Polystyrene correlation length

Fig. 4. Correlation length as a function of polymer concentration measured by neutron scattering by Daoud et al. (1975). Closed symbols denote polystyrenes of two different molecular weights in deuterated benzene open symbols denote deuterated polystyrenes of two molecular weights in carbon disulfide.

Fig. 5. Correlation length, scaled on Rt, as a function of reduced concentration X c/c as measured through static light-scattering by Wiltzius et al. (1983). Symbols denote various molecular weight polystyrenes in toluene and methyl ethyl ketone at 25°C.

The correlation length has been measured using scattering experiments, as discussed in Section 5.7. Small-angle neutron scattering (SANS) data on polystyrene in deuterated cyclohexane at 0 = 38.O°C are summarized in Fig. 5.8. These data are in good agreement with the power law expected by Eq. (5.52), shown as the line. 

Correlation length and radius of gyration for polystyrene in carbon... 

The thermic correlation lengths , derived from the interaction b are given in Table 15.6. Let us recall that the persistence length of atactic polystyrene is equal to 2 nm. Condition (15.3.29) is therefore satisfied. 

The value of Mf in polymer melts is tabulated in the literature, from which a is found to be 82 A for polystyrene and 34 A for polyethylene. This distance is mudi larger than the correlation length measured by neutron scattering or X-ray scattering. At present, it is not fully understood what factors determine a, but various semiempirical relations are available for Here we shall proceed regarding a as an... 

Wiltziiis et al. (1983, lOSd) have compared the dynamic and static correlation length within a wide range of polystyrene concentrations in benzene, and melhylethylketonc. f was determined using Equation 22, and D meeisured from the first cumulant K (q — 0) of dynamic scaling (Equation 3.3-85). was evaluated by... 

Figure 1.16. Dynamic and stalk f correlation length ratio in polystyrene solutions in toluene (transparent signs) and in methylcthylketonc (black signs) " as a function of polymer concentration (Wiltzius et al., 1984) [Reprinted with permission from P.Wiltzius, H.R.Haller, D.S.Cannell, D.W.Schaefcr. Phys. Rev. Lott. 53 (198-1) 83-1-837 Copyright 1984 by the American Physical Society]...

Figure 4.16. Scaling plot for the correlation length evaluated in static light-scattering measurements for solutions of polystyrene in toluene and methyl ethyl ketone. The reduced correlation length i/Rgo is plotted as a function of l6/9)A2Mc in a double logarithmic scale. The dashed line has a slope of —3/4. (From Ref. 48.)...

Figure 4.29. Correlation length estimated from the cooperative diffusion coefficient. Data were obtained for polystyrene of different molecular weights in various good solvents. (From Ref. 51.)...

However, the susceptibility becomes spatially dependent and thus finite at qy>. This means that at small scales the fluctuations are suppressed and the thermodynamic properties are controlled by the instrumental scale L = q. When the correlation length considerably exceeds L, is replaced by L. Figure 7.12 shows the osmotic susceptibility of polystyrene-cyclohexane solutions obtained for various temperatures, and two length scales... 

HAM Hamano, K., Kuwahara, N., and Kaneko, M., Scaled functions of osmotic compressibility and correlation length of polystyrene in diethyl malonate, Phys. Rev. A, 20, 1135, 1979. 

Fig. 7.41. The variation of the correlation length, , as a function of T — Tc for polystyrene in cyclohexane (a) and PDMS in supercritical CO2 (b). The slopes give the values of the critical index, v. (Reproduced with permission from [239]. Copyright 1999 American Chemical Society.)...

Contrary to the earlier beliefs, dynamical properties of semidilute solutions at the theta temperature are much more difficult to comprehend than properties of good-solvent solutions. Here, without going either into the details of the experimental determination or theoretical considerations, we will review different experimental results obtained on polystyrene solutions. Our aim is to show that, at the theta temperature, the mesh size of the transient gel is not proportional to the correlation length of the concentration fluctuations. The coexistence of these two characteristic lengths explains why some dynamical properties do not obey scaling laws at the theta temperature. 

W. Brown and K. Mortensen. Comparison of correlation lengths in semidilute polystyrene solutions in good solvents by quasi-elastic light scattering and small-angle neutron scattering. Macromolecules, 21 (1988), 420-425. 

The effect of fiber diameter on the tensile strength of a glass-fiber-reinforced polystyrene composite is shown in Figure 5.100. Some reinforcements also have a distribution of fiber diameters that can affect properties. Recall from the previous section that the fiber aspect ratio (length/diameter) is an important parameter in some mechanical property correlations. 

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