Dynamic mechanical response of polymer networks

The dynamic-mechanical response of flexible polymer networks is studied in the framework of tube model, in the limit of small affine deformations, using the approach based on Rayleighian dissipation function. The dynamic complex modulus G* is calculated from the analysis of a network strand relaxation to the new equilibrium conformation around the distorted primitive path. Chain equilibration is achieved via a sliding motion of polymer segments along the tube, eliminating the inhomogeneity of the polymer density caused by the deformation. The characteristic relaxation time of this motion separates the low-frequency limit of the complex modulus from the high-frequency one, where the main role is played by chain entanglements, analogous to the rubber plateau in melts. The dependence of storage and loss moduli, G' and G'', on crosslink and entanglement densities gives an interpolation between polymer melts and crosslinked networks. We discuss the experimental implications of the rather short relaxation time and the slow square-root variation of the moduli and the loss factor tan at higher frequencies.Comment: Journal of Chemical Physics (Oct-2000); Lates, 4 EPS figures include

High Resolution Ex Vivo Diffusion Tensor Distribution MRI of Neural Tissue

Neural tissue microstructure plays a key role in developmental, physiological and pathophysiological processes. In the continuing quest to characterize it at ever finer length scales, we use a novel diffusion tensor distribution (DTD) paradigm to probe microstructural features much smaller than the nominal MRI voxel size. We first assume the DTD is a normal tensor variate distribution constrained to lie on the manifold of positive definite matrices, characterized by a mean and covariance tensor. We then estimate the DTD using Monte Carlo signal inversion combined with parsimonious model selection framework that exploits a hierarchy of symmetries of mean and covariance tensors. High resolution multiple pulsed field gradient (mPFG) MRI measurements were performed on a homogeneous isotropic diffusion phantom (PDMS) for control, and excised visual cortex and spinal cord of macaque monkey to investigate the capabilities of DTD MRI in revealing neural tissue microstructural features using strong gradients not typically available in clinical MRI scanners. DTD-derived stains and glyphs, which disentangle size, shape, and orientation heterogeneities of microscopic diffusion tensors, are presented for all samples along with the distribution of the mean diffusivity (MD) within each voxel. We also present a new glyph to visualize the symmetric (kurtosis) and asymmetric parts of the fourth-order covariance tensor. An isotropic mean diffusion tensor and zero covariance tensor was found for the isotropic PDMS phantom, as expected, while the covariance tensor (both symmetric and asymmetric parts) for neural tissue was non-zero indicating that the kurtosis tensor may not be sufficient to fully describe the microstructure. Cortical layers were clearly delineated in the higher moments of the MD spectrum consistent with histology, and microscopic anisotropy was detected in both gray and white matter of neural tissue. DTD MRI captures crossing and splaying white matter fibers penetrating into the cortex, and skewed fiber diameter distributions in the white matter tracts within the cortex and spinal cord. DTD MRI was also shown to subsume diffusion tensor imaging (DTI) while providing additional microstructural information about tissue heterogeneity and microscopic anisotropy within each voxel.Peer reviewe

Diffusion coefficient measurement using a temperature‐controlled fluid for quality control in multicenter studies

Purpose: To present the use of a quality control ice‐water phantom for diffusion‐weighted magnetic resonance imaging (DW‐MRI). DW‐MRI has emerged as an important cancer imaging biomarker candidate for diagnosis and early treatment response assessment. Validating imaging biomarkers through multicenter trials requires calibration and performance testing across sites. Materials and Methods: The phantom consisted of a center tube filled with distilled water surrounded by ice water. Following preparation of the phantom, ≈30 minutes was allowed to reach thermal equilibrium. DW‐MRI data were collected at seven institutions, 20 MRI scanners from three vendors, and two field strengths (1.5 and 3T). The phantom was also scanned on a single system on 16 different days over a 25‐day period. All data were transferred to a central processing site at the University of Michigan for analysis. Results: Results revealed that the variation of measured apparent diffusion coefficient (ADC) values between all systems tested was ±5%, indicating excellent agreement between systems. Reproducibility of a single system over a 25‐day period was also found to be within ±5% ADC values. Overall, the use of an ice‐water phantom for assessment of ADC was found to be a reasonable candidate for use in multicenter trials. Conclusion: The ice‐water phantom described here is a practical and universal approach to validate the accuracy of ADC measurements with ever changing MRI sequence and hardware design and can be readily implemented in multicenter clinical trial designs. J. Magn. Reson. Imaging 2011. © 2011 Wiley‐Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87048/1/22363_ftp.pd

Magnetic resonance in porous media: Recent progress

Recent years have seen significant progress in the NMR study of porous media from natural and industrial sources and of cultural significance such as paintings. This paper provides a brief outline of the recent technical development of NMR in this area. These advances are relevant for broad NMR applications in material characterization.open283

Resolution limit of cylinder diameter estimation by diffusion MRI: The impact of gradient waveform and orientation dispersion

Diffusion MRI has been proposed as a non-invasive technique for axonal diameter mapping. However, accurate estimation of small diameters requires strong gradients, which is a challenge for the transition of the technique from preclinical to clinical MRI scanners, since these have weaker gradients. In this work, we develop a framework to estimate the lower bound for accurate diameter estimation, which we refer to as the resolution limit. We analyse only the contribution from the intra-axonal space and assume that axons can be represented by impermeable cylinders. To address the growing interest in using techniques for diffusion encoding that go beyond the conventional single diffusion encoding (SDE) sequence, we present a generalised analysis capable of predicting the resolution limit regardless of the gradient waveform. Using this framework, waveforms were optimised to minimise the resolution limit. The results show that, for parallel cylinders, the SDE experiment is optimal in terms of yielding the lowest possible resolution limit. In the presence of orientation dispersion, diffusion encoding sequences with square-wave oscillating gradients were optimal. The resolution limit for standard clinical MRI scanners (maximum gradient strength 60-80 mT/m) was found to be between 4 and 8 μm, depending on the noise levels and the level of orientation dispersion. For scanners with a maximum gradient strength of 300 mT/m, the limit was reduced to between 2 and 5 μm

Experimental tests of polymer reptation : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University

Pulsed Gradient Spin Echo Nuclear Magnetic Resonance (PGSE-NMR) and rheology measurements were used to test whether the dynamics of entangled polymer chains in semidilute solution follow the reptation theory. Nine molar masses from 1 to 20 million daltons at a fixed concentration of 4.96% w/v along with a range of concentrations from 4.96% to 23.58% w/v at fixed molar mass of 3 million daltons were studied using PGSE-NMR techniques. The response to mechanical deformation of five different concentrations from 4.96% to 23.58% w/v at fixed molar mass of 3.9 million daltons was also studied. The distance and time scales accessed by PGSE-NMR were 20 to 1000 nm and 10 to 3000 ms respectively. As a result the mean square segmental motion over three reptation regimes was obtained and the reptation finger print, 〈(r(t) - r(0))〉 ~ t1/4, was observed. The resulting concentration and molecular weight scaling laws for the tube disengagement time, center of mass diffusion and the tube diameter, which were obtained in PGSE-NMR and rheology experiments, were found to be in good agreement with the reptation theory and its standard modifications, and a good quantitative fit to the mean square displacement was given by this theory. Local anisotropic motion of polymer chains at the level of the Rouse time was observed using double-PGSE NMR methods. These suggested a possible cooperative motion of polymer chains in entangled environment which challenges the basic assumptions of the reptation theory. Evidence of intra-chain spin diffusion was found. As a consequence relevant corrections incorporating the phenomenon into the PGSE-NMR data had to be made