Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially filled with D$_2$O, were examined with NMR (nuclear magnetic resonance) microscopy for rendering proton spin density maps. The propagating proton/deuteron inter-diffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk, $d_w$, evaluated from the diffusion measurements on the one hand and the fractal dimension, $d_f$, deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

Critical fluctuations and random-anisotropy glass transition in nematic elastomers

We carry out a detailed deuterium NMR study of local nematic ordering in polydomain nematic elastomers. This system has a close analogy to the random-anisotropy spin glass. We find that, in spite of the quadrupolar nematic symmetry in 3-dimensions requiring a first-order transition, the order parameter in the quenched ``nematic glass'' emerges via a continuous phase transition. In addition, by a careful analysis of the NMR line shape, we deduce that the local director fluctuations grow in a critical manner around the transition point. This could be the experimental evidence for the Aizenman-Wehr theorem about the quenched impurities changing the order of discontinuous transition

Associations of Maternal Complaints to Levator Ani Muscle Trauma within 9 Months after Vaginal Birth: A Prospective Observational Cohort Study

Introduction: Pelvic floor trauma in the form of partial or complete avulsions of the levator ani muscle (LAM) affects 6-42% of women after vaginal birth and can cause tremendous long-term morbidity. Many studies assessed morphological pelvic floor trauma after childbirth but lacked to evaluate women's associated short-term complaints. A proper assessment of trauma and subjective complaints after birth could help to assess possible associations between them and their relevance to women's daily life. Therefore, we aimed to assess women's complaints within the first months after birth in association to their LAM trauma. Materials and methods: Between 3/2017 and 4/2019, we prospectively evaluated vaginal births of 212 primiparous women with singletons in vertex presentation ≥ 36 + 0 gestational weeks for levator ani muscle (LAM) trauma by translabial ultrasound, for pelvic organ prolapse by clinical examination, and for urogynecological complaints using questionnaires 1-4 days (P1), 6-10 weeks (P2), and 6-9 months (P3) after birth. The questionnaires were self-designed but oriented to and modified from validated questionnaires. Women's complaints were evaluated for P1-P3 according to their LAM trauma state. Results: At P1, 67% of women showed an intact LAM, whereas 14.6% presented a hematoma, 6.6% a partial avulsion (PAV), and 11.8% a complete avulsion (CAV). At P2, 75.9% showed an intact LAM, 9.9% a PAV, and 14.2% a CAV. At P3, 72.9% of women with a LAM trauma in P1 and/or P2 were assessed with 21.6% being intact and 39.2% having a PAV and CAV, respectively. Obstetrical and baseline characteristics differed slightly between the groups. When comparing the time before and during pregnancy with the time after childbirth, birth itself affected women's complaints in all LAM state groups, but the presence of a LAM trauma, especially a CAV, had more negative effects. Conclusions: Vaginal birth changes the anatomical structure of the maternal birth canal and genital tract, and it alters women's perceptions and body function. In our study, LAM trauma did not change these effects tremendously within the first months. Therefore, other maternal, fetal, and obstetrical factors need consideration for the explanation of maternal complaints, in addition to long-term effects of trauma and dysfunction of the LAM and other birth canal structures

The Measurement of pO2 by O2 Electrode in the Presence of Changing pCO2

Studies on the transport of O2 and CO2 in the alveoli and blood have focused on simultaneous measurements of the two gases with classical instruments; an interaction between the two gases has been assumed (see Bohr Effect and Rahn-Otis Plot). Nevertheless, of late years with wide use of the Kimmich-Kreuzer Oxygen Electrode in liquids and gases, the measurements have included oxygen alone. These small (2mm) polarographic catheter electrodes have been used in both physiologic and bioengineering applications. Within a particular range of polarization voltage, the electrode current is limited by O2 diffusion across a membrane; i.e., at a constant polarization voltage, current is linearly related to pO2. Since it is often the case that measurements of pO2 are taken while pCO2 is changing, CO2 effects on the electrode current should be known and corrected for. In the present experiments, electrical currents at 5% and 21% O2 with varying amounts of CO2 were measured. Polarograms (a plot of current v. voltage) made in the presence and absence of CO2 were compared. The pO2 measurement is significantly affected by CO2 at 21% O2, but not a 5% O2; i.e., the O2 value changed with different CO2 levels. These results are particularly interesting since the electrode membrane is a physical model of the alveolar membrane

A model for the generic alpha relaxation of viscous liquids

Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more low-lying beta processes [Olsen et al, Phys. Rev. Lett. {\bf 86} (2001) 1271]. Assuming that long-wavelength fluctuations dominate the dynamics, a model for the dielectric alpha relaxation based on the simplest coupling between the density and dipole density fields is proposed here. The model, which is solved in second order perturbation theory in the Gaussian approximation, reproduces the generic features of alpha relaxation

The twice renormalized rouse formalism of polymer dynamics. Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended including terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts such as the reptation (tube) model or the polymer mode-mode coupling formalism, the predictions perfectly compare with all results of recent spin-lattice relaxation dispersion and diffusion experiments as well as computer simulations. On the other hand, the twice renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity largely is a manifestation of collective many-chain modes. In the rigorous sense, no such multi-chain treatment has been established so far to our knowledge. The necessity to consider inter-chain cooperativity in any really comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Polymer chain dynamics predicted by n-renormalized rouse models: Numerical studies

Features of the renormalized and twice renormalized Rouse models were examined numerically. Based on numerical evaluations of the generalized Langevin equation in renormalization approaches, nonexponential normal mode autocorrelation functions were derived, that can be described over two orders of magnitude by stretched exponential functions. The mode number dependence of the stretching parameter was evaluated. The consequences of the nonexponential correlation functions on dynamical properties are discussed. As a basis for predictions for the behavior of diffusion and spin-lattice relaxation dispersion, the time dependence of the mean-squared segment displacement and of the autocorrelation function of the segment tangential vector, respectively, were obtained taking into account finite chain lengths

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by a stretched exponential function Cp(t) ∝ exp([-(t/ τ*p)βp , where βp is the stretching parameter dependent on the number p of the Rouse mode and τ*p is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉nRR In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〉b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied

Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: Application to polymer melts

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades. © 2007 American Institute of Physics