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PubMed2003

Stationary diffusion gradients associated with photosynthetic carbon flux-a study of compartmental versus diffusion-reaction models.

Metabolic processes usually involve diffusion of compounds in addition to their metabolic reactions. Such processes are adequately described by reaction-diffusion models (in the form partial differential equations) which are usually difficult and tedious to solve. Compartmental models (ordinary differential equations) are much easier to analyse but may be inadequate since they do not allow for spatial gradients. However, a compartmental model can be considered as the limit of a reaction-diffusion model for very fast diffusion (all diffusion coefficients D(j)--> infinity ). A compartmental model m(c) is termed "associated" to the reaction-diffusion model m(rd) if m(c) is the limit of m(rd) for all D(j)--> infinity. From the analytical solutions of a reaction-diffusion model and its associated compartmental model the extent of a diffusion gradient of m(rd) can be estimated by means of parameters from both m(c) and m(rd). This approach is extended to more complicated models that cannot be solved analytically. Gradients can be neglected and, consequently, the compartmental description be used, if the characteristic length s of the diffusion path is small compared with the distance a particle travels in time T(e), where T(e) is the characteristic time for the compartmental model. This ratio of lengths can also be expressed as the ratio of two times, namely the residence time s(2)/D(X) and the turnover time X(C)/v, where X(C) and v are the steady-state concentration of X and its import rate, respectively, for the associated compartmental model. Characteristic times are given for several simple reaction-diffusion systems in rectangular and spherical geometries. Intracellular gradients of HCO(3)(-) and CO(2) are calculated for some flux situations relevant to photosynthetic carbon fixation in green microalgae.

Biological Transport↗
PubMed2006

Accuracy of the diffusive gradients in thin-films technique: diffusive boundary layer and effective sampling area considerations.

When using the diffusive gradients in thin-films (DGT) technique in well-stirred solutions, the diffusive boundary layer has generally been ignored on the assumption that it is negligibly thin compared to the total thickness of delta g, i.e., the sum of the thickness of the prefilter and diffusive gel. Deployment of devices with different diffusive layer thicknesses showed that the thickness of the DBL was approximately 0.23 mm in moderate to well-stirred solutions, but substantially thicker in poorly or unstirred solutions. Measurement of the distribution of Cd in the DGT resin gel at high spatial resolution (100 microm) using laser ablation inductively coupled plasma mass spectrometry showed that the effective sampling window had a larger diameter (2.20 cm) than the geometric diameter of the exposure window (2.00 cm). Lateral diffusion in the gel, which had previously been neglected, therefore increased the effective surface area of the device by approximately 20%. The concentrations measured by DGT agreed well with the known concentrations in standard solutions for all diffusion layer thicknesses, when the effective area and the appropriate diffusive boundary layer (DBL) were used. The extent of the error associated with neglecting the DBL and using the geometric window area depends on the gel layer thickness and the true thickness of the DBL, as determined by the deployment geometry and flow regime. When DGT measurements were made in well-stirred solutions using a 0.80-mm diffusive gel, the effect of neglecting the DBL and using the inappropriate geometric area offset each other, with the error being <+/-10%. For precise measurements, and especially work involving speciation or kinetic measurements, where DGT devices with different diffusive gel layer thicknesses are deployed, it is necessary to use the effective area and the appropriate DBL thickness in the full DGT equation, which allows for the use of layer-specific diffusion coefficients.

Cadmium↗
PubMed2005

Magnetic resonance diffusion-weighted imaging in the diagnosis of diffuse liver diseases in rats.

