the donor. The dual pulse excitation scheme implemented here allows for all-optical switching of the fluorescence intensity at the single-molecule level. The population of higher excited states at the donor site was found to significantly increase the photobleaching probability.

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…

Studying RNA Using Single Molecule Fluorescence Resonance Energy Transfer

87RbNMR spectra of hydrogen-bondedRb3D(SO4)2andRb3H(SO4)2crystals

The paraelectric and antiferroelectric phases of ${\mathrm{Rb}}_{3}{\mathrm{D}(\mathrm{S}\mathrm{O}}_{4}{)}_{2}$ and ${\mathrm{Rb}}_{3}{\mathrm{H}(\mathrm{S}\mathrm{O}}_{4}{)}_{2}$ were investigated using rubidium NMR. The angle dependence of the second order quadrupole shifted central ${}^{87}\mathrm{Rb}$ transitions was recorded at 300 K. It was found to be in full agreement with the symmetry elements of a monoclinic $A2/a$ structure. The temperature dependence of the magnitude and asymmetry of the electrical field gradient (EFG) tensors at the Rb sites was determined using powder samples and revealed no differences between protonated and deuterated specimens. The antiferroelectric transi…

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…

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.

Single Semiconductor Nanocrystals under Compressive Stress: Reversible Tuning of the Emission Energy

The photoluminescence of individual CdSe/CdS/ZnS core/shell nanocrystals has been investigated under external forces. After mutual alignment of a correlative atomic force and confocal microscope, individual particles were colocalized and exposed to a series of force cycles by using the tip of the AFM cantilever as a nanoscale piston. Thus, force-dependent changes of photophysical properties could be tracked on a single particle level. Remarkably, individual nanocrystals either shifted to higher or to lower emission energies with no indications of multiple emission lines under applied force. The direction and magnitude of these reversible spectral shifts depend on the orientation of nanocrys…

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…

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

The orientational glass studied by nuclear magnetic resonance

Single crystals of the orientational glass have been studied using iodine NMR for temperatures 1.8 K < T < 300 K. Two-dimensional spectroscopy has shown that the quadrupole-perturbed central transitions are predominantly inhomogeneously broadened. The orientational glass transition is already accompanied by a considerable increase of that broadening in the regime of fast motion. Evidence for a random-field smearing of the random-bond-induced freezing process is obtained. Measurements of the spin - lattice relaxation time reveal the existence of a broad distribution of orientational correlation times at low temperatures.

Anisotropic motion of toluene above and below the glass transition studied by 2H NMR

Abstract 2 H nuclear magnetic resonance spin-lattice relaxation experiments on two selectively deuterated toluene molecules have been performed over a wide temperature range, spanning liquid and glassy states, to examine anisotropic molecular dynamics. In the liquid regime, the relaxation data are analyzed by the model of anisotropic rotational diffusion. A more phenomenological ansatz is used for the whole temperature regime to obtain information about anisotropic reorientation and its temperature dependence. We find that the anisotropy is reduced in the supercooled state and the motion becomes approximately isotropic below 140 K which is interpreted as the onset of cooperative reorientati…

Mode-coupling crossover in viscous toluene revealed by neutron and light scattering

The dynamics of supercooled toluene, studied in a GHz-THz range by incoherent neutron and depolarized light scattering, is found to be in full accord with mode coupling predictions. Around the susceptibility minimum, neutron spectra are wavenumber independent and proportional to light scattering data; the fast β-relaxation scaling law applies; amplitude and frequency diverge with power laws that extrapolate towards a crossover temperature Tc K.

Influence of data treatment on the shape of 2H NMR T1 curves

A new interpretation of 2H T1 data of glass-forming systems in the range of the range of the caloric glass transition temperature has been proposed. It is shown that with the traditional treatment of the data the timescale of structural relaxation has an influence on the observed spin-lattice relaxation times. Avoiding this problem with a different treatment of the experimental data, it is possible to compare the 2H T1 data directly with corresponding 1H data.

