Diffusion of macromolecule

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

Schaeffer JR, RC Gong, MS Bitrick Jr. (1992). Restricted diffusion of macromolecules by endothelial cell monolayers and small pore filters. Am J Physiol 263 L227-L236. 

Observed monomer concentrations are presented by Figure 2 as a function of cure time and temperature (see Equation 20). At high monomer conversions, the data appear to approach an asymptote. As the extent of network development within the resin advances, the rate of reaction diminishes. Molecular diffusion of macromolecules, initially, and of monomeric molecules, ultimately, becomes severely restricted, resulting in diffusion-controlled reactions (20). The material ultimately becomes a glass. Monomer concentration dynamics are no longer exponential decays. The rate constants become time dependent. For the cure at 60°C, monomer concentration can be described by an exponential function. 

Ehrenberg M. and Rigler R. (1976) Fluorescence Correlation Spectroscopy Applied to Rotational Diffusion of Macromolecules, Quart. Rev. Biophys. 9, 69-81. 

The unconventional applications of SEC usually produce estimated values of various characteristics, which are valuable for further analyses. These embrace assessment of theta conditions for given polymer (mixed solvent-eluent composition and temperature Section 16.2.2), second virial coefficients A2 [109], coefficients of preferential solvation of macromolecules in mixed solvents (eluents) [40], as well as estimation of pore size distribution within porous bodies (inverse SEC) [136-140] and rates of diffusion of macromolecules within porous bodies. Some semiquantitative information on polymer samples can be obtained from the SEC results indirectly, for example, the assessment of the polymer stereoregularity from the stability of macromolecular aggregates (PVC [140]), of the segment lengths in polymer crystallites after their controlled partial degradation [141], and of the enthalpic interactions between unlike polymers in solution (in eluent) [142], as well as between polymer and column packing [123,143]. 

Nucleation is initiated by local fluctuations of concentration within a metastable region. The activation energy of nucleation depends on the value of the interface energy required to create a nucleus. The droplet grows by diffusion of macromolecules into the nucleate domains. The natural form of the phase separation through NG mechanism is the sea-island type. 

The diffusion coefficient depends on a number of factors, including the molecular properties of solutes the structures of tissues, and temperature. The temperature-dependence is less critical for drug delivery, since the temperature in tumors is stable and close to the body temperature. The dependence of D on tissue structures is significant (Netti et al., 2000 Pluen et al., 2001). It is mediated through the size and the volume fraction of pores, the tortuosity of diffusion pathways, and the connectedness of pores (Yuan et al., 2001). Diffusion of macromolecules is faster in tissues with a lower collagen type I content (Pluen et al., 2001) or tissues treated with collagenase (Netti et al., 2000). However, there is no correlation between D and the concentration of total or sulfated glycosaminoglycans (Netti et al., 2000). 

Pluen, A., Boucher, Y., Ramanujan, S., McKee, T.D., Gohongi, T., di Tomaso, E. et al. (2001) Role of tumor-host interactions in interstitial diffusion of macromolecules Cranial Verses subcutaneous tumors. Proc. Natl. Acad. Sci. USA, 98, 4628 1633. 

Pluen, A., Netti, P. A., Jain, R.K. and Berk, D.A.(1999) Diffusion of macromolecules in agarose gels comparison of linear and globular configurations. Biophys. J., 77, 542-552. 

Flemstrom, G., et al. 1999. Adherent surface mucus gel restricts diffusion of macromolecules in rat duodenum in vivo. Am J Physiol 277 G375. 

It is the presence of these tight junctions that occludes the aqueous paracellular diffusional pathway between the endothelial cells, and blocks the free diffusion of macromolecules, polar solutes, and ions from blood plasma into the ECF of the brain. It is this impediment to the movement of ions that results in the high in vivo electrical resistance of the BBB, of approximately 1800 fl cm2 [17]. This high electrical resistance or low conductance of the potential paracellular pathway emphasizes the extreme effectiveness of the tight junctions in occluding this pathway by effectively reducing the movement of ions. The radius of a sodium... 

In summary, the effect of porosity on electrical conductivity and ion diffusivity in agarose gels is studied. Both electrical conductivity and ion diffusivity increase with porosity. The model obtained from the electrical conductivity data, i.e., Equation (7), can predict the diffusivity of macromolecules in 2% agarose gel for solutes with hydrodynamic radius less than the pore size of the gel. This study suggests that electrical conductivity method used in this study can be applied to investigating diffusion behavior of macromolecules in uncharged porous media. 

The use of column with superficially porous packing materials based on silica particles with nonporous cores is the most recently reported strategy for improving chromatographic performance. This technology, originally developed by Kirkland in the 1990s to limit diffusion of macromolecules into the pores [85], became commercially available in 2007 [86], In comparison with totally porous particles of similar diameters, the both A and C term of the Van Deemter curve are reduced [87, 88],... 

One can see that the approximation of the theory, based on the linear dynamics of a macromolecule, is not adequate for strongly entangled systems. One has to introduce local anisotropy in the model of the modified Cerf-Rouse modes or use the model of reptating macromolecule (Doi and Edwards 1986) to get the necessary corrections (as we do in Chapters 4 and 5, considering relaxation and diffusion of macromolecules in entangled systems). The more consequent theory can be formulated on the base of non-linear dynamic equations (3.31), (3.34) and (3.35). 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

Diffusion of Macromolecules in Mucus 2.7.1 Influence of Mesh Size... 

Noiva R. (1994) Enzymatic catalysis of disulfide formation. Protein Expr Purif. 5, 1-13 Olmsted S.S., Padgett J.L., Yudin A.I., Whaley K.J., Moench T.R. and Gone R.A. (2001) Diffusion of macromolecules and virus-like particles in human cervical mucus. Biophys J 81,1930-1937... 

The diffusion of small molecules in polymeric solids has been a subject in which relatively little interest has been shown by the polymer chemist, in contrast to its counterpart, i.e., the diffusion of macromolecules in dilute solutions. However, during the past ten years there has been a great accumulation of important data on this subject, both experimental and theoretical, and it has become apparent that in many cases diffusion in polymers exhibits features which cannot be expected from classical theories and that such departures are related to the molecular structure characteristic of polymeric solids and gels. Also there have been a number of important contributions to the procedures by which diffusion coefficients of given systems can be determined accurately from experiment. It is impossible, and apparently beyond the author s ability, to treat all these recent investigations in the limited space allowed. So, in this article, the author wishes to discuss some selected topics with which he has a relatively greater acquaintance but which he feels are of fundamental importance for understanding the current situation in this field of polymer research. Thus the present paper is a kind of personal note, rather than a balanced review of diverse aspects of recent diffusion studies. 

Macromolecules have large molecular weights and various random shapes that may be coil-like, rod-like, or globular (spheres or ellipsoids). They form true solutions. Their sizes and shapes affect their diffusion in solutions. Besides that, interactions of large molecules with the small solvent and/or solute molecules affect the diffusion of macromolecules and smaller molecules. Sometimes, reaction-diffusion systems may lead to facilitated and active transport of solutes and ions in biological systems. These types of transport will be discussed in Chapter 9. 

De Smedt S, Meyvis E, van Oostveldt P, Blonk J, Hennink W, Demeester J. The diffusion of macromolecules in dextran methacrylate solutions and gels as studied by confocal scanning laser microscopy. Macromolecules 1997, 30, 4863-4870. 

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