This award supports theoretical research and education in the area of polymer networks and entangled gels. The elastic properties of polymer networks and gels, used in a wide range of applications from hard rubber boots to soft gel replacements for eye lenses, are determined by chemical cross-links as well as by topological entanglements between network strands. Existing theories of gels treat entanglements in qualitatively the same way as crosslinks. However, experiments suggest that their relative role changes upon network swelling and deformation. Thus a microscopic theory is needed that provides a qualitative explanation of this phenomenon as well as a quantitative description of macroscopic properties of deformed and swollen entangled gels.
The PI aims to develop a theory that will allow the calculation of the elastic modulus and equilibrium swelling of entangled gels along with stress-strain dependence for their uniaxial and biaxial deformations. The theory will be extended to explore novel networks with unique properties such as high deformability and low elastic modulus. The effect of trapped entanglements in swollen and deswollen gels will be modeled, emphasizing their qualitative difference from temporary entanglements in polymeric liquids. The dependence of topological interactions on network deformations will be calculated, and used to understand why the strength of these interactions becomes weaker in elongation directions and stronger in compression directions. New numerical methods will be developed to determine the dependence of entanglement parameters, such as confining tube diameter and persistence length, on deformation of polymeric systems with fixed topology. These methods will be used to test the assumptions and predictions of different theories of entangled networks.
This project will provide graduate students and postdoctoral fellows with an excellent opportunity for training in valuable analytical and numerical techniques. Some of the results of this research will be used to develop material for a textbook. The proposed project will stimulate the interest of high school students in modern scientific methods by engaging them in active research. Examples of elastic gels will be used in the design of the updated "Zoom In" exhibit at the Morehead Planetarium and Science Center as well as in lectures by PI to high school students at the "Science Spectrum" and "Science at the Edge" series.
NONTECHNICAL SUMMARY This award supports theoretical research and education on networks of long chain-like molecules, including interpenetrating chains that are swollen by a solvent, like water. The unique interplay of solid-like properties on large length scales and liquid-like properties on small length scales makes these polymer networks and gels the world?s most deformable elastic materials. Their elastic properties, used in a wide range of applications from hard rubber boots to soft gel replacements for eye lenses, are determined by chemical interactions between the chain-molecules as well as by entanglements among chain-molecules in the network. Most theories for the elastic and mechanical properties of these kinds of materials treat the effects of entanglements in polymer networks qualitatively the same way as chemical bonds creating hard links between polymer strands. Experiments suggest, however, that the relative role of the two physical effects changes upon network swelling and deformation caused by external conditions. The PI aims to fill the need for a microscopic theory that can explain this phenomenon and describe the properties of these materials.
The theory has the potential to uncover new routes for designing soft materials with a desired set of properties. The project will provide undergraduate and graduate students as well as postdoctoral fellows with an excellent opportunity of training in valuable analytical and numerical techniques. Some of the results of this research will be used in the developing materials for a textbook. The proposed project will stimulate the interest of high school students in modern scientific methods by engaging them in active research. Examples of elastic gels will be used in the design of the updated "Zoom In" exhibit at the Morehead Planetarium and Science Center as well as in lectures by PI to high school students at the "Science Spectrum" and "Science at the Edge" series.
