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1.
Adv Biol (Weinh) ; : e2400087, 2024 Jul 08.
Artículo en Inglés | MEDLINE | ID: mdl-38977422

RESUMEN

Mesenchymal-epithelial transition (MET) is essential for tissue and organ development and is thought to contribute to cancer by enabling the establishment of metastatic lesions. Despite its importance in both health and disease, there is a lack of in vitro platforms to study MET and little is known about the regulation of MET by mechanical cues. Here, hyaluronic acid-based hydrogels with dynamic and tunable stiffnesses mimicking that of normal and tumorigenic mammary tissue are synthesized. The platform is then utilized to examine the response of mammary epithelial cells and breast cancer cells to dynamic modulation of matrix stiffness. Gradual softening of the hydrogels reduces proliferation and increases apoptosis of breast cancer cells. Moreover, breast cancer cells exhibit temporal changes in cell morphology, cytoskeletal organization, and gene expression that are consistent with mesenchymal-epithelial plasticity as the stiffness of the matrix is reduced. A reduction in matrix stiffness attenuates the expression of integrin-linked kinase, and inhibition of integrin-linked kinase impacts proliferation, apoptosis, and gene expression in cells cultured on stiff and dynamic hydrogels. Overall, these findings reveal intermediate epithelial/mesenchymal states as cells move along a matrix stiffness-mediated MET trajectory and suggest an important role for matrix mechanics in regulating mesenchymal-epithelial plasticity.

2.
Phys Chem Chem Phys ; 26(21): 15472-15483, 2024 May 29.
Artículo en Inglés | MEDLINE | ID: mdl-38751347

RESUMEN

Conjugated molecules and polymers are being designed as acceptor and donor materials for organic photovoltaic (OPV) cells. OPV performance depends on generation of free charge carriers through dissociation of excitons, which are electron-hole pairs created when a photon is absorbed. Here, we develop a tight-binding model to describe excitons on homo-oligomers, alternating co-oligomers, and a non-fullerene acceptor - IDTBR. We parameterize our model using density functional theory (DFT) energies of neutral, anion, cation, and excited states of constituent moieties. A symmetric molecule like IDTBR has two ends where an exciton can sit; but the product wavefunction approximation for the exciton breaks symmetry. So, we introduce a tight-binding model with full correlation between electron and hole, which allows the exciton to coherently explore both ends of the molecule. Our approach predicts optical singlet excitation energies for oligomers of varying length as well as IDTBR in good agreement with time-dependent DFT and spectroscopic results.

3.
Nat Commun ; 15(1): 2170, 2024 Mar 09.
Artículo en Inglés | MEDLINE | ID: mdl-38461153

RESUMEN

All-polymer solar cells (all-PSCs) offer improved morphological and mechanical stability compared with those containing small-molecule-acceptors (SMAs). They can be processed with a broader range of conditions, making them desirable for printing techniques. In this study, we report a high-performance polymer acceptor design based on bithiazole linker (PY-BTz) that are on par with SMAs. We demonstrate that bithiazole induces a more coplanar and ordered conformation compared to bithiophene due to the synergistic effect of non-covalent backbone planarization and reduced steric encumbrances. As a result, PY-BTz shows a significantly higher efficiency of 16.4% in comparison to the polymer acceptors based on commonly used thiophene-based linkers (i.e., PY-2T, 9.8%). Detailed analyses reveal that this improvement is associated with enhanced conjugation along the backbone and closer interchain π-stacking, resulting in higher charge mobilities, suppressed charge recombination, and reduced energetic disorder. Remarkably, an efficiency of 14.7% is realized for all-PSCs that are solution-sheared in ambient conditions, which is among the highest for devices prepared under conditions relevant to scalable printing techniques. This work uncovers a strategy for promoting backbone conjugation and planarization in emerging polymer acceptors that can lead to superior all-PSCs.

