Session H50: Polymer Melts

Coil-Globule Transition of Polymer -- Tricriticality of Theta

We demonstrate the tricriticality of the theta point in the coil-to-globule transition of a single flexible polymer chain by dynamic Monte Carlo (DMC) simulation. For homopolymer, at the tricritical point, the second order theta transition line approaches the first order collapse transition line as the chain length approaches the thermodynamic limit. Theta point of homopolymer has been estimated by following the ideal behavior of chain at the theta point. Temperature at which the constant volume specific heat (Cv) shows a peak is considered as the collapse temperature and the transition is of first order. In T-N plane, collapse temperature approaches towards the theta temperature as the chain length approaches to the thermodynamic limit. For copolymer (with periodic distribution of comonomer along the chain), the collapse temperature increases with increasing the stickiness parameter (viz., higher solvophobicity of the comonomers relative to monomers) and approaching towards the theta as the value of the stickiness parameter increases. Theta points of copolymers have been estimated from the theta point of homopolymer under the condition of the ideality of the theta point. The collapse temperatures for copolymer have been in a manner similar to homopolymers. Theta temperature vs. stickiness parameter represents a second order line whereas collapse temperature vs. stickiness parameter represents a first order line. We demonstrate that as the stickiness parameter increases, these two lines meet each other, close to the ``tricritical'' theta temperature.   

Microscopic Theory of Nanoparticle Diffusivity in Entangled and Unentangled Polymer Melts

We present a statistical dynamical theory at the level of forces for the violation of the Stokes-Einstein (SE) diffusion law of a spherical nanoparticle in entangled and unentangled polymer melts. Based on a combination of mode-coupling and polymer physics ideas, the non-hydrodynamic friction coefficient is related to microscopic structure and the length-scale-dependent polymer melt collective density fluctuation dynamics. When local packing correlations are neglected, analytic expressions are derived for the non-hydrodynamic diffusivity as a function of particle size, polymer radius-of-gyration, tube diameter, degree of entanglement and temperature; local packing effects are numerically investigated under athermal and attractive conditions. The conditions for the recovery of the SE law are qualitatively distinct for unentangled and entangled melts, and entanglement effects are the origin of large SE violations consistent with recent experiments. The influences of melt packing fraction and interfacial attraction strength are also qualitatively different depending on whether the polymers are entangled or not. The anomalous time-dependence of the nanoparticle mean square displacement is studied using a self-consistent Generalized Langevin Equation approach.   

Effect of Secondary Structure on the Persistence Length of a Poly N-substituted Glycine

A polymer containing helical secondary structure is shown to be nearly as flexible as a chemically analogous polymer containing no structure. Polypeptoids or poly N-substituted glycines are a class of sequence specific polymers in which chain shape can be controlled via monomer choice involving both sterics and chirality. In this study, a polypeptoid containing aromatic chiral sidechains was synthesized. Classical measurements such as circular dichroism and NMR have shown previously that the bulky chiral side chains cause the polypeptoid to adopt a helical conformation. However, small angle neutron scattering demonstrated that in acetonitrile, the persistence length of the helical polypeptoid was approximately 1 nm, only about 15{\%} of the fully extended helical length. This small persistence length indicates that the chain likely adopts several conformations in solution and is not rigidly locked into its helical shape throughout the entire length of the polymer   

Gibbs Ensemble Calculations of Phase Coexistence in Supramolecular Assembly of Block Copolymers

We propose a new self-consistent field theory method for calculating phase behavior in reversibly bonded supramolecular polymer melts. Previous studies formulated models for supramolecular assembly in the grand canonical ensemble to make use of the constraints imposed on the chemical potentials of the products from chemical equilibrium. Instead, we formulate the model in the canonical ensemble by including a term in the Hamiltonian that accounts for the reaction favorability/penalty. The chemical equilibrium statement is obtained by optimizing the Hamiltonian with the amount of reacted polymer. The canonical partition function can be easily adapted to the Gibbs ensemble whereby phase boundaries between coexisting phases can be conveniently simulated. As an illustration of our method, we examine a blend of AB diblock and B homopolymer with the ability to reversibly bond to form ABB diblock. In the limits of infinite reaction favorability and penalty, the system approaches cases of an ABB diblock-B homopolymer blend when the AB diblock is the limiting reactant and an AB diblock-B homopolymer blend, respectively. The interplay between reactant ratios (stoichiometry) and reaction favorability/penalty is explored for intermediate values of reactivity.   

Pressure-induced structural transition in an one-component polymer poly(4-methyl-1-pentene) in its melted state

Liquid-liquid transitions or amorphous-amorphous transitions are well-known in systems with small molecular or structural units, such as those seen in water, phosphorus, and silica glass. We studied pressure-induced structural change for isotactic poly(4-methyl-1-pentene) in its melted state, and found a structural transition for this one-component polymer melt. High-pressure in-situ x-ray diffraction and specific-volume measurements on the polymer melt have uncovered discontinuities in the pressure dependences of microscopic structure as well as those of macroscopic density. The results suggest the occurrence of a liquid-liquid phase transition.   

Anomalous diffusion of a polymer chain in an unentangled melt

Contrary to common belief, the hydrodynamic interactions (HI) in polymer melts are not screened beyond the monomer length and are important in transient regimes. We show that the viscoelastic HI effects (VHI) lead to anomalous dynamics of a tagged chain in an unentangled melt at $t < t_N$ ($t_N$, the Rouse time). The chain centre-of-mass (CM) mean-square displacement is enhanced (as compared to the Rouse diffusion) by a large factor increasing with chain length. We develop an analytical theory of VHI-controlled chain dynamics yielding negative CM velocity autocorrelation function which quantitatively agrees with our MD simulations without any fitting parameter. It is also shown that the Langevin friction force, when added in the model, strongly affects the short-$t$ CM dynamics which, however, can remain strongly enhanced. The transient VHI effects thus provide the dominant contribution to the subdiffusive CM motion universally observed in simulations and experiments on polymer melts.   

