Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

Relaxation phenomena in critical microemulsion systems

We discuss extensive sets of experimental data including static and dynamic light scattering, ultrasonic velocity measurements and high and low frequency dielectric relaxation, taken in the vicinity the critical point of a ternary microemulsion system. Upon approaching the critical point we observed a slowing down of the dielectric relaxation time and of the first cumulant of the time-dependent droplet density correlation function C²(t) which shows a non-exponential behavior at long time. These features can be well acccounted for by assuming that the microemulsion system is made of polydispersed transient fractal aggregates having a fractal dimension d_f=2.5 and a polydispersity index τ=2.2.     

Do proteins at low temperature behave as glasses? A single-molecule study

We have recorded long spectral diffusion trajectories from individual LH2 pigment-protein complexes from the purple bacterium Rhodobacter sphaeroides at 1.4 K. From these data, the spectral cumulants of the absorption lines of individual, protein-embedded BChl a pigments have been evaluated. It appears that the first and second cumulants cannot be described by the predictions of the well tested standard two-level system (TLS) model for spectral diffusion in glasses. The results of the present study clearly show that there is a fundamental difference between the relaxation behavior of our test protein and that of glasses.     

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

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

Observation of two diffusive relaxation modes in microemulsions by dynamic light scattering

Water-in-oil microemulsions stabilized by AOT and dispersed in n-alkane oils with a constant molar water-to-surfactant ratio were studied by dynamic light scattering. A dilution series (in the range of volume fraction of water plus surfactant, phi approximately 0.02-0.52) was used, which allowed us to extract information about droplet sizes, diffusion coefficients, interactions, and polydispersity from experimental data. We report the observation of two diffusive relaxation modes in a concentrated microemulsion (0.20 < phi < 0.5) due to density (collective diffusion) and concentration or polydispersity (self-diffusion) fluctuations. Below this concentration it was difficult to resolve two exponentials unambiguously, and in this case one apparent relaxation mode was observed. It was found that for a given composition self-diffusion is more pronounced in apparent relaxation mode for a shorter chain length alkane. The concentration dependence of these diffusion coefficients reflects the effect of hard sphere and the supplementary attractive interactions. It was observed that the attractive part becomes more pronounced in the case of a large alkane chain oil at a given temperature. This explains the shift of the region of microemulsion stability to lower temperatures for higher chain length alkanes. Increase in hydrodynamic radius, Rh, obtained from the diffusion coefficient extrapolated to infinite dilution was observed with increase of alkane chain length. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least 3 orders of magnitude longer than the estimated time between droplet collisions.     

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.     

Photon correlation spectroscopy of polymers in the glassy state

Photon correlation spectroscopy has proven to be a very useful technique for studying slowly relaxing density and optical anisotropy fluctuations in bulk polymers near the glass transition. When some of the fluctuations achieve relaxation times much longer than the typical averaging time for the intensity autocorrelation function (10⁴ s), the result must be treated in the partially heterodyned limit. Also, when the sample is near the glass transition but not at equilibrium the correlation function is not stationary in time because the system is relaxing as a whole toward the equilibrium state. The above effects are discussed theoretically and demonstrated experimentally in polystyrene as a function of temperature and pressure. Light scattering with coherent excitation also fluctuates in space as well as in time (as shown in the accompanying paper). The consequences of this effect are discussed. When most of the intensity is associated with fluctuations whose relaxation times are very long in polystyrene, there is still a broad relaxation function evident. This is characteristic of a secondary relaxation process.     