4.
ACS Macro Lett ; 13(3): 375-380, 2024 Mar 19.
Artículo en Inglés | MEDLINE | ID: mdl-38461421

RESUMEN

Identifying the origin of scattering from polymer materials is crucial to infer structural features that can relate to functional properties. Here, we use our recently developed virtual-site coarse graining to accelerate atomistic simulations and show how various molecular features govern wide-angle X-ray scattering from a conjugated polymer, poly(3-hexylthiophene) (P3HT). The efficient molecular dynamics simulations can represent the structure and capture the emergence of crystalline order from amorphous melts upon cooling while retaining atomistic details of chain configurations. The scattering extracted from simulations shows good agreement with wide-angle X-ray scattering experiments. Amorphous P3HT exhibits broad scattering peaks: a high-q peak from interchain side-group correlations and a low-q peak from interchain backbone-backbone correlations. During amorphous to crystalline phase transitions, the distance between backbones along the side-group direction increases because of lack of interdigitation in the crystalline phase. Scattering from π-π stacking emerges only after crystallization takes place. Intrachain correlations contribute negligibly to the scattering from the amorphous and crystalline phases.

5.
Mater Horiz ; 11(11): 2718-2728, 2024 Jun 03.
Artículo en Inglés | MEDLINE | ID: mdl-38506669

RESUMEN

Plastics have substantial societal benefits, but their widespread use has led to a critical waste management challenge. While mechanical recycling dominates the reuse of post-consumer plastics, it is limited in efficacy, especially for composites. To address this, we propose a direct reprocessing approach that enables the creation of hybrid, long-lasting, and durable composites from difficult-to-recycle plastics. This approach utilizes cold sintering, a process that consolidates inorganic powders through fractional dissolution and precipitation at temperatures far below conventional sintering; these temperatures are compatible with plastic processing. We show that this process can create inorganic-matrix composites with significant enhancements in tensile strength and toughness over pure gypsum, which is commonly found in construction waste. These composites can be recycled multiple times through direct reprocessing with the addition of only water as a processing promoter. This approach to recycling leads to composites with orders of magnitude lower energy demand, global warming potential, and water demand, when compared against common construction products. Altogether, we demonstrate the potential for cold sintering to integrate waste into high-performance recyclable composites.

6.
Artículo en Inglés | MEDLINE | ID: mdl-38424464

RESUMEN

Recent advances in the water-energy landscape hinge upon our improved understanding of the complex morphology of materials involved in water treatment and energy production. Due to their versatility and tunability for applications ranging from drug delivery to fuel cells, polymeric systems will play a crucial role in shaping the future of water-energy nexus applications. Electron tomography (ET) stands as a transformative approach for elucidating the intricate structures inherent to polymers, offering unparalleled insights into their nanoscale architectures and functional properties in three dimensions. In particular, the various morphological and chemical characteristics of polymer membranes provide opportunities for perturbations to standard ET for the study of these systems. We discuss the applications of transmission electron microscopy in establishing structure-function relationships in polymeric membranes with an emphasis on traditional ET and cryogenic ET (cryo-ET). The synergy between ET and cryo-ET to unravel structural complexities and dynamic behaviors of polymer membranes holds immense potential in driving progress and innovation across frontiers related to water-energy nexus applications. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering , Volume 15 is June 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

7.
Small ; : e2311832, 2024 Feb 22.
Artículo en Inglés | MEDLINE | ID: mdl-38386283

RESUMEN

The molecular foundations of epidermal cell wall mechanics are critical for understanding structure-function relationships of primary cell walls in plants and facilitating the design of bioinspired materials. To uncover the molecular mechanisms regulating the high extensibility and strength of the cell wall, the onion epidermal wall is stretched uniaxially to various strains and cell wall structures from mesoscale to atomic scale are characterized. Upon longitudinal stretching to high strain, epidermal walls contract in the transverse direction, resulting in a reduced area. Atomic force microscopy shows that cellulose microfibrils exhibit orientation-dependent rearrangements at high strains: longitudinal microfibrils are straightened out and become highly ordered, while transverse microfibrils curve and kink. Small-angle X-ray scattering detects a 7.4 nm spacing aligned along the stretch direction at high strain, which is attributed to distances between individual cellulose microfibrils. Furthermore, wide-angle X-ray scattering reveals a widening of (004) lattice spacing and contraction of (200) lattice spacing in longitudinally aligned cellulose microfibrils at high strain, which implies longitudinal stretching of the cellulose crystal. These findings provide molecular insights into the ability of the wall to bear additional load after yielding: the aggregation of longitudinal microfibrils impedes sliding and enables further stretching of the cellulose to bear increased loads.

