Phase diagram of elastic colloidsAthanasopoulou, Labrini (Avtor)
Ziherl, Primož (Mentor)
colloidselasticitycontinuum mechanicsfinite deformationsHertz theorypairwise additivitymany-body interactionscell approximationfinite-element analysisPoisson ratiodiametral compressionnon-close-packed latticesphase diagram.Experiments have shown that at large densities, spherical polymeric nanocolloids self-organize in a number of crystal structures and quasicrystals. Although not identical, the phase sequences of suspensions of dendrimers, star polymers, and block-copolymer micelles are remarkably consistent, often featuring the face- and body-centered cubic lattices (FCC and BCC, respectively), A15, simple hexagonal (H), σ lattice and layered dodecagonal quasicrystals (DQC). The common micromechanical feature of all these nanocolloidal particles, and thus the possible origin of the similarities of their phase diagrams, is softness. So far, the idea of attributing the observed phase behavior to particle softness has been explored explicitly using either simulations at a monomer-resolved level or using effective pair interactions. Although these studies confirm that the non-close-packed structures mentioned above are indeed stable, a different type of argument may be sought within continuum theories, which dispose of most molecular-level details. In this Thesis, we consider the particles as deformable elastic spheres which interact with each other on contact. We describe their repulsive potential using two strain energy density functions from the finite deformation theory: The modified Saint-Venant–Kirchhoff and the Ogden neo–Hookean model. Using the cell approximation, we compute the deformation free energy of a set of Bravais and non-Bravais lattices up to very large deformations and we use these results to construct the phase diagram of elastic spheres with a positive Poisson ratio. We also delimit the small deformation regime, where the Hertz theory of sphere-sphere contact is valid, from the large deformation regime, where non-pairwise interactions are dominant. We show that the validity of either regime depends on the coordination number and on the Poisson ratio, and that the pairwise additivity of contact interaction typically holds only at small indentations just a little beyond the liquid–FCC transition. Furthermore, we study the elastic behavior of a single spherical polymer brush (SPB) upon diametral compression for a set of functionalities and chain lengths. We observe a universal response of the SPBs, which is rationalized using scaling arguments and interpreted in terms of two different coarse-grained models applicable far beyond the small-strain regime. At small and intermediate compressions the deformation can be accurately reproduced by modeling the brush as a liquid drop, whereas at large compressions the brush behaves as a elastic sphere. We also estimate the efective Young modulus and the Poisson ratio of the SPB.20182018-08-23 07:45:01Doktorsko delo/naloga102361VisID: 88844COBISS_ID: 3213156sl