Dynamics of water probed with vibrational echo correlation spectroscopy

Vibrational echo correlation spectroscopy experiments on the OD stretch of dilute HOD in H(2)O are used to probe the structural dynamics of water. A method is demonstrated for combining correlation spectra taken with different infrared pulse bandwidths (pulse durations), making it possible to use data collected from many experiments in which the laser pulse properties are not identical. Accurate measurements of the OD stretch anharmonicity (162 cm(-1)) are presented and used in the data analysis. In addition, the recent accurate determination of the OD vibrational lifetime (1.45 ps) and the time scale for the production of vibrational relaxation induced broken hydrogen bond "photoproducts" ( approximately 2 ps) aid in the data analysis. The data are analyzed using time dependent diagrammatic perturbation theory to obtain the frequency time correlation function (FTCF). The results are an improved FTCF compared to that obtained previously with vibrational echo correlation spectroscopy. The experimental data and the experimentally determined FTCF are compared to calculations that employ a polarizable water model (SPC-FQ) to calculate the FTCF. The SPC-FQ derived FTCF is much closer to the experimental results than previously tested nonpolarizable water models which are also presented for comparison.     

Applications of Fluorescence Correlation Spectroscopy: Polydispersity Measurements

The method of histograms is applied to the determination of polydispersity of particles and molecules in solution from fluorescence correlation spectroscopy (FCS) data. This is an ill-posed problem, which can be overcome by using a common strategy for imposed regularization and constraint conditions. The method developed for evaluating the polydispersity is tested on both computer-generated correlation curves and real FCS data. The results obtained show that FCS measurements can be successfully used for the determination of polydispersity of suspensions, with an efficiency comparable to that of photon correlation spectroscopy (PCS). The advantage of FCS, however, is its better sensitivity to small particles (size <50 nm) and molecules in dilute solutions, as well as its better selectivity. The usefulness of FCS for environmental chemistry is discussed with regard to the obtained results. Copyright 1999 Academic Press.     

Dynamic light scattering by permanent gels: Partial heterodyne and nonergodic medium methods for data evaluation

Four relationships between the intensity and field correlation functions have been used in the analysis of the measured intensity correlation function in dynamic light scattering for four different polymer gel samples. The evaluation of diffusion coefficients was performed using inverse Laplace transformation (ILT) and the cumulante method, respectively. The diffusion coefficients derived from the nonergodic medium method are almost the same as those from the partial heterodyne method when ILT is used. ILT can give similar results by all four procedures even when large baselines for the nonergodic medium method exist. The cumulants method leads to incorrect diffusion coefficients from the correlation functions derived using the nonergodic medium method.     

Synthesis of amphoteric polystyrene particles using mixed initiators

The synthesis of amphoteric polystyrene latex particles, using a mixture of cationic (amidinium based) and anionic (carboxylic acid based) initiators in a surfactant-free emulsion polymerization reaction is investigated; this extends work described in an earlier paper by Bolt et al. Electrophoretic mobility measurements show the effect of the initiator concentration ratio on the isoelectric point (IEP) of the particles. A good correlation with theoretical predictions is obtained. Particle size and polydispersity are determined as a function of the lag time between the addition of each initiator. An increase in particle size and polydispersity is observed at short lag times. It is shown that this is due to the ratio of the cationic to anionic surface charge approaching unity during the reaction. At long lag times an increase in polydispersity may occur due to late-stage, secondary nucleation upon addition of the second initiator. Increasing the reaction pH to reduce the degree of ionization of the cationic initiator greatly reduces the polydispersity and has a significant effect on the IEP of the particles. This effect is ascribed to the burial of a fraction of the neutral amidine groups below the particle surface due to their increased solubility in the monomer. Slow addition of the second initiator was found to reduce the polydispersity of the particles, while maintaining an IEP value consistent with that expected for the ratio of initiators added.     