From strong to fragile glass formers: secondary relaxation in polyalcohols.

We have studied details of the molecular origin of slow secondary relaxation near T(g) in a series of neat polyalcohols by means of dielectric spectroscopy and (2)H NMR. From glycerol to threitol, xylitol, and sorbitol the appearance of the secondary relaxation changes gradually from a wing-type scenario to a pronounced beta peak. It is found that in sorbitol the dynamics of the whole molecule contributes equally to the beta process, while in glycerol the hydrogen bond forming OH groups remain rather rigid compared to the hydrogens bonded to the carbon skeleton.

Probing the electronic state of a single coronene molecule by the emission from proximate fluorophores.

We measured electronic transitions of the 2D graphene-type molecule hexa-peri-hexabenzocoronene (HBC) at the single-molecule level. The large intersystem crossing rate and long triplet state lifetime in the range of seconds are prohibitive for direct single-molecule observation. By covalently coupling fluorescent acceptor molecules (perylenecarboximide, PMI) to HBC, efficient singlet energy transfer gives rise to strong PMI fluorescence. Confocal single-molecule fluorescence microscopy with two excitation colours matching the HBC and PMI transition frequencies, respectively, was conducted. Single HBC-6PMI molecules were readily observed via the PMI emission. It was found that after selectiv…

Antiferroelectric phase transition inRb3D(SO4)2single crystals studied by87RbNMR

The quadrupole perturbed central transition of the magnetic ${}^{87}\mathrm{Rb}$ resonance was used to study ${\mathrm{Rb}}_{3}{\mathrm{D}(\mathrm{S}\mathrm{O}}_{4}{)}_{2}$ single crystals. Three resonance lines were found at room temperature. This result is in accord with the monoclinic space group reported for these crystals and does not require the previously invoked self-trapped proton states. The number of resonance lines quadruples below the antiferroelectric phase transition near 82 K. From the line splitting the order-parameter exponent of the low-temperature phase was found to be $\ensuremath{\beta}=0.2.$ Spin-lattice relaxation times have been determined in the fully protonated an…

Assembly and Separation of Semiconductor Quantum Dot Dimers and Trimers

Repeated precipitation of colloidal semiconductor quantum dots (QD) from a good solvent by adding a poor solvent leads to an increasing number of QD oligomers after redispersion in the good solvent. By using density gradient ultracentrifugation we have been able to separate QD monomer, dimer, and trimer fractions from higher oligomers in such solutions. In the corresponding fractions QD dimers and trimers have been enriched up to 90% and 64%, respectively. Besides directly coupled oligomers, QD dimers and trimers were also assembled by linkage with a rigid terrylene diimide dye (TDI) and separated again by ultracentrifugation. High-resolution transmission electron micrographs show that the …

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.

Correlation of primary relaxations and high-frequency modes in supercooled liquids. II. Evidence from spin-lattice relaxation weighted stimulated-echo spectroscopy

Using spin-lattice relaxation weighted stimulated-echo spectroscopy, we report evidence for a correlation of the primary and secondary relaxation times. The experiments are performed using deuteron nuclear magnetic resonance somewhat above the calorimetric glass-transition of ortho-terphenyl, D-sorbitol, and cresolphthalein-dimethylether. The data analysis is based on the procedure outlined in the accompanying theoretical paper [B. Geil, G. Diezemann, and R. B\"ohmer, Phys. Rev. E 74, 041504 (2006)]. Direct experimental evidence for a modified spin-lattice relaxation is obtained from measurements on a methyl deuterated acetyl salicylic acid glass. The limitations of the present experimental…

The glass transition in (KI)0.5(ND4I)0.5 mixed crystals as studied by deuteron spin-lattice relaxation

Abstract Nuclear spin resonance has been used to study the deuteron magnetization recovery in (KI)0.5(ND4I)0.5 mixed crystals. At high temperatures the spin-lattice-relaxation is exponential. For T ⪅ 45 K deviations from this simple behaviour occur, signalling the onset of spatial inhomogeneities due to the formation of an orientational glass. The results demonstrate that the transition of (KI)0.5(ND4I)0.5 into the glassy state is driven by the freezing of random bonds.