8.
ChemSusChem ; 17(13): e202301920, 2024 Jul 08.
Artículo en Inglés | MEDLINE | ID: mdl-38400831

RESUMEN

All-solid-state batteries have the potential for enhanced safety and capacity over conventional lithium ion batteries, and are anticipated to dominate the energy storage industry. As such, strategies to enable recycling of the individual components are crucial to minimize waste and prevent health and environmental harm. Here, we use cold sintering to reprocess solid-state composite electrolytes, specifically Mg and Sr doped Li7La3Zr2O12 with polypropylene carbonate (PPC) and lithium perchlorate (LLZO-PPC-LiClO4). The low sintering temperature allows co-sintering of ceramics, polymers and lithium salts, leading to re-densification of the composite structures with reprocessing. Reprocessed LLZO-PPC-LiClO4 exhibits densified microstructures with ionic conductivities exceeding 10-4 S/cm at room temperature after 5 recycling cycles. All-solid-state lithium batteries fabricated with reprocessed electrolytes exhibit a high discharge capacity of 168 mA h g-1 at 0.1 C, and retention of performance at 0.2 C for over 100 cycles. Life cycle assessment (LCA) suggests that recycled electrolytes outperforms the pristine electrolyte process in all environmental impact categories, highlighting cold sintering as a promising technology for recycling electrolytes.

9.
JACS Au ; 4(1): 177-188, 2024 Jan 22.
Artículo en Inglés | MEDLINE | ID: mdl-38274264

RESUMEN

Plant cell walls are abundant sources of materials and energy. Nevertheless, cell wall nanostructure, specifically how pectins interact with cellulose and hemicelluloses to construct a robust and flexible biomaterial, is poorly understood. X-ray scattering measurements are minimally invasive and can reveal ultrastructural, compositional, and physical properties of materials. Resonant X-ray scattering takes advantage of compositional differences by tuning the energy of the incident X-ray to absorption edges of specific elements in a material. Using Tender Resonant X-ray Scattering (TReXS) at the calcium K-edge to study hypocotyls of the model plant, Arabidopsis thaliana, we detected distinctive Ca features that we hypothesize correspond to previously unreported Ca-Homogalacturonan (Ca-HG) nanostructures. When Ca-HG structures were perturbed by chemical and enzymatic treatments, cellulose microfibrils were also rearranged. Moreover, Ca-HG nanostructure was altered in mutants with abnormal cellulose, pectin, or hemicellulose content. Our results indicate direct structural interlinks between components of the plant cell wall at the nanoscale and reveal mechanisms that underpin both the structural integrity of these components and the molecular architecture of the plant cell wall.

10.
Nat Commun ; 14(1): 7203, 2023 Nov 08.
Artículo en Inglés | MEDLINE | ID: mdl-37938236

RESUMEN

The instability of the surface chemistry in transition metal oxide perovskites is the main factor hindering the long-term durability of oxygen electrodes in solid oxide electrochemical cells. The instability of surface chemistry is mainly due to the segregation of A-site dopants from the lattice to the surface. Here we report that cathodic potential can remarkably improve the stability in oxygen reduction reaction and electrochemical activity, by decomposing the near-surface region of the perovskite phase in a porous electrode made of La1-xSrxCo1-xFexO3 mixed with Sm0.2Ce0.8O1.9. Our approach combines X-ray photoelectron spectroscopy and secondary ion mass spectrometry for surface and sub-surface analysis. Formation of Ruddlesden-Popper phase is accompanied by suppression of the A-site dopant segregation, and exsolution of catalytically active Co particles onto the surface. These findings reveal the chemical and structural elements that maintain an active surface for oxygen reduction, and the cathodic potential is one way to generate these desirable chemistries.

