Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres

Abstract

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains’ ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

The influence of molecular shape on glass-forming behavior in a minimalist trimer model

“…The observation that as the internal angle increases, the glass transition temperature also increases is consistent with other types of computational modeling that analyze changes in behavior based on the internal angle. 26,28,32 Additionally, this trend is also in line with materials like azobenzenes, where changes in the characteristic temperature (T g ) are registered depending on the isomer present in the molecule, whether it is cis or trans. 36,37 As mentioned previously, drawing an analogy to experimental observations, in this model, angles of S90 and S180 could be seen as representations of the cis and trans isomers, respectively.…”

“…For instance, several authors 23–26 have delved into how the angle in rigid trimer molecules influences crystallization behavior. In contrast, others 27,28 have explored the repercussions of bond angles in semiflexible polymers on local order and certain jamming transition properties. A recent study by Meenakshisundaram et al 29 focused on a mixture of rigid trimers, recognized for its aptitude to form glasses and prevent crystallization.…”

The Role of Polymer Chain Stiffness and Guest Nanoparticle Loading in Improving the Glass Transition Temperature of Polymer Nanocomposites

“…Here, S 2 and the director ( ) can be calculated by solving the tensor matrix: with I , the unit second-rank tensor. Here S 2 is the largest eigenvalue and the relevant unit eigenvector of the matrix Q [ 76 , 77 , 78 ].…”

Aggregation and structural phase transitions of semiflexible polymer bundles: A braided circuit topology approach

“… 8 Moreover, for polymer melts lowering the temperature can lead to a transition from a disordered melt phase to an ordered nematic and crystalline phase, as a consequence of increasing stiffness. 9 , 10 …”