Quasi-anomalous diffusion processes in entangled solutions of wormlike surfactant micelles

In this article, we present a detailed analysis of the dynamic properties of entangled solutions of semi-flexible, threadlike surfactant micelles. These aggregates were formed by self-association processes in aqueous solutions of cationic surfactants such as cetylpyridinium chloride (CPyCl) or cetyltrimethylammonium bromide (CTAB) after the addition of different amounts of sodium salicylate (NaSal). We performed dynamic light scattering (DLS) experiments in combination with rheological measurements in order to investigate the dynamic properties of these viscoelastic surfactant solutions. In all samples, we observed three distinct relaxation regimes: initial monoexponential decay, followed by a power-law behavior at intermediate observation times. A second monoexponential region was detected at very long times, and this terminal regime described the viscoelastic features of the samples. The fast decay mode was induced by local cooperative motions in the gellike network. The intermediate and slowest decay modes point to the existence of quasi-anomalous diffusion processes. These phenomena are characterized by linear-diffusion properties at long times, and they obeyed anomalous logarithmic slow-dynamics behavior at intermediate time zones. The anomalous diffusion properties at intermediate time scales can be induced by the bending motions of the rod-shaped micelles between two entanglement points. This regime, which was more extended at lower temperatures, was described by the power-law form of the correlation function. The power-law exponent depended on the chemical structure of the surfactants and the temperature. The power-law regime shifted toward earlier times as the gellike network evolved. The slowest mode of the correlation function coincided very well with the shear stress relaxation times of the three-dimensional, transient networks. We observed that the temperature dependence of the slowest mode followed Arrhenius laws. This result provides experimental evidence for thermally activated topological relaxation processes of random fluid phases. We obtained activation energies of approximately 30 kcal/mol, and these data coincided well with previously reported literature values, which were determined in similar surfactant solutions. Characteristic "screening lengths", over which viscous effects became important, could also be determined from the activation energy. The elastic modulus G0, calculated from the slowest mode of the correlation function, was in pretty good agreement with rheological data. The light-scattering spectra were consistent with the theoretical model of dynamical coupling of the concentration fluctuations to viscoelasticity. Since only minute sample volumes are required for advanced DLS experiments, this method to extract viscoelasticity is well suited for advanced studies of gellike biomaterials.     

Effects of nonionic surfactant C12E5 on the cooperative dynamics of water

A dielectric relaxation study of binary mixtures of nonionic surfactant C12E5 + water has been made as a function of temperature in the isotropic micellar, lamellar, and hexagonal regions of the phase diagram. Two dielectric dispersion steps were found and could be assigned to the intermolecular cooperative dynamics of water at the micellar interface and in the bulk water domains. A quantitative analysis is given. The relaxation amplitudes were used to determine effective hydration numbers. The activation energies of water relaxation were calculated from the relaxation times. The data indicate weaker surfactant-water and water-water interactions near the micellar interface compared to those of bulk liquid water. Further analysis revealed the presence of water clusters large enough to show a cooperative relaxation mode even at high surfactant concentrations. However, the relaxation time of this mode is larger compared to that of pure water. This points out the importance of confinement effects on water dynamics.     

An effective method for the discrimination of motional anisotropy and chemical exchange

Analysis of the ratio of transverse and longitudinal relaxation rates (R2/R1) is an approach commonly used for estimation of overall correlation time and identification of chemical exchange in biological macromolecules. However, this analysis fails to distinguish between chemical exchange and motional anisotropy. We describe a simple method for identifying chemical exchange and motional anisotropy using the product, R1R2. In the slow tumbling regime, the R1R2 product results in a constant value that is independent of overall correlation time and motional anisotropy. This analysis provides a simple method for rapidly estimating and dissociating the effects of motional anisotropy and chemical exchange in NMR heteronuclear spin relaxation data. We demonstrate the utility of the method with 15N relaxation data collected on the proteins E. coli ribonuclease H and the trimeric E. coli membrane associated lipoprotein lpp.     