Periciliary Brush Model of Airway Surface Layer of Lungs[i] Mucus clearance is the primary defense mechanism that protects airways from inhaled infectious and toxic agents. In the current gel-on-liquid mucus clearance model, a mucus gel is propelled on top of a "watery" periciliary layer surrounding the cilia. However, this model fails to explain the formation of a distinct mucus layer in health or why mucus clearance fails in disease. We propose a gel-on-brush model in which the periciliary layer is occupied by membrane-spanning mucins and mucopolysaccharides densely tethered to the airway surface. This brush prevents mucus penetration into the periciliary space and causes mucus to form a distinct layer. The relative osmotic moduli of the mucus and periciliary brush layers explain both the stability of mucus clearance in health and its failure in airway disease. Perfect Mixing of Immiscible Macromolecules[ii] The difficulty of mixing chemically incompatible substances — in particular macromolecules and colloidal particles — is a canonical problem limiting advances in fields ranging from health care to materials engineering. Although the self-assembly of chemically different moieties has been demonstrated in coordination complexes, supramolecular structures, and colloidal lattices among other systems, the mechanisms of mixing largely rely on specific interfacing of chemically, physically or geometrically complementary objects. Here, by taking advantage of the steric repulsion between brush-like polymers tethered to surface-active species, we obtained long-range arrays of perfectly mixed macromolecules with a variety of polymer architectures and a wide range of chemistries without the need of encoding specific complementarity. The net repulsion arises from the significant increase in the conformational entropy of the brush-like polymers with increasing distance between adjacent macromolecules at fluid interfaces. This entropic-templating assembly strategy enables long-range patterning of thin films on sub-100nm length scales. Step-Growth Polymerization of Nanoparticles[iii] Self-organization of nanoparticles is an efficient strategy for producing nanostructures with complex, hierarchical architectures. The past decade has witnessed great progress in nanoparticle self-assembly, yet the quantitative prediction of the architecture of nanoparticle ensembles and of the kinetics of their formation remains a challenge. We report on the marked similarity between the self-assembly of metal nanoparticles and reaction-controlled step-growth polymerization. The nanoparticles act as multifunctional monomer units, which form reversible, noncovalent bonds at specific bond angles and organize themselves into a colloidal polymer. We show that the kinetics and statistics of step-growth polymerization enable a quantitative prediction of the architecture of linear, branched, and cyclic self-assembled nanostructures; their aggregation numbers and size distribution; and the formation of structural isomers. 2012 Boulder Summer School on "Polymers and Soft Matter Physics" The PI co-organized the 2012 Boulder Summer School on "Polymers and Soft Matter Physics" http://boulder.research.yale.edu/Boulder-2012/index.html. Over sixty graduate and postdoctoral students from all over the world participated in this school. The PI coordinated lectures of 17 international leaders in the field into a comprehensive course on the fundamentals of polymer and soft matter science. By all accounts the school was a great success in building a community of young researchers in the field of polymer and soft matter science. Founded by physical chemists like Flory and brought into the mainstream of theoretical physics by visionaries like de Gennes, over the last eighty years polymer physics has grown into a mature, rich, and exciting discipline. Now expanded to include also colloids, liquid crystals, interfaces, etc, polymer and soft matter physics span fundamental statistical mechanics and field theory, most advanced materials, as well as technological and biological frontiers. Nevertheless, a comprehensive exposition to fundamental concepts of polymer and soft matter science is still largely missing, neglected in most physics departments, ignored by many workers in biological realm, and underappreciated even by chemical engineers. The goal of 2012 Boulder summer school was to fill this gap and provide the physics community with a relatively comprehensive course in the fundamentals of polymer and soft matter physics with emphasis on their biological applications. [i] "A Periciliary Brush Promotes the Lung Health by Separating the Mucus Layer from Airway Epithelia" by B. Button, L. Cai, C. Ehre, M. Kesimer, D. B. Hill, J. K. Scheehan, R. C. Boucher, and M. Rubinstein, Science 337, 937-941 (2012). Highlighted in "Walking on Solid Ground" by B. F. Dickey Science 337, 924 (2012). [ii] "Perfect mixing of immiscible macromolecules at fluid interfaces" by Sergei S. Sheiko, Jing Zhou, Jamie Arnold, Dorota Neugebauer, Krzysztof Matyjaszewski, Constantinos Tsitsilianis, Vladimir V. Tsukruk, Jan-Michael Y. Carrillo, Andrey V. Dobrynin, and Michael Rubinstein, Nature Materials 12, 735–740 (2013). Highlighted in "Macromolecular mixing: Entropic templating" by Igal Szleifer, Nature Materials 12, 693–694 (2013). [iii] "Step-Growth Polymerization of Inorganic Nanoparticles" by K. Liu, Z. Nie, N. Zhao, W. Li, M. Rubinstein, & E. Kumacheva, Science, 329, 197 (2010). Featured in "Polymerization to Order" "Nature Materials", 466, 298 (2010) and "Nanostructures Form Like Polymers" C &E News (July 12, 2010, p. 31).