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes

Spin-lattice relaxation rates R1(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R1(T) vs the spin-spin relaxation rate R2(T) and (ii) a plot of R1(T) vs an independently measured reference time τref(T). Using single-frequency s…

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…

Surface-induced order and diffusion in 5CB liquid crystal confined to porous glass.

Liquid crystals confined into small cavities are known to have a weak orientational order even above the nematic-isotropic transition temperature. The surface-induced order and molecular dynamics in this temperature range are studied with the aid of deuteron NMR spectra, spin relaxation times T(1) and T(2,) proton dipolar-correlation effect, and direct measurements of the effective diffusion coefficient for the liquid crystal 5CB confined to controlled-pore glasses. Our results show that an arrangement of molecules parallel to the wall is induced by local molecular interactions between the liquid crystal and solid, resulting in a weak and temperature independent surface order parameter, S(0…

Deuteron NMR investigations of glass and phase transitions in(KI)1−x(ND4I)xmixed crystals

Powdered potassium ammonium iodide mixed crystals with ammonium concentrations of 20% and 70% have been studied using deuteron NMR techniques. For the less doped sample the deuteron line starts to broaden and the spin-lattice relaxation time ${T}_{1}$ becomes nonexponential below about 20 K. These observations indicate the breakdown of ergodicity and the onset of orientational glass freezing. At the lowest temperatures ${T}_{1}$ reaches a plateau value. For the 70% sample a relatively abrupt onset of two-phase behavior at $Tl35\mathrm{K}$ is inferred from measurements of the spin-spin and spin-lattice relaxation times. These observations are taken to indicate an order-disorder transition to…

Correlative atomic force and confocal fluorescence microscopy: single molecule imaging and force induced spectral shifts (Conference Presentation)

A grand challenge in nanoscience is to correlate structure or morphology of individual nano-sized objects with their photo-physical properties. An early example have been measurements of the emission spectra and polarization of single semiconductor quantum dots as well as their crystallographic structure by a combination of confocal fluorescence microscopy and transmission electron microscopy.[1] Recently, the simultaneous use of confocal fluorescence and atomic force microscopy (AFM) has allowed for correlating the morphology/conformation of individual nanoparticle oligomers or molecules with their photo-physics.[2, 3] In particular, we have employed the tip of an AFM cantilever to apply c…

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.

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.

Quantification of the singlet-singlet annihilation times of individual bichromophoric molecules by photon coincidence measurements.

Singlet−singlet annihilation (SSA) times in individual bichromophoric molecules have been quantified by time-resolved photon coincidence measurements. An analytical expression has been derived to obtain the SSA times from the coincidence histograms. The results have been confirmed by Monte Carlo simulations. SSA was found to be about three times faster than the fluorescence lifetime of the chromophores. Considering the spectral overlap for SSA and for energy transfer from an excited to a ground state chromophore, we conclude that in the weak coupling limit for any arrangement of the two chromophores both processes occur on similar time scales.

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.

Geometry and time scale of the rotational dynamics in supercooled toluene

Multidimensional deuteron NMR provides powerful tools for studying molecular reorientation in supercooled liquids. We present results on selectively deuterated toluene-${d}_{5},$ which may be one of the molecularly most simple van der Waals glass formers. From two-time correlation functions the time scale of reorientation was obtained slightly above the calorimetric glass transition temperature. The applied stimulated echo method provides a geometry parameter that, in analogy to $q$-dependent scattering experiments, allows one to investigate the geometry of the elementary rotational process. Continuous time random walk computer simulations were used for the interpretation of the data. It is…

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…

State transition identification in multivariate time series (STIMTS) applied to rotational jump trajectories from single molecules