11.
J Am Chem Soc ; 145(42): 23321-23333, 2023 Oct 25.
Artículo en Inglés | MEDLINE | ID: mdl-37818621

RESUMEN

Partial cation exchange reactions can be used to rationally design and synthesize heterostructured nanoparticles that are useful targets for applications in photocatalysis, nanophotonics, thermoelectrics, and medicine. Such reactions introduce intraparticle frameworks that define the spatial arrangements of different materials within a heterostructured nanoparticle, as well as the orientations and locations of their interfaces. Here, we show that upon heating to temperatures relevant to their synthesis and applications, the ZnS regions and Cu1.8S/ZnS interfaces of heterostructured ZnS-Cu1.8S nanorods migrate and restructure. We first use partial cation exchange reactions to synthesize a library of seven distinct samples containing various patches, bands, and tips of ZnS embedded within Cu1.8S nanorods. Upon annealing in solution or in air, ex situ TEM analysis shows evidence that the ZnS domains migrate in different ways, depending upon their sizes and locations. Using differential scanning calorimetry, we correlate the threshold temperature for ZnS migration to the superionic transition temperature of Cu1.8S, which facilitates rapid diffusion throughout the nanorods. We then use in situ thermal TEM to study the evolution of individual ZnS-Cu1.8S nanorods upon heating. We find that ZnS domain migration occurs through a ripening process that minimizes small patches with higher-energy interfaces in favor of larger bands and tips having lower-energy interfaces, as well as through restructuring of higher-energy Cu1.8S/ZnS interfaces. Notably, Cu1.8S nanorods containing multiple patches of ZnS thermally transform into ZnS-Cu1.8S heterostructured nanorods having ZnS tips and/or central bands, which provides mechanistic insights into how these commonly observed products form during synthesis.

12.
Front Plant Sci ; 14: 1212126, 2023.
Artículo en Inglés | MEDLINE | ID: mdl-37662163

RESUMEN

Calcium is important for the growth and development of plants. It serves crucial functions in cell wall and cell membrane structure and serves as a secondary messenger in signaling pathways relevant to nutrient and immunity responses. Thus, measuring calcium levels in plants is important for studies of plant biology and for technology development in food, agriculture, energy, and forest industries. Often, calcium in plants has been measured through techniques such as atomic absorption spectrophotometry (AAS), inductively coupled plasma-mass spectrometry (ICP-MS), and electrophysiology. These techniques, however, require large sample sizes, chemical extraction of samples or have limited spatial resolution. Here, we used near-edge X-ray absorption fine structure (NEXAFS) spectroscopy at the calcium L- and K-edges to measure the calcium to carbon mass ratio with spatial resolution in plant samples without requiring chemical extraction or large sample sizes. We demonstrate that the integrated absorbance at the calcium L-edge and the edge jump in the fluorescence yield at the calcium K-edge can be used to quantify the calcium content as the calcium mass fraction, and validate this approach with onion epidermal peels and ICP-MS. We also used NEXAFS to estimate the calcium mass ratio in hypocotyls of a model plant, Arabidopsis thaliana, which has a cell wall composition that is similar to that of onion epidermal peels. These results show that NEXAFS spectroscopy performed at the calcium edge provides an approach to quantify calcium levels within plants, which is crucial for understanding plant physiology and advancing plant-based materials.

13.
Polymers (Basel) ; 15(9)2023 Apr 23.
Artículo en Inglés | MEDLINE | ID: mdl-37177141

RESUMEN

Alkyd resins are oil-based polymers that have been widely used for generations in the surface coating industry and beyond. Characterization of these resins is of high importance to understand the influence of its components on its behavior, compatibility with other resins, and final quality to ensure high durability. Here, NMR spectroscopy and GPC were used for characterizing differences in the chemical structure, molecular distribution, and dispersity between oil-based and fatty acid-based alkyd polymers made from sacha inchi and linseed oils. Sancha inchi (Plukentia volubilis L.) is a fruit-bearing plant native to South America and the Caribbean, and has a rich unsaturated fatty acid content. The effect of vegetable oil and polyol selection on the synthesis of alkyd resins for coating applications was analyzed. The influence of two different synthesis methods, monoglyceride and fatty acid processes, was also compared. Important structural differences were observed using NMR: one-dimensional spectra revealed the degree of unsaturated fatty acid chains along the polyester backbone, whereas, 2D NMR experiments facilitated chemical shift assignments of all signals. GPC analysis suggested that alkyd resins with homogeneous and high molecular weights can be obtained with the fatty acid process, and that resins containing pentaerythritol may have uniform chain lengths.