BACKGROUND: The diagnosis of diffuse hepatic lesions in early stage is a tough task at any time for clinical conventional imaging. Magnetic resonance diffusion-weighted imaging (MR DWI) can detect the changes of tissue structure at molecular level. This study was designed to determine the value of DWI in the diagnosis of diffuse liver lesions in early stage. METHODS: Diffuse liver lesions were induced by diethylnitrosamine in 42 rats of test group. Fourteen rats in control group were fed with pure water. Dynamic changes of MR DWI were observed every week in both groups during the early stage of diffuse liver lesions (1 to 12 weeks after drug administration in the test group). Apparent diffusion coefficient (ADC) values of liver parenchyma in different stages and pathologic changes were analyzed. RESULTS: The process of diffuse hepatic lesions in the test group was classified into three stages according to pathological changes, namely hepatitis, hepatic fibrosis and cirrhosis. No obvious morphological changes were shown by conventional imaging in both groups during this stage. But MR DWI demonstrated heterogeneous signal changes in early stage of hepatic cirrhosis in the test group. No significant change of ADC values was found in the control group between different weeks (P > 0.05). The ADC values of the test group declined from the fifth week, and after the tenth week the ADC values were significantly different between the test and control groups at gradient factor (b) value 300 sec/mm(2) (P < 0.05). At b value 600 and 1000 sec/mm(2), significant difference was seen between the two groups from the sixth week onward. The range of ADC value of the groups was (1.7 - 0.9) +/- (0.40 - 0.04) mm(2)/sec (b = 600) and (1.38 - 0.75) +/- (0.07 - 0.35) mm(2)/sec (b = 1000), respectively. Dominant pathological changes included swelled hepatocytes within 1 to 4 weeks after the administration of diethylnitrosamine in the test group, hyperplasia of fibrous tissues in 5 - 8 weeks and formation of cirrhotic nodules in 9 - 12 weeks. CONCLUSIONS: MR functional DWI could detect diffuse liver lesions earlier than conventional morphological imaging. ADC value as a marker for early diagnosis of diffuse liver lesions could also be used to inspect changes of the lesions.

Animals↗
PubMed2000

Assignment of the water slow-diffusing component in the central nervous system using q-space diffusion MRS: implications for fiber tract imaging.

Diffusion-weighted NMR spectroscopy (MRS) was performed on isolated bovine optic nerve and rat brain (in vitro) to characterize the multiexponential water signal decay in diffusion experiments. q-Space analysis of the diffusion data was used to obtain structural information about the investigated neuronal tissues. This analysis provided displacement distribution profiles of the water in the sample. Two diffusing components were identified from these profiles, thus enabling us to obtain the following information about the slow decaying component: 1) displacement of this component is restricted to a diffusing distance of approximately 2 microm; 2) it has a longer T2 than the rapidly diffusing component; and 3) the population fraction of this component depends on the orientation of the nerve fiber. When the diffusion was measured perpendicular to the long axis of the bovine optic nerve, the weighting of this population was 41 +/- 2%, whereas parallel to the long axis of the nerve it was found to be 14 +/- 2%. In the randomly oriented brain tissue, the population of this component was only 7 +/- 3%. These observations led to the conclusion that the slow-decaying component originates mainly from restricted water diffusion in the neuronal fibers. In view of these findings, in vitro and in situ diffusion-weighted images with high b values (with long delta) were acquired to obtain highly detailed images of white matter fiber tracts in the central nervous system. These images provide detailed information on white matter fiber tract location and allow spinal cord maturation to be followed with high accuracy.

Aging↗
PubMed2004

Biexponential diffusion tensor analysis of human brain diffusion data.

Several studies have shown that in tissues over an extended range of b-factors, the signal decay deviates significantly from the basic monoexponential model. The true nature of this departure has to date not been identified. For the current study, line scan diffusion images of brain suitable for biexponential diffusion tensor analysis were acquired in normal subjects on a clinical MR system. For each of six noncollinear directions, 32 images with b-factors ranging from 5 to 5000 s/mm2 were collected. Biexponential fits yielded parameter maps for a fast and a slow diffusion component. A subset of the diffusion data, consisting of the images obtained at the conventional range of b-factors between 5 and 972 s/mm2, was used for monoexponential diffusion tensor analysis. Fractional anisotropy (FA) of the fast-diffusion component and the monoexponential fit exhibited no significant difference. FA of the slow-diffusion biexponential component was significantly higher, particularly in areas of lower fiber density. The principal diffusion directions for the two biexponential components and the monoexponential solution were largely the same and in agreement with known fiber tracts. The second and third diffusion eigenvector directions also appeared to be aligned, but they exhibited significant deviations in localized areas.

