Tobacco mosaic virus viscosity

Figure 4.21 Effect of axial ratio and particle concentration on relative viscosity. Data are for tobacco mosaic virus particles. Adapted from M. A. Lauffer, 7. Am. Chem. Soc., 66, 1188. Copyright 1944 by The American Chemical Society, Inc.

The ratio (a/b), called the axial ratio of the ellipsoid, is frequently used as a measure of the deviation from sphericity of a particle. It plays an important role, for example, in our discussions of sedimentation and viscosity in Chapters 2 and 4, respectively. In the event that a > b, the prolate ellipsoid approximates a cylinder and, as such, is often used to describe rod-shaped particles such as the tobacco mosaic virus particles shown in Figure 1.12a. Likewise, if a < b, the oblate ellipsoid approaches the shape of a disk. Thus, even the irregular clay platelets of Figure 1.12b may be approximated as oblate ellipsoids. 

Figure 4.12a shows plots of the intrinsic viscosity —in volume fraction units —as a function of axial ratio according to the Simha equation. Figure 4.12b shows some experimental results obtained for tobacco mosaic virus particles. These particles —an electron micrograph of which is shown in Figure 1.12a—can be approximated as prolate ellipsoids. Intrinsic viscosities are given by the slopes of Figure 4.12b, and the parameters on the curves are axial ratios determined by the Simha equation. Thus we see that particle asymmetry can also be quantified from intrinsic viscosity measurements for unsolvated particles. 

Dilute polyelectrolyte solutions, such as solutions of tobacco mosaic virus (TMV) in water and other solvents, are known to exhibit interesting dynamic properties, such as a plateau in viscosity against concentration curve at very low concentration [196]. It also shows a shear thinning at a shear strain rate which is inverse of the relaxation time obtained from the Cole-Cole plot of frequency dependence of the shear modulus, G(co). 

The exponent a in the intrinsic viscosity-molecular weight relationship ([rj] = K.M ) of a polymer is associated with the expansion of the polymer in solution, and hence with the conformation and stiffness of the polymer (Table 24). The a values of tobacco mosaic virus, Kevlar and helical poly(a-amino acids) are close to 2, which means that they take rigid-rod structures. The a values of vinyl polymers are usually 0.5-0.8, indicating randomly coiled structures. In contrast, the a values of substituted polyacetylenes are all about unity. This result indicates that these polymers are taking more expanded conformations than do vinyl polymers. This is atrributed to their polymer-chain stiffness stemming from both the alternating double bonds and the presence of bulky substituents. 

It seems probable that, as with desoxyribosenucleic acid, the size of the particles of ribosenucleic acid depends upon the treatment to which the acid has been subjected, the size being smaller when less mild methods of isolation are applied. Bawden and Pirie had pointed out that the size of the tobacco mosaic virus ribosenucleic acid particles is larger than that of the particles of yeast ribosenucleic acid as usually prepared. Loring has now found that purified, commercial yeast ribosenucleic acid solutions have about the same specific viscosity as have solutions of the alkali-treated ribosenucleic acid of tobacco mosaic virus hence, their molecular sizes are probably of the same order (about 15,000). 

The experimental data (Lee and Meyer, 1991) on the viscosities of PBG and tobacco mosaic virus (TMV) were compared with the theories, as shown in the Table 6.9. A good agreement was found between them for both PBG and TMV. 

Figure 4. Flory-Mandelkern correlation of intrinsic viscosity, molecular weight, and translational diffusion coefficient for a variety of polymer solvent systems, demonstrating the insensitivity of these data to the structure of the macromolecule ( X PS/tetrahydrofuran (37) (O), protein random coils in 6M guanidine hydrochloride-0,IM mercaptoethanol (26) (X), tobacco mosaic virus in aqueous solution (11) ( ), bovine serum albumen in aqueous solution (37).

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