Mathematical properties of polydisperse systems, 2. Application to light scattering

Greschner, Georg S.

doi:10.1002/macp.1973.021700117

Cited by 43 publications

(18 citation statements)

References 17 publications

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“…28 The differences in R, between using eq 5a and the modified formula were calculated and averaged 0.3%, with a maximum of 0.7% in one case. The corrections are small and were ignored.…”

Section: Resultsmentioning

confidence: 99%

Radii of gyration and screening lengths of polystyrene in toluene as a function of concentration

King¹,

Boyer²,

Wignall³

et al. 1985

Macromolecules

123

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Small-angle neutron scattering (SANS) experiments on solutions of polystyrene (PSH) and its deuterated homologue (PSD) in deuterated toluene have been performed over a wide range of concentration.Several redundant measurements demonstrated that the high-concentration technique of extracting single-chain scattering functions is highly reliable. Radii of gyration and screening lengths were fitted to power laws and were found to be R N c-".lW and f N c-".'O. The resulta differ significantly from predictions by scaling theory, though the dependence of E on c is in good accord with that previously found by other researchers. These experiments were also analyzed by using recent theoretical results of Muthukumar and Edwards. Measurements at different concentrations yielded a reasonably consistent value of the excluded volume interaction parameter.

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“…28 The differences in R, between using eq 5a and the modified formula were calculated and averaged 0.3%, with a maximum of 0.7% in one case. The corrections are small and were ignored.…”

Section: Resultsmentioning

confidence: 99%

Radii of gyration and screening lengths of polystyrene in toluene as a function of concentration

King¹,

Boyer²,

Wignall³

et al. 1985

Macromolecules

123

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“…͑9͒ is the result of convoluting Eq. ͑8͒ and a particle size distribution function, such as the Zimm-Schultz distribution: 36,43,44 …”

Section: -6mentioning

confidence: 99%

On the difference in scattering behavior of cyclic and linear polymers in bulk

Gagliardi

Arrighi

Ferguson

et al. 2005

The Journal of Chemical Physics

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It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane ͑PDMS͒ and, through the analysis of the small angle neutron scattering ͑SANS͒ profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q ͑−2͒ dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q ͑−2͒ that is expected on the basis of Monte Carlo calculations and from the Casassa equation ͓E. F. Casassa, J. Polym. Sci. A 3, 605 ͑1965͔͒. It is also shown that, for rings, the Debye equation ͓P. Debye, J. Appl. Phys. 15, 338 ͑1944͔͒ is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to M w Ϸ 10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for M w Ͼ 11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change.

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“…The ratio, N w /N n , is called the "polydispersity index" (sometimes the right-hand side of eq 13 is abbreviated by U and called the "polydispersity coefficient" 10 or the "non-uniformity" 42 ). Equation 13shows that N n is in general smaller than N w , which in turn is smaller than N z .…”

Section: Model and Chain Length Averagesmentioning

confidence: 99%

Statics and Dynamics of Bidisperse Polymer Melts: A Monte Carlo Study of the Bond-Fluctuation Model

et al. 1998

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As a first step toward the computer simulation of polydisperse polymeric melts, a lattice model containing two types of chains with lengths N 1 = 20 − x and N 2 = 20 + 4x (0 ≤ x ≤ 10 ) is studied. This variation of x, together with the fixed composition of 80% of short and 20% of long chains, leads to a polydispersity of 1 ≤ N w/N n ≤ 2 (N w, N n: weight-, number-average chain lengths). To represent dense melts, the bond-fluctuation model at a volume fraction, φ = 1/2, of occupied lattice sites is used. The simulation treats both the athermal case (chain connectivity and excluded volume interaction only) and a thermal case, where additionally a choice for the bond length and bond angle potentials is made, which has recently been proposed to mimic polyethylene. For both cases number-, mass-, and z-averages of various static and dynamic quantities are calculated and compared with the results of the monodisperse melt. The main results are as follows. Whereas structural properties of the mono- and bidisperse melts agree with each other, dynamic properties are different. Short chains are slowed down by long ones, and long chains are in turn accelerated by the short species. This leads to a weaker chain length dependence of the chain's diffusion coefficient and relaxation time, which are then closer to the predictions of the Rouse theory than in the monodisperse case. For the thermal model, the stronger slowing down of the long compared to the short chains can be interpreted in terms of Arrhenius laws with an activation energy that increases with chain length.

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Mathematical properties of polydisperse systems, 2. Application to light scattering

Cited by 43 publications

References 17 publications

Radii of gyration and screening lengths of polystyrene in toluene as a function of concentration

Radii of gyration and screening lengths of polystyrene in toluene as a function of concentration

On the difference in scattering behavior of cyclic and linear polymers in bulk

Statics and Dynamics of Bidisperse Polymer Melts: A Monte Carlo Study of the Bond-Fluctuation Model

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