Adult↗
PubMed2004

Characterizing non-Gaussian diffusion by using generalized diffusion tensors.

Diffusion tensor imaging (DTI) is known to have a limited capability of resolving multiple fiber orientations within one voxel. This is mainly because the probability density function (PDF) for random spin displacement is non-Gaussian in the confining environment of biological tissues and, thus, the modeling of self-diffusion by a second-order tensor breaks down. The statistical property of a non-Gaussian diffusion process is characterized via the higher-order tensor (HOT) coefficients by reconstructing the PDF of the random spin displacement. Those HOT coefficients can be determined by combining a series of complex diffusion-weighted measurements. The signal equation for an MR diffusion experiment was investigated theoretically by generalizing Fick's law to a higher-order partial differential equation (PDE) obtained via Kramers-Moyal expansion. A relationship has been derived between the HOT coefficients of the PDE and the higher-order cumulants of the random spin displacement. Monte-Carlo simulations of diffusion in a restricted environment with different geometrical shapes were performed, and the strengths and weaknesses of both HOT and established diffusion analysis techniques were investigated. The generalized diffusion tensor formalism is capable of accurately resolving the underlying spin displacement for complex geometrical structures, of which neither conventional DTI nor diffusion-weighted imaging at high angular resolution (HARD) is capable. The HOT method helps illuminate some of the restrictions that are characteristic of these other methods. Furthermore, a direct relationship between HOT and q-space is also established.

Anisotropy↗
PubMed2000

In vitro diffusion of mitomycin-C into human sclera after episcleral application: impact of diffusion time.

The purpose of this study was to investigate the impact of different diffusion times of mitomycin-C (MMC) on the intrascleral concentration vs depth profile of MMC in an experimental model. Scleral quadrants of eight human donor eyes were exposed to sponges soaked with MMC for an application time of 1 min. After irrigation with 40 ml saline, we allowed further diffusion of MMC in the sclera for 1, 5, 14 and 29 min until the specimens were further processed. A central 8 mm diameter scleral disk was horizontally dissected with a kryotome at -20 degrees C. MMC concentrations of six layers of 140 microm thickness were analysed by means of high-performance liquid chromatography. The MMC concentrations (microg g(-1)) of layer 1 were: 13.45+/- 5.9 (mean +/- S.D. at 2 min diffusion time), 7.6+/-2.5 (6 min diffusion), 5.6+/-3.1 (15 min diffusion) and 3.6+/-1.7 (30 min diffusion). The corresponding MMC concentrations of layer 6 were: 0.61+/-0.48, 1.47 +/-0.66, 1.83+/-0.42 and 2.98+/-0.97 microg g(-1). The superficial concentration of intrascleral MMC decreased with increasing diffusion time, the deep concentrations increased. After 30 min of diffusion time, equal concentrations of MMC were found in all layers. Even with current low-dose application regimens of MMC the concentrations in the inner side of the sclera rapidly increase beyond the limits of the therapeutic range. Owing to this fast diffusion of MMC, the only means of reducing ciliary body concentrations of MMC is to reduce the dose.

Administration, Topical↗
PubMed1999

A linear relationship exists among brain diffusion eigenvalues measured by diffusion tensor magnetic resonance imaging.

Diffusion in biological tissues can be measured by magnetic resonance diffusion tensor imaging The complex nature of anisotropic diffusion in the brain has been described by a diffusion tensor which contains information about the magnitude of diffusion in different directions. Each tensor contains a set of three eigenvalues which are related to the major, intermediate, and minor axes of a diffusion ellipsoid. This investigation demonstrates that the various sets of diffusion eigenvalues from different regions of the brain lie along a line in ordered eigenvalue space. Sets of ordered diffusion eigenvalues were considered points in ordered eigenvalue space. The line which best fit the data by minimizing the total squared deviations was determined. A new coordinate system was constructed through translation and rotation which spanned ordered eigenvalue space. Eigenvalues from both monkey brain and human brain were studied. It was found that the sets of eigenvalues from both species have significant linear trends. Moreover, the same line may describe the brain eigenvalues from both species. It is likely that this linear relationship of the eigenvalues observed in an ordered eigenvalue plot is related to a combination of (1) conservation of total isotropic diffusion and (2) the degree of orientational dispersion of the microfibers within each voxel.

