31 research outputs found

    Dimensional Description of Cyclic Macromolecules

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    ABSTRACT: Cyclic structures are often used to model and simulate long chain molecules due to the simplification of no chain-end effects. Many technically important and biologically relevant molecules are cyclics. Further, ring polymers display dramatic viscosity enhancement when blended with linear polymers in the melt. It has been proposed that cyclic melts may display a topologically driven coil collapse at high molecular weights reminiscent of cyclic DNA. Despite the structural simplicity and importance of cyclics a quantitative analytic distinction between cyclics and linear chains in the melt or in solution has been elusive since both linear and cyclic macromolecules display similar disordered, fractal structures. A dimensional analysis of cyclic polymers and its use to describe scattering data from cyclic macromolecules is presented. The validity of the new approach to describe cyclic structures is demonstrated using experimental data, and the Casassa form factor, previously used for cyclic polymers, is critically revisited. The scaling model is also used to quantify cyclic coil collapse in simulations from the literature

    Toward Resolution of Ambiguity for the Unfolded State

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    The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA

    Hierarchical approach to aggregate equilibria

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    Hierarchical aggregation is generally viewed as a kinetic phenomenon governed by kinetic growth laws, such as in the Smoluchowski equation, and modeled using diffusion or reaction limited kinetic growth models. Some aggregates, especially those controlled by surface grafting or surfactants, display reversible stability. For these equilibrated aggregates a simple thermodynamic model is proposed to describe the size distribution and the enthalpy and entropy of aggregation. The model uses the average degree of aggregation, z_{i(i−1)}, as the central quantifying parameter. Here i is an index reflecting the hierarchical level of structure in an aggregate, for instance, composed of crystals (i=0), clustered primary particles (i=1), aggregates (i=2), and agglomerates of aggregates (i=3). A change in Gibbs free energy for aggregation is given by ΔG_{i(i−1)}=−RTln(1/z_{i(i−1)}) for each level (i>0). This expression is advantageous since the degree of aggregation is directly determined in small-angle neutron and x-ray scattering, by transmission electron microscopy, simulation, or through spectroscopy. The atomistic hierarchical model enables an understanding of the mechanism of equilibrium aggregation since it provides expressions for entropy and enthalpy of aggregation at each structural/thermodynamic level. The model can be extended to describe pseudoequilibrium for industrially relevant materials such as condensation polymers. Applications in organic pigments and wormlike micelles are also briefly demonstrated

    Branch content of metallocene polyethylene

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    ABSTRACT: Small-angle neutron scattering (SANS) is employed to investigate the structure and longchain branch (LCB) content of metallocene-catalyzed polyethylene (PE). A novel scaling approach is applied to SANS data to determine the mole fraction branch content (φ br ) of LCBs in PE. The approach also provides the average number of branch sites per chain (n br ) and the average number of branch sites per minimum path (n br,p ). These results yield the average branch length (z br ) and number of inner segments n i , giving further insight into the chain architecture. The approach elucidates the relationship between the structure and rheological properties of branched polymers. This SANS method is the sole analytic measure of branch-onbranch structure and average branch length for topologically complex macromolecules

    Free Energy of Scission for Sodium Laureth-1-Sulfate Wormlike Micelles

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    Wormlike micelles (WLMs) are nanoscale, self-assembled components of many products from shampoos to fracking fluids due to their viscoelasticity. Their rheological behavior is largely governed by the contour length of the micelles and the concomitant propensity of the micelles to overlap and entangle. The large contour lengths, on the order of micrometers, is the result of a delicate balance between the scission enthalpy of the wormlike micelles on the one hand and entropic factors such as the mixing entropy of dispersion, the ordering of water molecules and counterions, and the mobility of branch points on the other hand. The structure and contour length of wormlike micelles assembled from sodium laureth-1-sulfate was determined at various temperatures using small-angle neutron scattering. The results allow the calculation of the enthalpy and entropy as well as the free energy of scission and are employed to critically evaluate the common methods to determine micellar scission energy from mean-field theory. Interesting behavior is observed when comparing branched and unbranched WLMs that may reflect on mechanistic differences in chain scission
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