Angular distribution of intensity of rayleigh scattering from comblike branched molecules

Casassa, Edward F.; Berry, G. C.

doi:10.1002/pol.1966.160040605

Cited by 87 publications

(65 citation statements)

References 15 publications

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“…14 The P(q) function derived by Benoit for star-branched polymers on the assumption of a Gaussian distribution of the chain elements is 16,17 where f is the number of arms and V ) ( f /(3f -2)) 1/2 qR g . As the star becomes denser (increasing f), u ) q max R g is expected to decrease and reach a limit of 3.76, closer to 3.…”

Section: Resultsmentioning

confidence: 99%

Conformation of Arborescent Polymers in Solution by Small-Angle Neutron Scattering: Segment Density and Core−Shell Morphology

et al. 2007

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The radius of gyration (R g ) was determined as a function of generation number for arborescent polystyrenes with two different side chain mass average molecular mass (M w ≈ 5000, 5K, versus 30 000, 30K) by small-angle neutron scattering (SANS) measurements. The R g values obtained were analyzed in terms of the Zimm-Stockmayer model for randomly branched polymers, the scaling relation R g ∝ M w V , and the expansion factor R s ) (R g ) goodsolvent /(R g ) Θsolvent . The R g and scaling exponent V ) 0.26 ( 0.01 found for G0 through G3 polymers with 5K side chains in cyclohexane-d correspond to the values predicted by the Zimm-Stockmayer model. The R g for G0 through G3 polymers with 30K side chains deviate from the model with V ) 0.32 ( 0.02, corresponding to V ) 0.33 expected for hard spheres. Deuterated polystyrene (PS-d) side chains were grafted onto G2 and G3 polystyrene (PS) cores. These copolymers, G2PS-graft-PS-d and G3PS-graft-PS-d, were characterized as spheres with a well-defined PS core-PS-d shell structure by the SANS contrast matching method. The shape and the segment radial density profile of the core and shell for GPS-graft-PS-d were determined based on P(r) and ∆F(r) obtained by indirect Fourier transformation and deconvolution methods (P(r), pair distance distribution function and ∆F(r) ) F(r) -F(solvent), scattering length density contrast profile).

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Section: Resultsmentioning

confidence: 99%

Conformation of Arborescent Polymers in Solution by Small-Angle Neutron Scattering: Segment Density and Core−Shell Morphology

et al. 2007

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“…In most branching analysis, measured g ′ is usually related with the theoretical g rw , not experimentally measured g . Casassa and Berry reported the theoretical prediction of the contraction factor g rw of comb‐shaped polymers based on random walk statistics . Among a few different model architectures of the model comb polymers, the theoretical prediction of g rw for a random comb is as follows

g_{rw} = λ + \frac{normal2}{f} λ {(1 - λ)}^{normal2} + (\frac{normal3 f - normal2}{f^{2}}) {(1 - λ)}^{normal3}

where λ is the weight fraction of backbone, and f is the number of branches.…”

Section: Resultsmentioning

confidence: 99%

Branching Analysis of Comb‐Shaped Polystyrene with Long Chain Branches

Lee

Chang

2017

Macro Chemistry & Physics

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Model comb-shaped polystyrene (PS) samples are synthesized by anionic polymerization and the as-prepared PS heterogeneous combs are further fractionated by temperature gradient interaction chromatography (TGIC) to obtain well-defined random combs with 1-4 branches at random positions on a backbone. Size exclusion chromatography-triple detection and TGICtriple detection analyses are carried out with the fractionated PS random combs in a good and a theta solvent, respectively. The experimentally observed geometric contraction factor (g), the ratio of the mean square radius of gyration and the hydrodynamic contraction factor (g′), and the ratio of the intrinsic viscosity are compared. It is observed that the two contraction factors follow the relationship of g′ = g ε reasonably well and the exponent ε of the PS combs is found as ∼1 in a good solvent and ∼0.66 in a theta solvent. Furthermore, it is found that the theoretical g rw is not in good agreement with the experimental results.

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“…This behavior reflects the structure of star polymers. In the case of regular combshaped homo-polymers at a q state, a mean-square radius of gyration hS 2 i comb can be derived (for large m) as [31,32] hS 2 i comb Z l C ð1KlÞ 7=3 ð3nK2Þ n 2 ! mb 2 6…”

Section: The Specific Dimensions Of the Poly(psm) N Star Polymersmentioning

confidence: 99%

Anionic living polymerization of macromonomers: Preparation of a particle-like purging reagent and characterization of poly(macromonomer)s

Inoue

Yamashita

2005

Polymer

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A cross-linked polystyrene particle (Merrifield resin, R-C 6 H 5 ) was reacted with benzoyl chloride in nitrobenzene to produce R-C 6 H 4 -COC 6 H 5 having a benzophenone group, and the R-C 6 H 5 -COC 6 H 5 was reacted with a sodium mirror in THF under 10 K5 mmHg to produce R-C 6 H 5 -CO K C 6 H 5 Na C containing a benzophenone sodium as a particle-like purging reagent (PPBNa). (4-vinylbenzyl)Polystyrene macromonomers (PSM4: M n Z4.6 2 !10 3 , M w /M n Z1.0 3 and PSM7: M n Z7.1 0 !10 3 , M w /M n Z1.0 2 ) were dried under 10 K6 mmHg for more than 72 h, purified by a special procedure using the PPBNa, and then were living anionically polymerized by sec-BuLi in benzene or n-BuLi in tetrahydrofuran to produce the corresponding poly(PSM) n star polymers. The resultant star polymers were characterized by gel permeation chromatography equipped with low-angle laser light-scattering (GPC-LALLS), membrane osmometry (OSM), and light-scattering (LS). Anionic living polymerization of the PSM macromonomers was confirmed by the fact that the molecular weight of the poly(PSM) n increased and by the fact that the initiation efficiency was constant despite an increase in the polymer yields. Some solution properties and specific dimensions characteristic to the poly(PSM) n star polymers are discussed by comparing the GPC-LALLS, OSM, and LS results for those polymers with the results for linear polystyrenes. q

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Angular distribution of intensity of rayleigh scattering from comblike branched molecules

Cited by 87 publications

References 15 publications

Conformation of Arborescent Polymers in Solution by Small-Angle Neutron Scattering: Segment Density and Core−Shell Morphology

Conformation of Arborescent Polymers in Solution by Small-Angle Neutron Scattering: Segment Density and Core−Shell Morphology

Branching Analysis of Comb‐Shaped Polystyrene with Long Chain Branches

Anionic living polymerization of macromonomers: Preparation of a particle-like purging reagent and characterization of poly(macromonomer)s

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