Animals↗
PubMed2005

Flow-based fiber tracking with diffusion tensor and q-ball data: validation and comparison to principal diffusion direction techniques.

In this study, we evaluate the performance of a flow-based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity. We introduce a novel speed function for surface evolution that is derived from either diffusion tensor (DT) data, high angular resolution diffusion (HARD) data, or a combined DT-HARD hybrid approach. We use the model-free q-ball imaging (QBI) approach for HARD reconstruction. The anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts, noise, and subvoxel partial volume averaging of fiber directions. The surface evolution approach, using the full diffusion tensor as opposed to the principal diffusion direction (PDD) only, is compared to PDD-based line propagation fiber tracking. Additionally, DT reconstruction is compared to HARD reconstruction for fiber tracking, both using surface evolution. We show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions, which can be difficult to map with PDD-based methods. We then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly.

Algorithms↗
PubMed1995

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes.

Tracer diffusion coefficients of integral membrane proteins (IMPs) in intact plasma membranes are often much lower than those found in blebbed, organelle, and reconstituted membranes. We calculate the contribution of hydrodynamic interactions to the tracer, gradient, and rotational diffusion of IMPs in plasma membranes. Because of the presence of immobile IMPs, Brinkman's equation governs the hydrodynamics in plasma membranes. Solutions of Brinkman's equation enable the calculation of short-time diffusion coefficients of IMPs. There is a large reduction in particle mobilities when a fraction of them is immobile, and as the fraction increases, the mobilities of the mobile particles continue to decrease. Combination of the hydrodynamic mobilities with Monte Carlo simulation results, which incorporate excluded area effects, enable the calculation of long-time diffusion coefficients. We use our calculations to analyze results for tracer diffusivities in several different systems. In erythrocytes, we find that the hydrodynamic theory, when combined with excluded area effects, closes the gap between existing theory and experiment for the mobility of band 3, with the remaining discrepancy likely due to direct obstruction of band 3 lateral mobility by the spectrin network. In lymphocytes, the combined hydrodynamic-excluded area theory provides a plausible explanation for the reduced mobility of sIg molecules induced by binding concanavalin A-coated platelets. However, the theory does not explain all reported cases of "anchorage modulation" in all cell types in which receptor mobilities are reduced after binding by concanavalin A-coated platelets. The hydrodynamic theory provides an explanation of why protein lateral mobilities are restricted in plasma membranes and why, in many systems, deletion of the cytoplasmic tail of a receptor has little effect on diffusion rates. However, much more data are needed to test the theory definitively. We also predict that gradient and tracer diffusivities are the same to leading order. Finally, we have calculated rotational diffusion coefficients in plasma membranes. They decrease less rapidly than translational diffusion coefficients with increasing protein immobilization, and the results agree qualitatively with the limited experimental data available.

Animals↗
PubMed2006

Axial and radial diffusivity in preterm infants who have diffuse white matter changes on magnetic resonance imaging at term-equivalent age.

OBJECTIVE: Diffuse excessive high signal intensity (DEHSI) is observed in the majority of preterm infants at term-equivalent age on conventional MRI, and diffusion-weighted imaging has shown that apparent diffusion coefficient values are elevated in the white matter (WM) in DEHSI. Our aim was to obtain diffusion tensor imaging on preterm infants at term-equivalent age and term control infants to test the hypothesis that radial diffusivity was significantly different in the WM in preterm infants with DEHSI compared with both preterm infants with normal-appearing WM on conventional MRI and term control infants. METHODS: Diffusion tensor imaging was obtained on 38 preterm infants at term-equivalent age and 8 term control infants. Values for axial (lambda1) and radial [(lambda2 + lambda3)/2] diffusivity were calculated in regions of interest positioned in the central WM at the level of the centrum semiovale, frontal WM, posterior periventricular WM, occipital WM, anterior and posterior portions of the posterior limb of the internal capsule, and the genu and splenium of the corpus callosum. RESULTS: Radial diffusivity was elevated significantly in the posterior portion of the posterior limb of the internal capsule and the splenium of the corpus callosum, and both axial and radial diffusivity were elevated significantly in the WM at the level of the centrum semiovale, the frontal WM, the periventricular WM, and the occipital WM in preterm infants with DEHSI compared with preterm infants with normal-appearing WM and term control infants. There was no significant difference between term control infants and preterm infants with normal-appearing WM in any region studied. CONCLUSIONS: These findings suggest that DEHSI represents an oligodendrocyte and/or axonal abnormality that is widespread throughout the cerebral WM.

