Polystyrenes square radii

Polystyrene square radii of gyration and second virial coefficient for cyclic and linear chains. Macrocyclic fractions with 11,500 < /W < 181 000 [223, 224]... 

Figure 9 Scaling relationship between root-mean-square radius and molecular weight for polystyrene using GPC/MALLS. (From Wyatt, P. Hicks, D. L., Jackson, C., and Wyatt, G. K., Am. Lab., 20, 108,1988. With permission.)...

Figure 6. Log M versus local root-mean-square radius for a broad polystyrene standard (-----) and narrow polystyrene standards (m).

Problem 4.18 For the polystyrene sample in Problem 4.17 calculate (a) the second virial coefficient, (b) the root mean square end-to-end distance, and (c) the root-mean-square radius of gyration. 

Fig-1- Variation of the apparent mean-square radius of gyration app (solid lines) and the apparent reciprocal hydrodynamic radius app (dotted lines) as a function of the solvent refractive index ns and refractive index increment dn/dc for a heterogeneous star mol ecule (AB)f with f= 18 block B, polyisoprene, M=230 000 block A, polystyrene, M=150 000... 

Columns 7 and 8 contain quantities associated with the Brownian state of the samples the Z average, °Rg,z> of the mean square radius of gyration and the constant °A = °Rg.z/M. These constants are measured in the limit of zero concentration in poor solvents, at a temperature T TP, where Tv is defined in Chapter 14, Section 2.2 teams A, C, and E used cyclohexane, team D used trans-decalin. The reference temperatures to the Brownian state are, for cyclohexane 34.5 °C (team A) and 34.6 °C (teams C and E), for trans-decalin 20.5°C. In Chapter 16, we shall see that the experimental value of 7f. is more precisely 34 °C for polystyrene in cyclohexane. The fact that T does not correspond exactly to Tf is of minor importance here. 

The square radius of the polystyrene chain of molecular mass Mw = 3.8 x 106... 

The method used to obtain these results is, however, not very convincing. It has not been proved that the samples of teams A and C are close enough to the Kuhnian state. Moreover, the temperatures of the solutions are different for teams A and C, and this introduces a systematic error in the results. Nevertheless, we shall adopt (15.3.46) as the best experimental expression for the asymptotic law relating the square radius of gyration to the molecular mass for polystyrene in benzene at 25 °C. On the other hand, for polystyrene in CS2, we shall adopt the older result7... 

Abe, R, Einaga, Y., Yoshizaki, T., and Yamaka, H., Excluded volume effects on the mean-square radius of gyration of oligo- and polystyrenes in dilute solutions, Macromolecules, 26, 1884-1890 (1993a). 

Figure 5.1 The root mean-squared radius of gyration, (Rq), of polystyrene of molecular weight M = 1.2 X 10 g/mol in Decalin as a functmn of temperature. (From Nose, T. and Chu, B., Macromolecules, 12, 1122, 1979. With permission.)...

Figure 4.19. Reduced mean square radius of gyration, R, of polystyrene in carbon disulfide, plotted as a function of the polymer concentration c. Data were obtained in smaU-angle neutron scattering. The straight line has a slope of —1/4. (From Ref. 49.)...

Fig. 8. Mean square radius of gyration of polystyrenes in toluene, o, linear. +, 4-star,, 6-star. Data from Refs. ...

Fig. 9.6 Radius of gyration (Rq)/(R j (lower curve) and average squared end-to-end distance (upper curve) versus / for a good solvent. ) is the mean-squared radius of gyration for a single polymer chain. The solid circles are data for polystyrene and polyisoprene from Ref 180. The crosses are from the off-lattice MC simulations of Freire et al. for N = 49 or 55. The other symbols are from MD simulations for monomers interaeting with a purely repulsive Lennard-Jones interaction, eq. (9.3), at T=l.2e/ke for A=100(o) and at r=4.0e/fc s for = 2.5(7 for A = 50(A) and 100 ( ). The solid line has slope of 0.41. (From Ref 117.)...

