Segmental diffusion viscosity

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

When the encounter probability of reactive groups and the rate of reaction becomes controlled by the segmental mobility (viscosity of the medium), overall diffusion control sets In. The overall diffusion control is typical of polymer systems In which, as a result of the chemical reaction, the system passes from the liquid (rubbery) state Into the glassy state. 

The two groups are hindered by increasing viscosity from associating (entering the reaction volume) and dissociating (going out of the reaction volume) by the same factor. However, the rate constant kz can Itself become controlled by segmental diffusion. 

Equation 2 can be checked by drawing a log-log-plot of the experimental data, obtained at different temperatures in various solvents, as shown in Figure 5. In the case of a pure segmental diffusion process, we find a straight line of slope 1. Figure 5 shows that this holds for MMA over a wide range of temperatures and viscosities. 

Figure 5. Segmental diffusion constant depending on temperature and solvent viscosity data are calculated according to Equation 1 and the graph according to Equation 2...

Termination reactions occur between two relatively large radicals, and termination rates arc limited by the rates at which the radical ends can encounter each other. As a result, kt is a decreasing function of the dimensions of the reacting radical. The segmental diffusion coefficient and the termination rate constant increase as the polymer concentration increases from zero. This initial increase is more pronounced when the molecular weight of the polymer is high and/or when the polymerization is carried out in a medium which is a good solvent for the polymer. For similar reasons, k t is inversely proportional to the viscosity of reaction medium. A model has been proposed that accounts for these variations in k, in low-conversion radical polymerizations [15,16]. 

As polymerization proceeds and viscosity increases, at some point the translational diffusion decreases faster than the increase in segmental diffusion and rapid autoacceleration or the gel effect (Stage II) occurs. When the polymer concentration becomes high enough, the chain radicals become more crowded and entangled with each other. As a result, the rate... 

Reactions that are bimolecular can be affected by the viscosity of the medium. The translational motions of flexible polymeric chains are accompanied by concomitant segmental rearrangements. Whether this applies to a particular reaction, however, is hard to tell. For instance, two dynamic processes affect reactions, like termination rates, in chain-growth polymerizations. If the termination processes are controlled by translational motion, the rates of the reactions might be expected to vary with the translational diffusion coefhcients of the polymers. Termination reactions, however, are not controlled by diffusions of entire molecules, but only by segmental diffusions within the coiled... 

Diffusion theories have been proposed that relate the rate constant of termination to the initial viscosity of the polymerization medium. The rate-determining step of termination, the segmental diffusion of the chain ends, is inversely proportional to the microviscosity of the solution [123]. Yokota and Itoh [124] modified the rate equation to include the viscosity of the medium. According to that equation, the overall polymerization rate constant should be proportional to the square root of the initial viscosity of the system. 

Based on their observations. North and Reed concluded that the differences in kt between the different methacrylates that they had studied were too large to be explained on the basis of translational diffusion. Instead, they proposed a simplified segmental diffusion model, in which the length of the ester tail determined the resistance to diffusion of the chain end out of the polymer coil into a region where it could react with another radical. Consequently, for monomers with a longer ester chain there is more resistance against segmental reorientation and, hence, bulk viscosity had less influence [62]. 

There are clear similarities between segmental diffusion and solvent and small-molecule diffusion. At lower viscosities (// < 2,5 cP, respectively), the associated transport coefficient scales as / . For larger viscosities, the associated transport coefficient scales as / " for a in the range 0.55-0.82 or 0.7, respectively. These... 

S. Adams and D. B. Adolph. Viscosity dependence of the local segmental diffusion of anthracene-labeled 1,2-polybutadiene in dilute solution. Macromolecules, 31 (1998), 5794-5799. 

S. Glowinkowski, D. J. Gisser, and M. D. Ediger. Carbon-13 nuclear magnetic resonance measurements of local segmental diffusion of polyisoprene in dilute solution nonlinear viscosity dependence. Macromolecules, 23 (1990), 3520-3530. 

The original Kramers equation had a = 1 at all /, not the a 0.4-0.8 seen here at larger q. However, as seen in Chapter 5, solvent diffusion actually has the viscosity-dependence of Eq. 15.3 with an 7-dependent a, namely a = 1 at smaller qtoa = 2/3 at q larger than 5 cP. The small-molecule self-diffusion coefficient and the segmental diffusion time thus show consistent dependences on q. The spirit of the Kramers approach, namely that the rate of diffusion-driven molecular motions should track the solution fluidity q in the same way that the rates of solvent and small-molecule diffusion track the solution fluidity, appears to be preserved by experiment. 

Fitting yields a surface tension )> = 4.5mNm" that compares to the prediction using the expression of Helfand and Sapse, which yields )> = 3.3mNm". The local viscosity as derived from the Rouse theory implies the involvement of 13 PI units. The Rouse rate also controlling the 2D segmental diffusion corresponds to the homopolymer value. 

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