On the mean radius of gyration of a polymer chain

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

In-Situ Rheological Studies of Cationic Lignin Polymerization in an Acidic Aqueous System

The chemistry of lignin polymerization was studied in the past. Insights into the rheological behavior of the lignin polymerization system would provide crucial information required for tailoring lignin polymers with desired properties. The in-situ rheological attributes of lignin polymerization with a cationic monomer, [2-(methacryloyloxy)ethyl] trimethylammonium chloride (METAC), were studied in detail in this work. The influences of process conditions, e.g., temperature, component concentrations, and shear rates, on the viscosity variations of the reaction systems during the polymerization were studied in detail. Temperature, METAC/lignin molar ratio, and shear rate increases led to the enhanced viscosity of the reaction medium and lignin polymer with a higher degree of polymerization. The extended reaction time enhanced the viscosity attributing to the larger molecular weight of the lignin polymer. Additionally, the size of particles in the reaction system dropped as reaction time was extended. The lignin polymer with a larger molecular weight and Rg behaved mainly as a viscose (tan δ > 1 or G″ > G') material, while the lignin polymer generated with smaller molecular weight and shorter Rg demonstrated strong elastic characteristics with a tan (δ) lower than unity over the frequency range of 0.1-10 rad/s.

Phenomenological Changes in Lignin Following Polymerization and Its Effects on Flocculating Clay Particles

Cationic kraft lignin (CKL) macromolecules were produced via polymerizing kraft lignin (KL) with [2-(acryloyloxy)ethyl]trimethylammonium chloride (ATAC) or [2-(methacryloyloxy)ethyl]trimethylammonium methyl sulfate (METAM). Despite slightly different charge densities (2.3-2.5 mmol/g) of CKL, lignin-METAM (KL-METAM) had a significantly larger molecular weight and radius of gyration. A correlation was observed between the structure of CKLs and their impacts on the surface hydrophilicity of kaolin particles. In interacting with kaolin particles, KL-METAM generated larger and stronger flocs with looser structures than did KL-ATAC. Compared to ATAC, METAM had one additional methyl substituent on its structure, which provided fundamental evidence on how a small group (i.e., a methyl group) on the structure of a cationic monomer can have a substantial influence on its polymerization with lignin and subsequently on the efficiency of the induced macromolecule as a flocculant in a kaolin suspension system.

Micromechanical model for isolated polymer-colloid clusters under tension

Binary polymer-colloid (PC) composites form the majority of biological load-bearing materials. Due to the abundance of the polymer and particles, and their simple aggregation process, PC clusters are used broadly by nature to create biomaterials with a variety of functions. However, our understanding of the mechanical features of the clusters and their load transfer mechanism is limited. Our main focus in this paper is the elastic behavior of close-packed PC clusters formed in the presence of polymer linkers. Therefore, a micromechanical model is proposed to predict the constitutive behavior of isolated polymer-colloid clusters under tension. The mechanical response of a cluster is considered to be governed by a backbone chain, which is the stress path that transfers most of the applied load. The developed model can reproduce the mean behavior of the clusters and is not dependent on their local geometry. The model utilizes four geometrical parameters for defining six shape descriptor functions which can affect the geometrical change of the clusters in the course of deformation. The predictions of the model are benchmarked against an extensive set of simulations by coarse-grained-Brownian dynamics, where clusters with different shapes and sizes were considered. The model exhibits good agreement with these simulations, which, besides its relative simplicity, makes the model an excellent add-on module for implementation into multiscale models of nanocomposites.

Structure and mechanical properties of artificial protein hydrogels assembled through aggregation of leucine zipper peptide domains

Artificial protein hydrogels made from a triblock protein (designated AC10A, where A is an acidic zipper domain and C10 comprises 10 repeats of the nonapeptide sequence exhibit normalized plateau storage moduli (G'∞/nkT) less than 0.13 at all concentrations, pH values, and ionic strengths examined. These gels are surprisingly soft due to loop formation at the expense of bridges between physical junctions. Molecular-level evidence of loop formation is provided by strong fluorescence energy transfer (FRET) between distinct chromophores placed at the C- and N-termini of labelled chains diluted in an excess of unlabelled chains. The tendency to form loops originates from the compact size of the random coil midblock (mean RH(C10)≈ 20 Å, determined from quasi-elastic light scattering of C10), and is facilitated by the ability of the leucine zipper domains to form antiparallel aggregates. Although the aggregation number of the leucine zipper domains is small (tetrameric, determined from multi-angle static light scattering of AC10 diblock), the average center-to-center distance between aggregates is roughly 1.5 times the average end-to-end distance of the C10 domain in a 7% w/v network. To avoid stretching the C10 domain, the chains tend to form loops. Changes in pH or ionic strength that expand the polyelectrolyte midblock favor bridging, leading to greater G'∞ as long as leucine zipper endblocks do not dissociate. Understanding of the network structure provided successful design strategies to increase the rigidity of these hydrogels. In contrast to intuitive design concepts for rubber and gel materials, it was shown that increasing either the length or the charge density of the midblock increases rigidity, because fewer chains are wasted in loop formation.

A theoretical study of conformational properties of dendritic block copolymers of first generation

Conformational properties of a dendritic block copolymer of the first generation are studied by means of an analytic calculation and dimensionality techniques. The polymer can have different functionalities and branch lengths in the interior region and the exterior shell. Three parameters are included in order to describe the intensity of the interactions between the same or different monomeric units. Based on the average end to end distances of the branches effective angles are defined in order to study how the microscopic parameters control the position and activity of the end groups, but also the hollowness in the internal region and the tweezing ability of the external shell of the macromolecule.