Diffusion coefficient molecular weight dependence

A simple estimate of the diffusion coefficients can be approximated from examining the effects of molecular size on transport through a continuum for which there is an energy cost of displacing solvent. Since the molecular weight dependence of the diffusion coefficients for polymers obeys a power law equation [206], a similar form was chosen for the corneal barriers. That is, the molecular weight (M) dependence of the diffusion coefficients was written as ... 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

Fig. 25. Molecular-weight dependence of limiting sedimentation coefficient (81) and diffusion coefficient (50) for PBLG in DMF...

Further, reptation theory asserts26) that the molecular-weight dependence of the diffusion coefficient in an entangled gel should have the form... 

Kobayashi, H. Molecular weight dependence of intrinsic viscosity, diffusion constant, and second virial coefficient of polyacrylonitrile. J. Polymer Sci. 39, 369-388 (1959). 

An important question is to decide how far one can believe that a self-diffusion coefficient varying like N is characteristic of reptation. It has been argued that additional molecular weight dependences could exist and compensate for departures from the N 2 law [48 to 52]. Such an effect can come from the local monomer-monomer friction coefficient w hich appears as a prefactor in equation 8, hidden in the diffusion coefficient D. Several processes can combine and lead to a local friction which is molecular weight dependent, and W hich decreases when the polymer molecular weight is decreased. This is, for example, the... 

The diffusion coefficient at high cs decreases with increasing molecular weight. This is similar to neutral polymers where the diffusion coefficient is inversely dependent on the friction factor, which is proportional by the power law to polymer molecular weight, i.e., D =/ 1 = M v. The diffusion coefficient at low cs is, on the other hand, independent of polymer molecular weight. This can be also documented by a more detailed data set on molecular weight standards of NaPSS [13] (Figure 8). 

Fig. 7. Molecular weight dependence of diffusivity. (a) The effective diffusion coefficient, D, has been plotted as a function of molecular weight for dextrans (Nugent and Jain, 1984a, b Gerlowski and Jain, 1986), albumin (Nugent and Jain, 1984a, b), and IgG (Clauss and Jain, 1990) in water, normal tissue, and tumor tissue. Symbols , dextran, aqueous O, bovine serum albumin, aqueous O, rabbit IgG, tumor , dextran, normal tissue , bovine serum albumin normal tissue , rabbit IgG, normal tissue. The half-filled symbols refer to the tumor data, (b) The effective diffusion coefficient plotted versus the Stokes-Einstein radius. Symbols as in (a) plus X, sodium fluorescein, tumor +, sodium fluorescein, normal tissue. (From Clauss and Jain, 1990, with permission.) Currently, we are measuring diffusion coefficient of molecules and particles larger than 50 A in radius.

The termination reaction of free radical polymerization is a typical example of an intermacromolecular diffusion controlled reaction.3 Photophysical studies carried out in the 1980 s demonstrated for the first time that the reaction is solvent- and molecular weight-dependent. The experiments involved triplet quenching of probes attached to polymer chain ends. A benzil group was linked to the end of one PS sample (PS-B) and an anthryl group was linked to the end of a second PS sample (PS-A). The quenching rate coefficient kq of the benzil phosphorescence by anthryl groups is given by Eq. (3.26), where r0 is the lifetime of benzil phosphorescence in the absence of anthryl and ris the benzil phosphorescence lifetime in the presence of anthryl in concentration [A],... 

For a protein incorporated in a matrix, the rate of release (i.e., the effective diffusion coefficient and Ft) depends on the molecular weight of the protein, the size of the dispersed particles, the loading, and the molecular weight of the polymer. For example, matrices of EVAc containing dispersed particles of bovine serum albumin (BSA) release protein for an extended period (Figure 9.11). The rate of release from the matrix depends on BSA loading (the number of BSA particles dispersed per unit volume of matrix) and BSA particle size. The rate of release from these matrices can be characterized by an effective diffusion coefficient or tortuosity, which must depend on the characteristics (i.e., particle size and loading) of the device. Tables 9.2 and 9.3 list the tortuosity values calculated from fits of the desorption equation to available literature data of protein release from EVAc slabs. 

This steep molecular weight dependence of the calculated intramembrane diffusion coefficient is somewhat unexpected. For diffusion in water, the experimental values of the diffusion coefficient bear an or dependence, a form... 

Figure 15 Self-diffusion data at 25 C in the toluene-water-alcohol-sodium dodecyl sulfate system (weight ratios 12.5 35.0 35.0 17.5) as a function of increasing chain length of the alcohol. The filled circles correspond to alcohol diffusion coefficients normalized by the diffusion coefficient of neat alcohol, which removes the trivial molecular weight dependence. Note that the self-diffusion coefficient of water decreases by more than two orders of magnitude as the cosurfactant is changed from butanol to decanol. (Data taken from Ref 95.)...

Schweizer and collaborators have elaborated an extensive mode-coupling model of polymer dynamics [52-54]. The model does not make obvious assumptions about the nature of polymer motion or the presence or absence of particular long-lived dynamic structures, e.g., tubes it yields a set of generalized Langevin equations and associated memory functions. Somewhat realistic assumptions are made for the equilibrium structure of the solutions. Extensive calculations were made of the molecular weight dependences for probe diffusion in melts, often leading by calculation rather than assumption to power-law behaviors for various transport coefficients. However, as presented in the papers noted here, the model is applicable to melts rather than solutions Momentum variables have been completely suppressed, so there are no hydrodynamic interactions. Readers should recall that hydrodynamic interactions usually refer to interactions that are solvent-mediated. 

Molecular weight dependence of the self and probe diffusion coefficients ) and Dp for molecular weight P probes in solutions of matrix polymers at a fixed concentration c. The fits are to stretched exponentials Z oexp(—aM ) in matrix molecular weight M. The Table gives the best-fit parameters, the percent root-mean-squaxe fractional fit error %RMS, the system, and the reference. Square brackets [ ] denote paxameters that were fixed rather than floated. Abbreviations as per previous Tables, and DBP-dibutylphthalate. 

For the cure study of radical reactions, such as the unsaturated polyester resin-styrene copolymerisation, a different and more elaborated approach incorporating a molecular weight dependent diffusion coefficient, shouldbe employed to take the Trommsdorff, or gel, effect into account. 

The diffusion coefficient D thus depends on the known or measurable quantities R, T, JVl, V2, and and on three unknowns the molecular weight M2, the asymmetry factor /, and the parameter T, . It cannot be interpreted molecularly without f urther assumptions. For unsolvated... 

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