Angular Distribution of Intensity of Rayleigh Scattering from Comblike Branched Molecules

1968 ◽  
Vol 41 (2) ◽  
pp. 437-451
Author(s):  
Edward F. Casassa ◽  
Guy C. Berry
Keyword(s):  
Angular Distribution ◽  
Rayleigh Scattering ◽  
Large Fraction ◽  
Limited Range ◽  
Radius Of Gyration ◽  
Molecular Weights ◽  
Vinyl Polymers ◽  
Linear Chains ◽  
Angular Distribution Function ◽  
Number Of Branches

Abstract The angular distribution function P(θ) for intensity of light scattered by a dilute solution of comblike branched molecules has been determined for three situations of some interest for evaluation of experimental data: (1) the molecules are identical with branches of equal length attached equidistantly along linear backbone chains; (2) the molecules are homogeneous in mass, with the same number of branches on each molecule, but the branches are distributed at random along the chain; (3) branches and main chains are still uniform, but the molecules are heterogeneous in mass with the number of branches per molecule distributed according to the binomial distribution and the branches in any molecule spaced randomly along the backbone. Examination of numerical results shows that the scattering functions for models (1) and (2) arc not very different. The function for case (3) is somewhat different from the others when the mean number of branches per molecule is small but they contain a large fraction of the mass of the molecule. Over a limited range of the pertinent variables (corresponding roughly to observations on typical vinyl polymers of molecular weights up to 106) all three functions agree quite well with P(θ) for homogeneous linear chains with the same mean square radius of gyration.

scholarly journals Modeling Replenishment of Ultrathin Liquid Perfluoropolyether Z Films on Solid Surfaces Using Monte Carlo Simulation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
M. S. Mayeed ◽  
T. Kato
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Liquid Films ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Carbon Surface ◽  
Radius Of Gyration ◽  
Constant Multiple ◽  
Molecular Weights ◽  
Lattice Polymer

Applying the reptation algorithm to a simplified perfluoropolyether Z off-lattice polymer model an NVT Monte Carlo simulation has been performed. Bulk condition has been simulated first to compare the average radius of gyration with the bulk experimental results. Then the model is tested for its ability to describe dynamics. After this, it is applied to observe the replenishment of nanoscale ultrathin liquid films on solid flat carbon surfaces. The replenishment rate for trenches of different widths (8, 12, and 16 nms for several molecular weights) between two films of perfluoropolyether Z from the Monte Carlo simulation is compared to that obtained solving the diffusion equation using the experimental diffusion coefficients of Ma et al. (1999), with room condition in both cases. Replenishment per Monte Carlo cycle seems to be a constant multiple of replenishment per second at least up to 2 nm replenished film thickness of the trenches over the carbon surface. Considerable good agreement has been achieved here between the experimental results and the dynamics of molecules using reptation moves in the ultrathin liquid films on solid surfaces.

Spectral and angular distribution of Rayleigh scattering from plasmon-coupled nanohole chains

2009 ◽  
Vol 94 (2) ◽  
pp. 021112 ◽  
Author(s):  
Yury Alaverdyan ◽  
Eva-Maria Hempe ◽  
A. Nick Vamivakas ◽  
Haibo E ◽  
Stefan A. Maier ◽  
...  
Keyword(s):  
Angular Distribution ◽  
Rayleigh Scattering

scholarly journals Biobased Polymers via Radical Homopolymerization and Copolymerization of a Series of Terpenoid-Derived Conjugated Dienes with exo-Methylene and 6-Membered Ring

Molecules ◽  
2020 ◽  
Vol 25 (24) ◽  
pp. 5890
Author(s):  
Takenori Nishida ◽  
Kotaro Satoh ◽  
Masami Kamigaito
Keyword(s):  
Conjugated Dienes ◽  
Membered Ring ◽  
Feed Ratio ◽  
Vinyl Monomers ◽  
Monomer Reactivity Ratios ◽  
Molecular Weights ◽  
Vinyl Polymers ◽  
Biobased Polymers ◽  
Reversible Addition ◽  
Raft Agent

