This award supports theoretical and computational research on the motion of nanoparticles in a polymer matrix. The mean square displacement of microscopic particles larger than polymer chains provides information about rheological properties of the surrounding matrix. However, structure and dynamics of complex polymeric materials on sub-molecular length scales as well as microscopic details of polymer-particle interactions are poorly understood. The PI will analyze the motion of nanoparticles smaller than the surrounding polymer chains. Particularly interesting is the coupling of the nanoparticle dynamics to dynamical modes of matrix polymer chains on length scales equal to or smaller than the particle size and to modes of chains adsorbed or grafted to the particle.
A theory of the dynamical coupling between nanoparticles and a polymer matrix will be systematically developed starting from a model of non-sticky particles freely diffusing in polymer networks and gels. Mobility of these trace particles is highly sensitive to the relation between their dimensions and the diameter of the confining tube of the entangled matrix chains. Upon uniaxial and biaxial deformation of polymer networks and gels, the corresponding change of the tube diameter causes anisotropic diffusion of tracer nanoparticles. A method for characterization of the non-affine deformation of the confining tube by measuring the anisotropy of nanoparticle mobility will be developed and tested by computer simulations. The developed models will also enable quantitative analysis of translational and rotational diffusion of non-spherical nanoparticles, such as nanorods with diameter smaller than the mesh size of polymer gels and length longer than this mesh size.
The model will be extended to the case of sticky nanoparticles that exhibit hindered diffusion through polymeric liquids or solids due to chains attached to these particles. The time dependence of the mean square displacement of the sticky particles will reflect both dynamics of attached chains as well as of the surrounding polymer matrix. The proposed theory will allow separation of both contributions and determination of the structure and dynamics of the polymer layer adsorbed on nanoparticles. This theory will be modified to treat the finite lifetime of the bonds between particles and adsorbed polymers and the lifetime of labile bonds in reversible networks.
The theory of mobility of sticky particles will be extended to treat heterogeneous medium with a distribution of local sticky regions using an activated hopping model. A general solution of this model will be obtained to allow the derivation of the distribution of attraction strengths of different sticky regions from the analysis of particle trajectories.
This project will provide training opportunities for undergraduate and graduate students as well as postdoctoral fellows in analytical and numerical techniques for soft materials. Some of the results of this research will be used in the development of new problem sets and supplementary materials for the PIs textbook "Polymer Physics." The project will also be used as a tool for engage the interest of high school students in modern scientific methods by engaging them in active research.
NONTECHNICAL SUMMARY
This award supports theoretical and computational research to study nanoparticles, particles some 100,000 times smaller than the diameter of a human hair, moving within a material made up of a tangle of long chain-like molecules called polymers. Understanding the mechanisms by which the nanoparticles move provides useful information about the properties of materials made of polymers. The PI will develop a theory that can handle nanoparticles of different sized and shape, as well as kind, including nanoparticles with smooth surfaces and nanoparticles that have polymers attached to them which tend to make them "sticky" as they interact with the polymers that make up the material. This research will has impact on technological applications, such as optimizing composite materials and designing nanoparticles for drug delivery applications.
This project will provide training opportunities for undergraduate and graduate students as well as postdoctoral fellows in analytical and numerical techniques for soft materials. Some of the results of this research will be used in the development of new problem sets and supplementary materials for the PI's textbook "Polymer Physics." The project will also be used as a tool for engage the interest of high school students in modern scientific methods by engaging them in active research.