14.
Sci Rep ; 13(1): 5421, 2023 04 03.
Artículo en Inglés | MEDLINE | ID: mdl-37012389

RESUMEN

The primary cell wall is highly hydrated in its native state, yet many structural studies have been conducted on dried samples. Here, we use grazing-incidence wide-angle X-ray scattering (GIWAXS) with a humidity chamber, which enhances scattering and the signal-to-noise ratio while keeping outer onion epidermal peels hydrated, to examine cell wall properties. GIWAXS of hydrated and dried onion reveals that the cellulose ([Formula: see text]) lattice spacing decreases slightly upon drying, while the (200) lattice parameters are unchanged. Additionally, the ([Formula: see text]) diffraction intensity increases relative to (200). Density functional theory models of hydrated and dry cellulose microfibrils corroborate changes in crystalline properties upon drying. GIWAXS also reveals a peak that we attribute to pectin chain aggregation. We speculate that dehydration perturbs the hydrogen bonding network within cellulose crystals and collapses the pectin network without affecting the lateral distribution of pectin chain aggregates.


Asunto(s)
Celulosa , Pectinas , Celulosa/química , Pectinas/química , Incidencia , Pared Celular/química , Membrana Celular , Plantas , Difracción de Rayos X
15.
Nat Mater ; 22(3): 329-337, 2023 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-36849816

RESUMEN

Stability and current-voltage hysteresis stand as major obstacles to the commercialization of metal halide perovskites. Both phenomena have been associated with ion migration, with anecdotal evidence that stable devices yield low hysteresis. However, the underlying mechanisms of the complex stability-hysteresis link remain elusive. Here we present a multiscale diffusion framework that describes vacancy-mediated halide diffusion in polycrystalline metal halide perovskites, differentiating fast grain boundary diffusivity from volume diffusivity that is two to four orders of magnitude slower. Our results reveal an inverse relationship between the activation energies of grain boundary and volume diffusions, such that stable metal halide perovskites exhibiting smaller volume diffusivities are associated with larger grain boundary diffusivities and reduced hysteresis. The elucidation of multiscale halide diffusion in metal halide perovskites reveals complex inner couplings between ion migration in the volume of grains versus grain boundaries, which in turn can predict the stability and hysteresis of metal halide perovskites, providing a clearer path to addressing the outstanding challenges of the field.

16.
Methods Enzymol ; 678: 121-144, 2023.
Artículo en Inglés | MEDLINE | ID: mdl-36641206

RESUMEN

Resonant soft X-ray scattering (RSoXS), a technique that combines X-ray absorption spectroscopy and X-ray scattering, can probe the nano- and meso-scale structure of biological assemblies with chemical specificity. RSoXS experiments yield scattering data collected at several photon energies, for example across an elemental absorption edge of interest. Collecting a near-edge X-ray absorption fine structure (NEXAFS) spectrum complements RSoXS experiments and determines X-ray energies that are best suited for RSoXS measurements. The analysis of RSoXS data is similar in many ways to analysis of small angle X-ray scattering using hard X-rays, with an added dimension that includes an X-ray energy dependence. This chapter discusses procedures for predicting scattering contrast and thereby identifying energies suitable for RSoXS measurements using NEXAFS spectra, analyses of 2D RSoXS images through integration into 1D profiles, and strategies for elucidating the origin of RSoXS scattering features. It also discusses existing and potential methods for interpretation of RSoXS data to gain detailed structural insights into biological systems.


Asunto(s)
Fotones , Rayos X , Espectroscopía de Absorción de Rayos X
17.
Adv Healthc Mater ; 12(6): e2201836, 2023 01.
Artículo en Inglés | MEDLINE | ID: mdl-36495554

RESUMEN

Hydrogen sulfide (H2 S) is a gaseous signaling molecule in the human body and has attracted attention in cancer therapy due to its regulatory roles in cancer cell proliferation and migration. Accumulating evidence suggests that continuous delivery of H2 S to cancer cells for extended periods of time suppresses cancer progression. However, one major challenge in therapeutic applications of H2 S is its controlled delivery. To solve this problem, polymeric micelles are developed containing H2 S donating-anethole dithiolethione (ADT) groups, with H2 S release profiles optimal for suppressing cancer cell proliferation. The micelles release H2 S upon oxidation by reactive oxygens species (ROS) that are present inside the cells. The H2 S release profiles can be controlled by changing the polymer design. Furthermore, the micelles that show a moderate H2 S release rate exert the strongest anti-proliferative effect in human colon cancer cells in in vitro assays as well as the chick chorioallantoic membrane cancer model, while the micelles do not affect proliferation of human umbilical vein endothelial cells. This study shows the importance of fine-tuning H2 S release profiles using a micelle approach for realizing the full therapeutic potential of H2 S in cancer treatment.