A series of exo-methylene 6-membered ring conjugated dienes, which are directly or indirectly obtained from terpenoids, such as β-phellandrene, carvone, piperitone, and verbenone, were radically polymerized. Although their radical homopolymerizations were very slow, radical copolymerizations proceeded well with various common vinyl monomers, such as methyl acrylate (MA), acrylonitrile (AN), methyl methacrylate (MMA), and styrene (St), resulting in copolymers with comparable incorporation ratios of bio-based cyclic conjugated monomer units ranging from 40 to 60 mol% at a 1:1 feed ratio. The monomer reactivity ratios when using AN as a comonomer were close to 0, whereas those with St were approximately 0.5 to 1, indicating that these diene monomers can be considered electron-rich monomers. Reversible addition fragmentation chain-transfer (RAFT) copolymerizations with MA, AN, MMA, and St were all successful when using S-cumyl-S’-butyl trithiocarbonate (CBTC) as the RAFT agent resulting in copolymers with controlled molecular weights. The copolymers obtained with AN, MMA, or St showed glass transition temperatures (Tg) similar to those of common vinyl polymers (Tg ~ 100 °C), indicating that biobased cyclic structures were successfully incorporated into commodity polymers without losing good thermal properties.

Structure of Polymer Chains Confined in Vycor

1996 ◽  
Vol 464 ◽  
Author(s):  
Jyotsana Lal ◽  
Sunil K. Sinha ◽  
Loic Auvray
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Form Factor ◽  
Small Angle Neutron Scattering ◽  
Pore Diameter ◽  
Polymer Chains ◽  
Bulk Solution ◽  
Radius Of Gyration ◽  
Single Chain ◽  
Molecular Weights

ABSTRACTWe observe by Small Angle Neutron Scattering (SANS) the structure of polystyrene chains in semi-dilute solutions confined in model porous medium, Vycor. The size of the free polymer chains in solution is always larger than the pore diameter, 70 Å. The use of a suitable mixture of hydrogenated and deuterated solvents and polymers enables us to directly measure the form factor of one single chain among the others. The penetration of the chain in the porous media is almost complete for the concentration (Φ = 20%) and the range of molecular weights (35000 <M< 800000) used. The measured radius of gyration of confined chains is always smaller than the radius of gyration of free chains in the equivalent bulk solution.

A note on the enhancement of J values in optically thick scattering atmospheres

1991 ◽  
Vol 69 (8-9) ◽  
pp. 1166-1174 ◽  
Author(s):  
Jacek W. Kaminski ◽  
John C. McConnell
Keyword(s):  
Multiple Scattering ◽  
Rayleigh Scattering ◽  
Large Fraction ◽  
Coherent Scattering ◽  
Single Scattering ◽  
Average Density ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Surface Reflection ◽  
Thick Medium

In a planetary atmosphere the J value is determined by the angular-averaged radiance, or the average density of photons in an element of volume. The average density may be enhanced by multiple scattering of photons in a conservative, or near-conservative scattering atmosphere. We show that in a conservative semi-infinite medium this enhancement will be a factor of 5, for optical depths greater than about 20 for coherent scattering. We investigate the modification of the J values owing to multiple scattering in an optically thick medium of various optical depths, various single-scattering albedos of the scattering medium, and a range of surface albedos. We have applied the results to the calculation of J values in clouds in the terrestrial atmosphere and in the Rayleigh-scattering atmosphere of Uranus. We note that J values in a realistic atmosphere may be enhanced by as much as a factor of 5 throughout a large fraction of the atmosphere over those calculated without multiple scattering and surface reflection.

Activities and Ionic Distributions in Cobalt Silicate Melts

1971 ◽  
Vol 49 (5) ◽  
pp. 683-690 ◽  
Author(s):  
I. B. Smith ◽  
C. R. Masson
Keyword(s):  
Silica Content ◽  
Silicate Melts ◽  
Molecular Weights ◽  
Polymer Theory ◽  
Linear Chains ◽  
Experimental Values ◽  
The Relationship ◽  
Gas Chromatographic Separation ◽  
Good Agreement ◽  
Binary Silicate

Activities of CoO in CoO–SiO2 melts were measured at 1450–1500 °C by equilibrating the melts, held in Pt–Rh containers, with atmospheres of known oxygen potential. Activities were calculated by the relationship[Formula: see text]where aCo, the activity of cobalt in the container, was determined in separate experiments.The results were compared with theoretical activity–composition curves based on the application of polymer theory to silicate melts. The results were in good agreement with theoretical curves calculated on the assumption of linear chains. In contrast, for all other binary silicate melts so far investigated the results are best represented in terms of theory in which all chain configurations are allowed. Ionic distributions and number average and weight average molecular weights were calculated as functions of the silica content from the experimental data. The calculated proportions of monomeric ion, SiO44−, dimer Si2O76−, and trimer Si3O108− were in reasonable agreement with experimental values based on trimethylsilylation and gas-chromatographic separation of the ionic constituents in quenched melts.

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