Water behavior in mesoporous materials as studied by NMR relaxometry

Water in mesoporous materials possessing a two-dimensional hexagonal structure has been studied by the variation of its NMR longitudinal relaxation time T(1) as a function of the static magnetic field value, or equivalently of the NMR measurement frequency. This technique, dubbed relaxometry, has been applied from 5 kHz (measurement frequency) up to 400 MHz with various instruments including a variable-field spectrometer operating between 8 and 90 MHz. Moreover, the range 0-5 kHz could be investigated by transverse relaxation, T(2) denoting the corresponding relaxation time, and relaxation in the rotating frame, T(1ρ) denoting the corresponding relaxation time. Measurements of proton relaxation rates (inverse of relaxation times) have been performed with H(2)O and HOD (residual protons of heavy water) at water volumes of 80%, 60%, and 40% relative to the porous volume. Comparison between H(2)O and HOD shows clearly that, above 1 MHz where both sets of data are superposed, relaxation is purely intermolecular and due to paramagnetic relaxation (dipolar interactions of water protons with unpaired electrons of paramagnetic entities). Below 1 MHz, it is possible to subtract the intermolecular contribution (given by HOD data) from H(2)O data so that one is left with intramolecular relaxation which is solely due to water reorientational motions. The analysis of these low-frequency data (in terms of Lorentzian functions) reveals two types of water within the pores: one interacting strongly with the surface and the other corresponding to a second layer. High-frequency data, which arise from paramagnetic relaxation, exhibit again two types of water. Due to their correlation times, one type is assigned to relatively free water within the pores while the other type corresponds to bulk (interparticular) water. Their proportions, given as a function of the volume fraction, are consistent with the above assignments.     

Quantifying the diffusion of a fluid through membranes by double phase encoded remote detection magnetic resonance imaging

We demonstrate that a position correlation magnetic resonance imaging (MRI) experiment based on two phase encoding steps separated by a delay can be used for quantifying diffusion across a membrane. This method is noninvasive, and no tracer substance or concentration gradient across the membrane is required. Because, in typical membranes, the T1 relaxation time of the fluid spins is usually much longer than the T2 time, we developed and implemented a new position correlation experiment based on a stimulated spin-echo, in which the relaxation attenuation of the signal is dominated by T1 instead of T2. This enables using relatively long delays needed in the diffusion measurements. The sensitivity of the double encoded experiment detected in a conventional way is still low because of the low filling factor of the fluid inside the NMR coil around the sample. We circumvent this problem by using the remote detection technique, which significantly increases the sensitivity, making it possible to do the measurements with gaseous fluids that have a low spin-density compared to liquids. We derive a model that enables us to extract a diffusion constant characterizing the diffusion rate through the membrane from the obtained correlation images. The double phase encoded MRI method is advantageous in any kind of diffusion studies, because the propagator of fluid molecules can directly be seen from the correlation image.     

Relaxation of flexible chains in dilute and non‐dilute systems. Dynamic Monte Carlo results for linear and star chains

A dynamic Monte Carlo algorithm is employed to investigate the dynamics of flexible linear and star chains on a cubic lattice at different concentrations. Some results for similar systems are also obtained with an off‐lattice algorithm. Diffusion coefficient, relaxation times and mean size data are combined into friction‐independent ratios in good agreement with the theoretical predictions from the Rouse theory. The relaxation times and amplitudes corresponding to the Rouse normal modes are analyzed in terms of their variation with the mode order. The end‐to‐end vector correlation times obtained from the simulations for linear chains are compared with the theoretical expression obtained from the Rouse theory. Deviations from this theory are observed for the contribution of the different modes in the non‐dilute systems. Finally, the time correlation function corresponding to a subchain's end‐to‐end vector is investigated. The results also show deviations from the Rouse theory, which are in qualitative agreement with the features observed in data from dielectric relaxation experiments of block copolymers.     

Time dependent stretching of aging dynamics in a generalized hydrodynamic model for supercooled liquids

The nonequilibrium dynamics and aging behavior of a supercooled liquid is investigated from an analysis of the correlation of density fluctuations at two different times. The dynamic correlation functions are computed by solving numerically the equations of nonlinear fluctuating hydrodynamics. The aging time dependence follows a modified stretched exponential form with a relaxation time which is dependent on the aging time. This is similar to the behavior seen in the aging data of dielectric response functions of a typical glass forming liquid.