Asunto(s)
Sulfuro de Hidrógeno , Neoplasias , Humanos , Especies Reactivas de Oxígeno/metabolismo , Micelas , Sulfuro de Hidrógeno/farmacología , Sulfuro de Hidrógeno/metabolismo , Células Endoteliales/metabolismo , Neoplasias/tratamiento farmacológico , Polímeros/farmacología
18.
Methods Enzymol ; 677: 357-383, 2022.
Artículo en Inglés | MEDLINE | ID: mdl-36410955

RESUMEN

The complex structure of biological assemblies is crucial for function yet challenging to discern given the chemical similarities between constituent components. Hard X-ray techniques, for example, rely on small density differences between domains that lead to modest scattering intensities. Resonant soft X-ray scattering (RSoXS) uses X-rays below 2keV to access absorption edges of low-Z elements. In this way, RSoXS can enhance scattering contrast between domains of different chemical compositions or bonding motifs, thus providing structural information about specific chemical motifs. RSoXS is emerging as a technique applicable for biological systems, having been used to characterize protein structure in solution and polysaccharide organization in plant cell walls. Sample environment instrumentation, however, is challenging in the current state of the art, particularly with liquid samples. This chapter contains a brief introduction to RSoXS and current beamline capabilities, and provides methods to prepare, store, and mount biological samples for RSoXS characterization. Furthermore, key details during RSoXS and X-ray absorption data acquisition are highlighted and some future opportunities in RSoXS instrumentation for biological systems are discussed.


Asunto(s)
Proteínas , Sincrotrones , Rayos X , Proteínas/química , Pared Celular
19.
J Chem Theory Comput ; 18(11): 6932-6939, 2022 Nov 08.
Artículo en Inglés | MEDLINE | ID: mdl-36219653

RESUMEN

The local structure of conjugated polymers governs key optoelectronic properties, such as charge conduction and photogeneration at donor-acceptor interfaces. Because conjugated polymers are large, stiff, and relax slowly, all-atom molecular dynamics simulations are computationally expensive. Here, we describe a coarse-graining method that exploits the stiffness of constituent aromatic moieties by representing each moiety as rigidly bonded clusters of atoms wherein virtual sites replace several atoms. This approach significantly reduces the degrees of freedom while faithfully representing the shape and interactions of the moieties, resulting in 10 times faster simulations than all-atom simulations. Simulation of a donor polymer (P3HT) and a non-fullerene acceptor (O-IDTBR) validates the coarse-graining method by comparing structural properties from experiments, such as the density and persistence length. The fast simulation produces equilibrated systems with realistic morphologies. The simulation results of an equimolar mixture of P3HT, with a molecular weight of 1332 g mol-1, and an O-IDTBR mixture suggest that the interface width must be larger than 7 nm. Also, we investigate the effect of slow cooling on morphologies, particularly the number of close contacts that facilitates carrier transport. Slow cooling increases close contacts, and the effect is more pronounced in crystal-forming P3HT than in O-IDTBR, where bulky side-groups hinder crystal formation.

20.
ACS Cent Sci ; 8(2): 268-274, 2022 Feb 23.
Artículo en Inglés | MEDLINE | ID: mdl-35233458

RESUMEN

The relationship between Kuhn length l k , Kuhn monomer volume v 0, and plateau modulus G N 0, initially proposed by Graessley and Edwards for flexible polymers, and extended by Everaers, has a large gap in experimental data between the flexible and stiff regimes. This gap prevents the prediction of mechanical properties from the chain structure for any polymer in this region. Given the chain architecture, including a semiflexible backbone and side chains, conjugated polymers are an ideal class of material to study this crossover region. Using small angle neutron scattering, oscillatory shear rheology, and the freely rotating chain model, we have shown that 12 polymers with aromatic backbones populate a large part of this gap. We also have shown that a few of these polymers exhibit nematic ordering, which lowers G N 0. When fully isotropic, these polymers follow a relationship between l k , v 0, and G N 0, with a simple crossover proposed in terms of the number of Kuhn segments in an entanglement strand N e.

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