Papers by Ramnath Ramachandran
A recent method to quantify molecular topology of various materials using small angle scattering ... more A recent method to quantify molecular topology of various materials using small angle scattering will be presented. Small angle x-ray and neutron scattering has been used to characterize ceramic aggregates and polymer structures systems respectively. The structural differences in various systems arise from the competition between thermal and spacial constraints. The details in ceramic aggregates like branch fraction, number of segments in an aggregate and the short circuit path, coordination number, the number end groups etc are extracted. Amongst the polymer systems, details of topological quantification of polymer systems such as stars, cyclics and branched polymers like polyolefins will be presented. In polyolefins, the method provides a unique measure of the average long-chain branch length and the hyperbranched (branch-on-branch) characteristics. The quantification using scaling models are important in order to understand the structure-property relationship amongst materials.
Physical Review E, 2016
Mass fractal scaling, reflected in the mass fractal dimension d f , is independently impacted by ... more Mass fractal scaling, reflected in the mass fractal dimension d f , is independently impacted by topology, reflected in the connectivity dimension c, and by tortuosity, reflected in the minimum dimension d min. The mass fractal dimension is related to these other dimensions by d f = cd min. Branched fractal structures have a higher mass fractal dimension compared to linear structures due to a higher c, and extended structures have a lower dimension compared to convoluted self-avoiding and Gaussian walks due to a lower d min. It is found, in this work, that macromolecules in thermodynamic equilibrium display a fixed mass fractal dimension d f under good solvent conditions, regardless of chain topology. These equilibrium structures accommodate changes in chain topology such as branching c by a decrease in chain tortuosity d min. Symmetric star polymers are used to understand the structure of complex macromolecular topologies. A recently published hybrid Unified scattering function accounts for interarm correlations in symmetric star polymers along with polymer-solvent interaction for chains of arbitrary scaling dimension. Dilute solutions of linear, three-arm and six-arm polyisoprene stars are studied under good solvent conditions in deuterated p-xylene. Reduced chain tortuosity can be viewed as steric straightening of the arms. Steric effects for star topologies are quantified, and it is found that steric straightening of arms is more significant for lower-molecular-weight arms. The observation of constant d f is explained through a modification of Flory-Krigbaum theory for branched polymers.
We have recently derived a method for the description of complex molecular and nanostructural top... more We have recently derived a method for the description of complex molecular and nanostructural topologies based on a statistical analysis. The method has been applied to a wide range of materials from long chain branched polyolefins, hyperbranched polymers, star polymers, H-branched polymers to cyclics, biopolymers, and branched nanostructured aggregates. This method, when applied to neutron scattering data from dilute polymer solutions, yields the mole fraction of a structure involved in long chain branching, the branching density, and the average branch length. Moreover, quantitative measures of the convolution or tortuosity of the structure and the connectivity of the molecules can be made, opening a new window for our understanding of complex molecular topologies. When applied to neutron scattering the approach is applied to the chain-scaling regime at low to moderate values of the scattering vector. At high scattering vector the Kuhn length is observed that has been shown to be ...
A new method to quantify topology in a variety of materials using static scattering will be discu... more A new method to quantify topology in a variety of materials using static scattering will be discussed. Specific examples using long chain branched polyethylene will be used to demonstrate the versatility of this technique. The results will be compared with NMR and rheology measurements. In polyolefins, the method provides a unique measure of the average branch length and the number of "inner" segments. Inner segments are characteristic of hyperbranched molecular topologies where branch-on-branch structures exist. The ability to quantify branch-on-branch structure using dilute solutions of hydrogenous polymers in deuterated solvent makes this method extremely appealing to those studying the synthesis of complex molecular topologies. We have adapted this method to study a wide range of complex topological materials from proteins to bio- and ceramic/carbon nano-aggregates. Synthetic and biopolymers display chain structures that often contain complex topologies ranging from st...
Physical Review E, 2015
Star polymers provide model architectures to understand the dynamic and rheological effects of ch... more Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from ν = 0.5 (d f = 2) due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated p-xylene.
