Macromolecules coefficient

Tao T 1969 Time-dependent fluorescence depolarization and Brownian rotational diffusion coefficients of macromolecules Biopolymers 8 609-32... 

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

Similar considerations apply to best volume flow rates for samples of different molar mass. For high molar mass samples, flow rates should be reduced to avoid shearing the macromolecule in the column. Moreover, a reduced flow rate is necessary because the diffusion coefficients of large molecules will get pretty small. This means that the macromolecule will pass by a pore in the packing material without having the time to enter it, if the linear flow rate is too high. 

Loading capacities in size exclusion chromatography are very low because all separation occurs within the liquid volume of the column. The small diffusion coefficients of macromolecules also contribute to bandspreading when loads are increased. The mass loading capacities for ovalbumin (MW 45,000) on various sizes of columns can be seen in Table 10.5. The maximum volume that can be injected in size exclusion chromatography before bandspreading occurs is about 2% of the liquid column volume. The maximum injection volumes for columns of different dimensions can also be seen in Table 10.5. 

Centrifugation methods separate macromolecules on the basis of their characteristic densities. Particles tend to fail through a solution if the density of the solution is less than the density of the particle. The velocity of the particle through the medium is proportional to the difference in density between the particle and the solution. The tendency of any particle to move through a solution under centrifugal force is given by the sedimentation coefficient, S ... 

The sedimentation coefficient s°, or its normalized form 5 0 w function of the conformation and flexibility of a macromolecule (via its translational frictional property) and its mass. So if we are going to obtain conformation and flexibility information we need to know the molecular weight (molar mass)... 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

Gosnell, DL Zimm, BH, Measurement of Diffusion Coefficients of DNA in Agarose Gels, Macromolecules 26, 1304, 1993. 

Holz, M Lucas, O Muller, C, NMR in the Presence of an Electric Current, Simultaneous Measurements of Ionic Mobilities, Transference Numbers, and Self-Diffusion Coefficients Using an NMR Pulsed-Gradient Experiment, Journal of Magnetic Resonance 58, 294, 1984. Hooper, HH Baker, JP Blanch, HW Prausnitz, JM, Swelling Equilibria for Positively Ionized Polyacrylamide Hydrogels, Macromolecules 23, 1096, 1990. 

Transport Properties Although the densities of SCFs can approach those of conventional liquids, transport properties are more favorable because viscosities remain lower and diffusion coefficients remain higher. Furthermore, CO2 diffuses through condensed-liquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. For example, at 35°C the estimated pyrene diffusion coefficient in polymethylmethacrylate increases by 4 orders of magnitude when the CO2 content is increased from 8 to 17 wt % with pressure [Cao, Johnston, and Webber, Macromolecules, 38(4), 1335-1340 (2005)]. 

Owing to its low water solubility and high octanol/water partition coefficients, dinitroaniline herbicides adsorb and bind to soil macromolecules and show minimal leaching potential. Dinitroanilines herbicides show good soil residue activities with soil half-lives ranging from 30 days for benfluralin and oryzalin to 6-7 months for trifluralin. Al-Dealkylation (aerobic conditions) and reduction of the nitro group to an amino moiety (anaerobic conditions) have been reported as major soil degradation pathways. 

JL Duda, YC Ni, JS Vrentas. An equation relating self-diffusion and mutual diffusion coefficients in polymer-solvent systems. Macromolecules 12 459-462, 1979. 

Kofinas et al. (1996) have prepared PEO hydrogels by a similar technique. In this work, they studied the diffusional behavior of two macromolecules, cytochrome C and hemoglobin, in these gels. They noted an interesting, yet previously unreported dependence between the crosslink density and protein diffusion coefficient and the initial molecular weight of the linear PEGs. 

The stability of the dispersions upon dilution at 50 °C and zero value of the osmotic second virial coefficient suggests that the surface of the particles at temperatures above the LCST may possess some hydrophilic character the macromolecules self-organise and build up particles with hydrated po-... 

Diffusion of dioxygen occurs 102 105 times more slowly with the diffusion coefficient D 10 7 10 10 cm2 s 1 Carbon-centered atom of P changes its orbital hybridization in this reaction and changes the C—C bond angles from 120° to 109°. Since P is macroradical and is surrounded by segments of macromolecules, this process occurs with an activation energy Solubility of dioxygen in the amorphous phase of polymer is about 3 x 10 4-2 x 10 3 mol L 1 atm-1... 

Thus, the strong C—F bond, the special arrangement of atoms in macromolecule, and low surface energy impart some unique physical properties to PTFE and other fluoropolymers high chemical and thermal resistance, nonstick character, low friction coefficient, and low wettability. This combination of properties... 

In any case, exceptions to the FIAM have been pointed out [2,11,38,44,74,76,78]. For example, the uptake has been shown to depend on the Cj M or rMI (e.g. in the case of siderophores [11] or hydrophobic complexes [43,50]), rather than on the free c M. Several authors [11,12,15] showed that a scheme taking into account the kinetics of parallel transfer of M from several solution complexes to the internalisation transporter ( ligand exchange ) can lead to exceptions to the FIAM, even if there is no diffusion limitation. Adsorption equilibrium has been assumed in all the models discussed so far in this chapter, and the consideration of adsorption kinetics is kept for Section 4. Within the framework of the usual hypotheses in this Section 3, we would expect that the FIAM is less likely to apply for larger radii and smaller diffusion coefficients (perhaps arising from D due to the labile complexation of M with a large macromolecule or a colloid particle, see Section 3.3). 

Generally, the activity coefficient y depends on the composition of solution. In the ranges of our narrow purposes of investigations of the macromolecules chemical potential conformation term influence on the osmotic pressure of polymeric solutions we will be neglect by the change of y lying y = const in all range of the macromolecules concentrations into solution. This permits to write... 

Since the rate constants of bimolecular diffusion-limited reactions in isotropic solution are proportional to T/ these data testify to the fact that the kt values are linearly dependent on the diffusion coefficient D in water, irrespective of whether the fluorophores are present on the surface of the macromolecule (human serum albumin, cobra neurotoxins, proteins A and B of the neurotoxic complex of venom) or are localized within the protein matrix (ribonuclease C2, azurin, L-asparaginase).1 36 1 The linear dependence of the functions l/Q and l/xF on x/t] indicates that the mobility of protein structures is correlated with the motions of solvent molecules, and this correlation results in similar mechanisms of quenching for both surface and interior sites of the macromolecule. 

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