Representation of Polymer melts as soft liquids with effective pair interactions

Descriptions at various levels of coarse-graining are of great interest in understanding the complex structure and dynamics of polymer liquids, as relevant processes take place at a wide variety of length and time scales. In this talk we present and analytically characterize effective interaction potentials to map a polymer melt onto a liquid of soft spheres or soft-colloid chains, with each soft colloid representing the center of mass of a chain or large subsection of a chain. The thermodynamics of the coarse-grained system using the effective potentials can be shown to agree with the thermodynamics of monomer-level descriptions across a range of thermodynamic states. The scaling of the effective pair potentials beyond the physical extent of the polymer with increasing chain interpenetration is shown to be essential to capturing the contribution to the thermodynamics of the melt due to many-polymer interactions in the soft coarse-grained description, despite its vanishingly small effect on structural correlations. Further development of the theory will consider its extension from soft-colloid chains to lower level bead and spring level descriptions with the aim of gaining insight into the thermodynamic properties of these widely used models.   

Entropy of Mixing: Rigid vs. Flexible Molecules: Effect of Varying Solvent on Dissolution Temperature

We report a study of the dissolution temperature of n-hexacontane, as a function of concentration, with 52 different solvents, aimed at understanding the effect of molecular flexibility on the entropy-of-mixing. The entropy-of-mixing of rigid molecules is commonly expected to go as ln(mole fraction), while for flexible polymers it is expected to follow Flory-Huggins ln(volume fraction). By isolating the entropy-of-mixing, we have experimentally found that rigidity, through ring structures, causes deviations from the Flory-Huggins behavior; and we have proposed and derived a cross-over form for the entropy-of-mixing which varies between ln(volume fraction) and ln(mole fraction) according to molecular rigidity   

Polymeric Fluid Flow Over Superhydrophobic Surfaces

Superhydrophobic (SHP) surfaces are characterized by their exceptionally low surface energies and distinct surface roughnesses that create a vapor layer between the fluid and the surface. The reduced contact area at the interface can create a dewetted state resulting in slip, drag reduction, and improved flow of fluids. Most previous superhydrophobic studies have utilized simple liquids (e.g. water) in focusing on characterization of the quiescent interface and on drag reduction or slip modifications of fluid flow. As polymeric fluid flows have exhibited similar slip and drag reduction phenomena, this study attempts to utilize SHP surfaces to improve the flow behavior of more complex multi-component fluids, such as polymer solutions. By merging the research fields of SHP surfaces and polymer fluids, we investigate the potential to enhance slip and drag reduction effects as a result of surface interactions. Microfluidic channels, interfacial rheometry and goniometry are used to evaluate slip length and fluid flow.   

Reconstructing Polymer Melt Dynamics Sped up due to Large-Scale Coarse-Graining

A theoretical approach to rescale the artificially fast dynamics of highly coarse-grained polymer melts is extended to chains represented as soft particles. The effective pair potential derived from first-principles to represent polymer chains with soft interactions is used to perform mesoscale molecular dynamics simulations of coarse-grained melts. This potential ensures the reproduction of the correct global structure and thermodynamics, but entropic and frictional corrections are necessary to reconstruct realistic dynamics. The behavior of the system is described by generalized Langevin equations derived for different levels of coarse-graining. The explicit analytical dependence on the thermodynamic and molecular parameters enhances the predictive power of the reconstruction method. The dynamics, reconstructed from mesoscale simulation, is in quantitative agreement with experiments and atomistic simulations.   

Steric Constraints in Fractal-Regime Star Polymers

Star polymers at high functionality, f, and high arm length, z$_{arm}$, display a collapsed core structure described by Daoud and Cotton in a colloidal regime (CR). At lower functionality (f$<\sim $8) and relatively low arm length, stars display a polymeric structure in a fractal regime (FR). For FR stars in good solvents the arms display steric interactions analogous to polymer chains tethered to a surface. We have used small-angle neutron scattering to quantify, for the first time, this steric interaction so as to understand the approach to the CR as a function of z$_{arm}$ and f as well as temperature and solvent type. Experimental data from model star polymers and literature data from polyurethane stars are considered as examples.   

Capillary break-up, gelation and extensional rheology of hydrophobically modified cellulose ethers

Cellulose derivatives containing associating hydrophobic groups along their hydrophilic polysaccharide backbone are used extensively in the formulations for inks, water-borne paints, food, nasal sprays, cosmetics, insecticides, fertilizers and bio-assays to control the rheology and processing behavior of multi-component dispersions. These complex dispersions are processed and used over a broad range of shear and extensional rates. The presence of hydrophobic stickers influences the linear and nonlinear rheology of cellulose ether solutions. In this talk, we systematically contrast the difference in the shear and extensional rheology of a cellulose ether: ethy-hydroxyethyl-cellulose (EHEC) and its hydrophobically-modified analog (HMEHEC) using microfluidic shear rheometry at deformation rates up to 10$^6$ inverse seconds, cross-slot flow extensional rheometry and capillary break-up during jetting as a rheometric technique. Additionally, we provide a constitutive model based on fractional calculus to describe the physical gelation in HMEHEC solutions.