Polymer, 2011
Commercial polyethylene is typically heterogeneous in molecular weight as well as in molecular to... more Commercial polyethylene is typically heterogeneous in molecular weight as well as in molecular topology due to variability in catalyst systems and catalyst activity. Further, processing of polyethylene after polymerization may also result in changes to the structure. While quantification of molecular weight is routine using gel permeation chromatography (GPC); quantification of the heterogeneity in molecular topology and microstructure is more difficult. In this paper, a novel method is used to examine the structure and branch content of a linear low-density polyethylene (LLDPE). The method uses a scaling model to analyze small-angle neutron scattering (SANS) data from dilute solutions of a series of LLDPE fractions. The scaling approach quantifies short-chain and long-chain branch content in polymers concurrently, thereby illustrating the distribution of these branches in the polyethylene fractions. Additionally, new quantities such as the average long-chain branch length and hyperbranch content are measured to provide further insight into the structure of these polymers. LLDPE used in this study is fractionated using temperature rising elution fractionation (TREF). Results from the analysis of these fractions show evidence of long-chain branching in commercial LLDPE which could be partly attributed to post-synthesis processing conditions.
A recent method to quantify molecular topology of various materials using small angle scattering ... more A recent method to quantify molecular topology of various materials using small angle scattering will be presented. Small angle x-ray and neutron scattering has been used to characterize ceramic aggregates and polymer structures systems respectively. The structural differences in various systems arise from the competition between thermal and spacial constraints. The details in ceramic aggregates like branch fraction, number of segments in an aggregate and the short circuit path, coordination number, the number end groups etc are extracted. Amongst the polymer systems, details of topological quantification of polymer systems such as stars, cyclics and branched polymers like polyolefins will be presented. In polyolefins, the method provides a unique measure of the average long-chain branch length and the hyperbranched (branch-on-branch) characteristics. The quantification using scaling models are important in order to understand the structure-property relationship amongst materials.
Macromolecules, 2009
Small-angle neutron scattering is used to investigate the structure and long-chain branch (LCB) c... more Small-angle neutron scattering is used to investigate the structure and long-chain branch (LCB) content of metallocene catalyzed polyethylene (PE). A novel scaling approach is applied to determine the mole fraction branch content (br φ) of LCBs in PE. The approach also provides the average number of branch sites per chain (n br), average number of branch sites per minimum path (n br,p), average branch length (z br) and number of inner segments (n i), giving insight into the chain architecture. The approach elucidates the relationship between the structure and rheological properties of branched PE.
Macromolecules, 2008
... and Amit S. Kulkarni. Department of Chemical and Materials Engineering, University of Cincinn... more ... and Amit S. Kulkarni. Department of Chemical and Materials Engineering, University of Cincinnati, Cincinnati, Ohio 45221. Douglas McFaddin, Jean Merrick-Mack and Vassilios Galiatsatos. Equistar Chemicals, LP, a LyondellBasell ...
Bulletin of the American Physical …, 2010
Neutron scattering data from symmetric star polymers with six poly (urethane-ether) arms, chemica... more Neutron scattering data from symmetric star polymers with six poly (urethane-ether) arms, chemically bonded to a C-60 molecule are fitted using a new scaling model and scattering function. The new scaling function can describe both good solvent and theta solvent conditions as well ...
Macromolecules
The versatility of a novel scaling approach in quantifying the structure of model well-defined 3-... more The versatility of a novel scaling approach in quantifying the structure of model well-defined 3-arm star polyethylene molecules is presented. Many commercial polyethylenes have long side branches, and the nature and quantity of these branches varies widely among the various forms. For instance, low-density polyethylene (LDPE) is typically a highly branched structure with broad distributions in branch content, branch lengths and branch generation (in hyperbranched structures). This makes it difficult to accurately quantify the structure and the inherent structure–property relationships. To overcome this drawback, model well-defined hydrogenated polybutadiene (HPB) structures have been synthesized via anionic polymerization and hydrogenation to serve as model analogues to long-chain branched polyethylene. In this article, model 3-arm star polyethylene molecules are quantified using the scaling approach. Along with the long-chain branch content in polyethylene, the approach also provi...
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Papers by Ramnath Ramachandran