Figure 5.10. Variation of the mean square radius of gyration for polystyrene chains in toluene solution at 15 C.

An example of a Maugis-Pollock system is polystyrene particles having radii between about 1 and 6 p.m on a polished silicon substrate, as studied by Rimai et al. [64]. As shown in Fig. 4, the contact radius was found to vary as the square root of the particle radius. Similar results were reported for crosslinked polystyrene spheres on Si02/silicon substrates [65] and micrometer-size glass particles on silicon substrates [66]. 

Fig. 4. The contact radius as a function of the square root of the particle radius for polystyrene spheres on a silicon substrate (from ref. [64]).

Figure 26-15 Larger CdSe quantum dots are eluted before smaller quantum dots by 0.1 M trioctylphosphine in toluene at 1.0 mL/min in size exclusion chromatography on a 7.5 x 300 mm cross-linked polystyrene column of 100-nm pore size Polymer Labs PLgel 5 (im. Triangles are CdSe and squares are polystyrene calibration standards. The size of the CdSe core was measured with a transmission electron microscope and the length of 1-dodecanethiol endcaps (0.123 nm) was added to the radius. [Data from K. M. Krueger. A. M. Al-Somall, J. C. Falkner, and V. L. Colvin, "Characterization of Nanocrystalline CdSe by Size Exclusion Chromatography," Anal. Chem. 2005, 77,3511.]...

Molar mass dependence of the radius of gyration from light scattering in dilute solutions for polystyrenes in a 0-solvent (cyclohexane at 0 = 34.5 °C, circles) and in a good solvent (benzene at 25 C, squares). Data are compiled in L. J. 

Perzynski et al.2 measured (by light scattering) the (mean) square J g(polystyrene chains of molecular mass Mw = 1.26 x 106 (S = 2092 nm2) for various temperatures T( TF) and for various volume fractions in the range 10 5 < q> < 10-4. The radii are extrapolated at zero concentration for a given temperature T, we write... 

There exists only fragmentary data in the literature for the experimental dependence of V2 on the particle radius. For example. Table 16.4 shows the data of Clarke and Vincent (1981a) for the floccidation of silica particles, sterically stabilized by polystyrene in ethyl benzene, by free polystyrene of molecular weight ca 7 000. An approximate dependence of V2 on the inverse square root of the particle size is indicated. 

Table 16.5). In this instance, however, the particles were dispersed in cyclohexane rather than ethyl benzene. Moreover, the dispersions were said to undergo phase separation rather than particle flocculation. The data reported by de Hek and Vrij for two particle sizes suggest that V2 is inversely related to the particle radius, rather than the square root of the particle radius. The radius dependence observed for this system is that which would be predicted if the ideal van t Hoff term was predominantly responsible for the osmotic pressure of the polymer solution, since AG would then be proportional to V2 a, i.e. V2 oc 1/a. This result is scarcely surprising since cyclohexane is a poor solvent for polystyrene (0=34°C). In those circumstances, only the ideal contribution to the osmotic pressure need be considered. The different radius dependences observed in such experiments is accordingly explained.

Concentration and molecular weight dependences of the probe radius of gyration Rg for molecular weight P probes in solutions of molecular weight M matrix polymers as functions of matrix concentration c. The fits are to stretched exponentials Rgo exp(—ac"), with the percent root-mean-square fractional fit error %RMS, the materials, and the reference. Materials include EB-ethyl benzoate, PMMA-polymethylmethacrylate, pS-polystyrene. 

Square of gyration radius Rc for one labeled polystyrene chain in a polystyrene solution of concentration c. Above c = c, decreases with a well-defined exponent. At high c, Ro returns to the ideal chain value. After Daoud t al.. Macromolecules 8, 804 (1975). 

Characteristic width of the photon beat spectrum Itk of polystyrene solutions as a function of the wave vector AT. The width is normalized by the diffusion width />o A, and the wave vector is expressed through KR when R is the coil radius. The squares and the triangles correspond to two very different molecular weights, suggesting that there is indeed a universal scaling form. From M. Delsanti, Ph.D. Thesis, Orsay, 1978. 

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