Brain↗
PubMed2001

Diffusion anisotropy of the internal capsule and the corona radiata in association with stroke and tumors as measured by diffusion-weighted MR imaging.

BACKGROUND AND PURPOSE: Diffusion-weighted MR images have enabled measurement of directionality of diffusion (anisotropy) in white matter. To investigate differences in the anisotropy for various types of pathologic findings and the association between the anisotropy of tracts and neurologic dysfunction, we compared the anisotropy of the posterior limb of the internal capsule and the corona radiata between patients with stroke and those with tumors and between patients with and without hemiparesis. METHODS: Thirty-three patients consisting of 11 with tumors and 22 with ischemic disease (16 acute infarction, four old infarction, and two transient ischemic attack) and nine control patients were studied with a 1.5-T MR imager. Diffusion-weighted images were obtained with diffusion gradients applied in three orthogonal directions. The diffusion anisotropy measurements were obtained from regions of interests defined within the internal capsule and the corona radiata. RESULTS: The diffusion anisotropy was significantly reduced in all internal capsules and coronae radiata involved by infarcts, tumors, and peritumoral edema compared with that of the control patients (P <.0001). This reduction was most prominent in the tracts involved by tumors (P <.05). The anisotropy of the internal capsules and coronae radiata was significantly decreased in cases with moderate-to-severe hemiparesis as compared with those with no or mild hemiparesis (P <.0001). Diffusion anisotropy tended to be also reduced in normal-appearing internal capsules and coronae radiata that were remote from the involved segment of the corticospinal tract. CONCLUSION: The degree of impaired diffusion anisotropy may vary in different pathologic conditions and correlate with neurologic dysfunction. The measurement of diffusion anisotropy may provide additional information relating to neurologic function and transneuronal effects.

Adolescent↗
PubMed2005

Interhemispheric asymmetry of brain diffusivity in normal individuals: a diffusion-weighted MR imaging study.

BACKGROUND AND PURPOSE: Previous neuroimaging studies have suggested asymmetries in brain diffusivity may exist. The purpose of this study was to assess whether water diffusivity in deep gray matter structures shown by diffusion-weighted (DW) imaging differs between the right and left cerebral hemispheres in normal individuals. METHODS: Brain MR imaging was obtained in 23 healthy volunteers. A multisection image without diffusion weighting, and images with weighting applied in the read, phase, and section directions with a b-factor of 1000 s/mm(2) were collected. Diffusivity was computed separately in each direction, and the results were averaged to form mean diffusivity maps. Quantitative diffusivity values were obtained from the globus pallidus, putamen, caudate, thalamus, white matter, and CSF by using a standardized region of interest template. Interhemispheric differences were assessed by using a paired sample t test. RESULTS: Mean diffusivity was higher in the: left (mean +/- SD: 0.689 x 10(-3)+/- 0.069 x 10(-3)mm(2)/s) versus right (0.642 x 10(-3)+/- 0.071 x 10(-3)mm(2)/s) caudate (% difference, P value: 7.0%, P = .001); right (0.745 x 10(-3)+/- 0.053 x 10(-3)mm(2)/s) versus left (0.706 x 10(-3)+/- 0.050 x 10(-3)mm(2)/s) globus pallidus (5.2%, P < .001); left (0.720 x 10(-3)+/- 0.059 x 10(-3)mm(2)/s) versus right (0.674 x 10(-3)+/- 0.052 x 10(-3)mm(2)/s) putamen (6.4%, P < .001); right (0.750 x 10(-3)+/- 0.040 x 10(-3)mm(2)/s) versus left (0.716 x 10(-3)+/- 0.031 x 10(-3)mm(2)/s) thalamus (4.5%, P < .001). No significant right versus left difference was seen in the CSF (P = .291), anterior frontal white matter (P = .834), or centrum semiovale (P = .320). CONCLUSION: Gray matter diffusivity may differ between hemispheres of the brain in healthy individuals. Analysis of deep gray matter lesions requires caution, as statistically significant interhemispheric differences may not always be indicative of disease.

