Hydrodynamic Diffusion Coefficients Research Articles

Synthesis and characterization of poly(urethane- g-acrylic acid)s

The free-radical copolymerization of a completely hard-block unsaturated polyurethane, based on methylene bis(4-phenylisocyanate), erythrol and butane-1,4-diol, with acrylic acid in the presence of 2,2′-azobisisobutyronitrile at 60°C under various reaction conditions is described. Grafting of poly(acrylic acid) onto the unsaturated polyurethane with pendant alkene groups was shown to be successful. Some of the characteristics of the ungrafted and grafted polyurethane copolymers were studied using microanalysis, gel permeation chromatography (g.p.c.), nuclear magnetic resonance, infra-red spectroscopy and differential scanning calorimetry. The resultant poly(urethane- g-acrylic acid)s, poly(U- g-AA)s, and the original unsaturated polyurethane were also studied viscometrically in a mixture of tetrahydrofuran and dimethylformamide (DMF) over the temperature range 26–56°C. Different-sized particles, formed in a solution of graft copolymer in water or DMF, were confirmed by photocorrelation scattering. These measurements indicated that predominantly two types of particle were present in both solutions, and values of the hydrodynamic radii and diffusion coefficients were obtained. The number-average molecular weights M ̄ n and weight-average molecular weights M ̄ W of the polyurethanes and poly(U- g-AA)s were determined by g.p.c. relative to polystyrene as a standard. Equilibrium water sorption measurements of the ungrafted polyurethanes were also carried out at room temperature.

The roto-translational diffusion of a molecule in a fluid

The coupling between the translational and rotational motions of a molecule in a fluid is investigated with the help of a diffusion equation for the self van Hove function G s. This equation is obtained from an exact balance equation for the microscopic density of molecules by introducing in the hydrodynamic limit phenomenological tensorial diffusion coefficients. Then substituting in this equation the expansion of G s on a complete basis set of rotational invariants we obtain an infinite system of coupled diffusion equations for the coefficients of the G s expansion. From the solution at wave vector k = 0 of this system we derive a new expression for the reorientational correlation times of a molecule.

Hydrodynamic resistance and diffusion coefficients of segmentally flexible macromolecules with two subunits

We present an algorithm for the calculation of the resistance coefficients and diffusion coefficients for the translational and rotational motions of a particle composed of two rigid subunits joined at a single point of articulation. By modeling each subunit as a collection of hydrodynamic resistance elements or beads, the method allows the full inclusion of all hydrodynamic interactions. The generalized coordinates have been chosen in such a way that it is easy to treat cases with seven, eight, or nine degrees of freedom (the subunits being joined at a hinge, a universal joint, or a swivel), as well as the intermediate cases where the internal motions are opposed by restoring forces, and analytic expressions are given for the resistance and diffusion coefficients for these cases. The examination of the dependence of the various coefficients on the choice of the origin of the coordinate system reveals that the rotational diffusion coefficients are independent of the location of the origin, so any convenient point (such as the point of articulation) can be used for the analysis of rotational diffusion. On the other hand, the calculated translational diffusion coefficient does depend on the choice of origin, and we discuss the still unresolved problem of how to find the origin that will give a value corresponding to the experimentally observed translational diffusion coefficient. One specific application of the method is examined in detail, that of a particle made up of three identical spheres with one sphere for each arm and the central sphere serving as the joint. The various rotational diffusion coefficients of the model particle are given, and it is seen that ignoring hydrodynamic interactions produces large effects in the calculated values. Calculations on this same model also demonstrate the sensitivity of the calculated translational diffusion coefficient both to the effects of ignoring hydrodynamic interactions and to the choice of coordinate system.

Hydrodynamic resistance and diffusion coefficients of a freely hinged rod

AbstractThe seven‐dimensional hydrodynamic resistance and diffusion tensors are evaluated for a rod which is freely hinged at its center and immersed in a viscous fluid. The hydrodynamic resistance tensor is first determined at the hinge, then transformed to other points and inverted to obtain the diffusion tensor. Hydrodynamic interactions between rod halves are neglected, which is asymptotically correct for long rods. In the long‐rod limit, the diffusion coefficient characterizing translations over macroscopic distances is decreased by 3–6% from that for a rigid straight rod of same total length, while the average end‐over‐end rotational diffusion coefficient for each rod half is increased 4.67 times.

Coordinate Systems for Modeling the Hydrodynamic Resistance and Diffusion Coefficients of Irregularly Shaped Rigid Macromolecules

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCoordinate Systems for Modeling the Hydrodynamic Resistance and Diffusion Coefficients of Irregularly Shaped Rigid MacromoleculesSteven Harvey and Jose Garcia de la TorreCite this: Macromolecules 1980, 13, 4, 960–964Publication Date (Print):July 1, 1980Publication History Published online1 May 2002Published inissue 1 July 1980https://doi.org/10.1021/ma60076a037RIGHTS & PERMISSIONSArticle Views315Altmetric-Citations52LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (635 KB) Get e-Alerts Get e-Alerts

Transport properties of particles with segmental flexibility. I. Hydrodynamic resistance and diffusion coefficients of a freely hinged particle

AbstractExpressions are derived for the hydrodynamic resistance tensor and the diffusion tensor of a particle consisting of two rigid subunits connected by a free hinge. No restrictions are placed on the shapes of the subunits. The resistance tensor is obtained by using two independent approaches: first, from the Rayleigh dissipation function and, second, from an examination of the generalized forces for the appropriate seven‐dimensional coordinate system. For the derivation of the generalized Einstein equation connecting the diffusion and resistance tensors, the Brownian motion is treated as a stochastic process. That derivation is based on the assumption that the restoring force for bending is negligible, and the Einstein relation holds instantaneously only if that assumption is true. The relationship between these tensors and the macroscopically observable parameters is discussed, and it is shown that the separate measurement of resistance and diffusion coefficients can be used to detect macromolecular flexibility. One example is treated, the diffusion of a particle composed of two long rods joined at a free hinge. Those calculations are carried out with the first‐order assumption of negligible hydrodynamic interactions between the subunits. For the hinged rod, the bending degree of freedom produces a 34% increase in the translational diffusion coefficient over that of a stiff rod of the same total length, while the rotational diffusion coefficient about the axis perpendicular to the plane of bending is increased by 125%.

Hydrodynamic Frictional and Diffusion Coefficients in Idealized Liquids. I. The Collisional Contribution

The approximate method of calculation of the collisional contribution to transport properties in liquids presented in an earlier paper is now extended to the calculation of the similar contribution to the frictional and diffusion coefficients. For the special case where the diffusing molecule is large compared to its neighbors, the calculated collisional contribution to the frictional coefficient is in good agreement with Stokes' law and the Langevin equation of colloid statistics is valid. However, for small diffusing molecules, the calculated frictional coefficient is not independent of the velocity of the given molecule. Numerical diffusion coefficients using molecular parameters obtained from sonic velocity data are about three times the experimental values as might be expected from the corresponding behavior of the calculated viscosity coefficient contribution previously reported. In spite of the failure of the Stokes equation for the frictional coefficient of small molecules, the Stokes-Einstein equation represents fairly satisfactorily the case of self-diffusion. This is due to the averaging over all velocities of the diffusing molecule.