Time resolved data from single molecule experiments often suffer from contamination with noise due to a low signal level. Identifying a proper model to describe the data thus requires an approach with sufficient model parameters without misinterpreting the noise as relevant data. Here, we report on a generalized data evaluation process to extract states with piecewise constant signal level from simultaneously recorded multivariate data, typical for multichannel single molecule experiments. The method employs the minimum description length principle to avoid overfitting the data by using an objective function, which is based on a tradeoff between fitting accuracy and model complexity. We val…

Statistical analysis of time resolved single molecule fluorescence data without time binning

We depict two algorithms to calculate correlation functions from two different time resolved single molecule fluorescence experiments without the need of time binning. Our first procedure allows to calculate the reduced linear dichroism from polarization resolved fluorescence data. Since we process single photon counts instead of time binned data, considerably faster fluctuations of the dichroism can be analyzed than with conventional methods. With our second procedure time resolved fluorescence obtained with a time correlated single photon counting setup can be analyzed with respect to fluorescence lifetime fluctuations. Again this new algorithm processes single photon events making time b…

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 …

Single molecule probing of dynamics in supercooled polymers

6 pages; International audience; Fluorescence experiments with single BODIPY molecules embedded in a poly(methyl acrylate) matrix have been performed at various temperatures in the supercooled regime. By using pulsed excitation, fluorescence lifetime and linear dichroism time trajectories were accessible at the same time. Both observables have been analyzed without data binning. While the linear dichroism solely reflects single particle dynamics, the fluorescence lifetime observable depends on the molecular environment, so that the dynamics from the polymer host surrounding a chromophore contributes to this quantity. We observe that the lifetime correlation decays slightly faster than polar…

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…

Slow and fast methyl group rotations in fragile glass-formers studied by NMR

Abstract The spin-lattice relaxation times of the selectively ring deuterated, fragile glass-formers propylene carbonate and toluene were compared with those measured for species which were specifically labeled at the methyl groups. It was found that the dynamics of the CD 3 group is strongly decoupled from that associated with the primary response of toluene, while for propylene carbonate the degree of decoupling is relatively weak. The experimental results could be described successfully using a model which takes into account the ring dynamics as well as those of the methyl group.

Pseudo-stochastic multiple-pulse excitation in dielectric spectroscopy: application to a relaxor ferroelectric

The nonlinear dielectric response of a lead titanate-doped lead magnesium niobate relaxor ferroelectric was studied using pseudo-stochastic binary electrical field excitation. The polarization was recorded for various pulse spacings and electrical field amplitudes. The decay of the field-polarization cross-correlation function could be accelerated by increasing the amplitude of the pulse fields. The extension of these experiments in order to record multidimensional dielectric spectra is illustrated.

Conformational Dynamics of the Dengue Virus Protease Revealed by Fluorescence Correlation and Single-Molecule FRET Studies.

The dengue virus protease (DENV-PR) represents an attractive target for counteracting DENV infections. It is generally assumed that DENV-PR can exist in an open and a closed conformation and that active site directed ligands stabilize the closed state. While crystal structures of both the open and the closed conformation were successfully resolved, information about the prevalence of these conformations in solution remains elusive. Herein, we address the question of whether there is an equilibrium between different conformations in solution which can be influenced by addition of a competitive inhibitor. To this end, DENV-PR was statistically labeled by two dye molecules constituting a FRET …

Intramolecular electronic excitation energy transfer in donor∕acceptor dyads studied by time and frequency resolved single molecule spectroscopy

Electronic excitation energy transfer has been studied by single molecule spectroscopy in donor/acceptor dyads composed of a perylenediimide donor and a terrylenediimide acceptor linked by oligo(phenylene) bridges of two different lengths. For the shorter bridge (three phenylene units) energy is transferred almost quantitatively from the donor to the acceptor, while for the longer bridge (seven phenylene units) energy transfer is less efficient as indicated by the occurrence of donor and acceptor emission. To determine energy transfer rates and efficiencies at the single molecule level, several methods have been employed. These comprise time-correlated single photon counting techniques at r…

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.