Adult↗
PubMed2000

Diffusion imaging of the spinal cord in vivo: estimation of the principal diffusivities and application to multiple sclerosis.

Magnetic resonance (MR) diffusion imaging is a useful technique with which to increase our understanding of pathologic damage to the central nervous system. To fully quantitate diffusion and anisotropy in the spinal cord, as in other tissues, it is necessary to determine the diffusion tensor. If spinal cord diffusion is assumed to be cylindrically symmetric and the orientation of the cord in the gradient frame is known, then it is shown that full quantification is possible from only three images, two of which are diffusion-weighted. Mean diffusivity and volume ratio were determined in the normal cord of four healthy volunteers and in seven cord lesions of three patients with clinically definite multiple sclerosis (MS) who had locomotor disability suggesting the presence of spinal pathology. MS cord lesions exhibited increased mean diffusivity reflecting structural damage to the cord white matter. Quantification of diffusion and anisotropy using spinal cord diffusion imaging provides new structural information in relation to spinal cord pathology in vivo.

Adult↗
PubMedDate not supplied

Dependence of apparent diffusion coefficients on axonal spacing, membrane permeability, and diffusion time in spinal cord white matter.

We used a numerical simulation of water self-diffusion among permeable cylinders to predict the dependence of MR-based apparent diffusion coefficients in white matter on axonal separation, barrier permeability, and diffusion time (T). The transverse apparent diffusion coefficient (tADC), calculated with simulated diffusion-sensitizing gradients perpendicular to the axon fibers, remains a function of T down to diffusion times as short as .1 microsec for a range of diffusion barrier permeability. As the diffusion time lengthens, the response of tADC depends on axon diameter, with decreases in tADC occurring earliest, and most dramatically, for the smallest fiber diameter simulated (2 microm). For a given axonal separation, asymptotic values of ADC are determined by permeability alone and are the same for 2-microm and 11-microm fibers of equal membrane permeability. The effect of increased relative intracellular volume is manifested primarily in a decrease in tADC at short T. Increases in interaxonal spacing increase the tADC at asymptotically long diffusion times and reduce the dependence on permeability. However, at the widest plausible axonal separations, permeability remains an important determinant of tADC. These simulations may enhance interpretation of measured tADC in the context of the underlying physiologic and structural changes at the cellular level that accompany white-matter disease.

Animals↗
PubMed2000

Restricted diffusion model for surface diffusion in reversed-phase liquid chromatography

The analysis of experimental results in reversed-phase liquid chromatography (RPLC) allows further discussion of the restricted diffusion model of surface diffusion formulated on the basis of the absolute rate theory. Chromatographic data were acquired on different RPLC systems with two series of homologous compounds, several stationary phases having different alkyl ligand densities and ligands of various lengths, and methanol/water mobile phases of different compositions. The enthalpy-entropy compensation observed and the linear free energy relationships found for surface diffusion suggest that the surface diffusion mechanism remains probably the same in all RPLC conditions studied. Whereas the isosteric heat of adsorption approaches zero with decreasing retention, the activation energy of surface diffusion tends toward a finite limit and the surface diffusion coefficient tends toward a value near the corresponding molecular diffusivity. These results support the validity of the restricted diffusion model. The influence of different factors on the validity of this model (i.e., the activation energy and the frequency factor of surface diffusion, and the surface tortuosity) was also considered.

Journal Article↗
PubMed2005

Simulations of concentrated suspensions of rigid fibers: relationship between short-time diffusivities and the long-time rotational diffusion.

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.

Journal Article↗