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

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

{2,6-Bis[(di-tert-butyl­phosphino)­methyl]­phenyl}chloridonickel(II)

In the title compound, [Ni(C24H43P2)Cl], the Ni atom adopts a distorted square-planar geometry, with the P atoms of the 2,6-bis­[(di-tert-butyl­phosphino)meth­yl]phenyl ligand trans to one another. The P—Ni—P plane is twisted out of the plane of the aromatic ring by 21.97 (6)°

A biomechanical perspective on perineal injuries during childbirth

Background and objective: Childbirth trauma is a major health concern that affects millions of women worldwide. Severe degrees of perineal trauma, designated as obstetric anal sphincter injuries (OASIS), and levator ani muscle (LAM) injuries are associated with long-term morbidity. While significant research has been conducted on LAM avulsions, less attention has been given to perineal trauma and OASIS, which affect up to 90% and 11% of vaginal deliveries, respectively. Despite being widely discussed, childbirth trauma remains unpredictable. This work aims to enhance the modeling of the maternal musculature during childbirth, with a particular focus on understanding the mechanisms underlying the often overlooked perineal injuries. Methods: A geometrical model of the pelvic floor muscles (PFM) and perineum (including the perineal body, ischiocavernosus, bulbospongiosus, superficial and deep transverse perineal muscles) was created. The muscles were characterized by a transversely isotropic visco-hyperelastic constitutive model. Two simulations of vaginal delivery were conducted with the fetus in the vertex presentation and occipito-anterior position, with and without the perineum. Results: The simulation that considered the perineum exhibited higher stresses over an extended area of the PFM, which suggests that including additional structures can impact the obtained results. The maximum stretch of the urogenital hiatus was 2.94 and the maximum stress was 23.86 kPa. The perineal body reached a maximum stretch of 1.95, which was more pronounced near the urogenital hiatus, where perineal tears may occur. The external anal sphincter's transverse diameter decreased by 51% and the maximum principal stresses were observed in the area close to the perineal body, where OASIS can occur. Conclusions: The present study emphasizes the importance of including most structures involved in vaginal delivery in its biomechanical analysis and represents another step further in the understanding of perineal injuries and OASIS. The superior region of the perineal body and its connection to the urogenital hiatus and anal sphincter have been identified as the most critical regions, highly susceptible to injury

Segment diffusion and nuclear magnetic resonance spin-lattice relaxation of polymer chains confined in tubes: Analytical treatment and Monte Carlo simulation of the crossover from Rouse to reptation dynamics

The dynamics of polymer chains in model tubes of variable diameter and varying chain and wall potentials was studied. The study was carried out using analytical treatment and Monte Carlo simulations of the crossover from Rouse to reptation dynamics. It was found that depending on the tube diameter, a crossover from Rouse to reptation behavior occurred

Self-diffusion in fluids in porous glass: Confinement by pores and liquid adsorption layers

Diffusion coefficients of 10 different polar and nonpolar liquids filled in porous glasses with mean pore diameters of 4 or 30 nm were determined with the aid of the NMR field-gradient technique. In the time scale of these experiments (0.3 to 500 ms) diffusion coefficients were found to be time independent. Within the experimental error, no influence of the polarity of the adsorbate can be stated. The diffusion coefficients of all investigated fluids in glass with 4 and 30 nm pores were reduced by factors of 0.17 and 0.63, respectively, relative to the bulk values. This relatively weak reduction can be explained by considering the known porosities of the adsorbents. The second objective of this study was to examine the diffusion behaviour below the melting point of adsorbates in porous glass. Fluids confined in pores do not freeze at the bulk freezing temperatures. In this respect, two phases must be distinguished. A maximal two monolayer thick film adsorbed on the inner surfaces does not crystallize at all, whereas the 'free' fraction of the fluid in the pores freezes at reduced temperatures according to the Gibbs-Thompson relation. The nonfrozen surface layers form a network in which self-diffusion can be investigated. Experiments have been carried out with cyclohexane. A reduction factor of 0.06 was found relative to the extrapolated values of the entirely unfrozen fluid in porous glass with a mean pore diameter of 30 nm. It is, thus, demonstrated that molecules in adsorption layers virtually retain their translational degrees of freedom along the surfaces. The lowering of the diffusivity is mainly due to the geometric restriction rather than to the interaction with the surface

Proton and deuteron field-cycling NMR relaxometry of liquids confined in porous glasses

Polar and non-polar liquids in porous glasses have been studied by proton and deuteron field-cycling NMR relaxometry. The mean pore diameters were 4 nm, 30 nm and 208 nm. The frequency dependence of the spin-lattice relaxation time T1 is strongly influenced by the polarity of the adsorbate. Non-polar liquids show a flat T1 dispersion compared with polar species. We designate the two cases as 'weak' and 'strong' adsorption respectively. Molecules of liquids at surfaces are known to adopt a preferential orientation, whereas they retain a high diffusivity. Therefore, reorientations mediated by translational displacements (RMTD) must contribute to the correlation function which decays on a timescale of up to eight orders of magnitude greater than in the bulk. The high diffusivity at the surface is made plausible by a mechanism called bulk-mediated surface diffusion recently proposed by Bychuk and O'Shaughnessy [O.V. Bychuk and B. O'Shaughnessy, J. Chem. Phys., 101 (1994) 772]. These authors found that the displacements effective on the surface can be described as the result of Levy walks. They therefore obey a Cauchy distribution. This work employs the Cauchy distribution for a numerical derivation of a surface correlation function, g(r/c), which correctly reproduces the typical correlation lengths of the substrate and thus renders the notion of the liquid molecules performing Levy walks reasonable. The difference in T1 dispersion behaviours of polar and non-polar adsorbates disappears when the free liquid is frozen while the approximately two monolayers thick surface film remains liquid. The T1 dispersions are then equally steep irrespective of the polarity. This indicates that a non-polar liquid confined to a thin, topologically two-dimensional layer on a polar surface undergoes the same relaxation mechanism as a strongly adsorbed polar liquid which is dominated by RMTD processes. | Polar and non-polar liquids in porous glasses have been studied by proton and deuteron field-cycling NMR relaxometry. The frequency dependence of the spin-lattice relaxation time T1 is strongly influenced by the polarity of the adsorbate. Non-polar liquids show a flat T1 dispersion compared with polar species. The difference in T1 dispersion behaviors of polar and non-polar adsorbates disappears when the free liquid is frozen while the approximately two monolayers thick surface film remains liquid. The T1 dispersions are then equally steep irrespective of the polarity. This indicates that a non-polar confined to a thin, topologically two-dimensional layer on a polar undergoes the same relaxation mechanism as a strongly adsorbed polar liquid dominated by RMTD processes