Near-Substrate Gradients in Chain Relaxation and Viscosity in a Model Low-Molecular Weight Polymer

Abstract

Polymers in the nanoscale vicinity of interfaces can exhibit large alterations in dynamics and glass formation behavior. These changes are accompanied by alterations in rheological response, yet the precise nature of gradients in viscosity and wholechain relaxation near interfaces is an open question. Here, we employ molecular dynamics simulations of a low-molecular weight glass-forming polymer between crystalline walls to probe this relationship. Results indicate that viscosity and whole-chain relaxation time gradients for this system obey the same qualitative phenomenology as do segmental relaxation time gradients, indicating that they emanate from the same underlying physics. At a quantitative level, however, our simulation and theoretical results indicate that unlike in small molecules, polymer viscous and whole-chain relaxation interfacial gradients should generally be expected to be weaker than underlying segmental relaxation time gradientsa consequence in large part of the typically weaker bulk temperature dependence of low-temperature viscosity and whole-chain relaxation than segmental dynamics in many polymers. Shifts in viscosity are shown to emerge from underlying alterations in the polymer's complex modulus near interfaces, with a highfrequency glassy plateau emerging at higher temperature and surviving to lower frequency near the walls. These results have implications for the rheological response of diverse nanostructured polymers including thin films, filled rubber, ionomers, and semicrystalline polymers, and they highlight the need for a generalization of the Rouse model to account for dynamical gradients.

Glass formation and dynamics of model polymer films with one versus two active interfaces

“…In analysing more deeply the local dynamics in these systems, we make use of a fractional power law decoupling relation between local and bulk dynamics that was discovered in our prior work 22 and has since been observed in a number of additional systems 33,35,36,54 and predicted theoretically. 33,36,55 As a consequence of this relation, which is predicted and observed to hold at low temperature, local dynamics near a surface are related to the bulk dynamics via the relationwhere τ * specifies an onset condition for this behaviour on cooling and ε is called the “decoupling parameter”.…”

Combined Mixing and Dynamical Origins of Tg Alterations Near Polymer–Polymer Interfaces

“…Relaxation times were computed by fitting the long-time response of this relaxation function to the Kohlraush–Williams–Watts (KWW) stretched exponential function for data smoothing and interpolation and then defining the relaxation time τ as the time at which this function relaxes to a value of 0.2. This set of conventions for translational relaxation time determination is widely employed in the simulation literature. ,,, …”

“…This set of conventions for translational relaxation time determination is widely employed in the simulation literature. 63,66,75,76 Relaxation time analysis is performed at both a whole-layer level and locally, by first binning particles into bins of thickness 0.875 as a function of distance from the interface (defined as the plane at which the mole fraction of both segment types is 0.5) and then performing the above analysis on particles in these local bins. Glass temperatures defined on a computational time scale are calculated by fitting the temperature dependence of the above relaxation time to the Vogel− Fulcher−Tammann (VFT) 77,78 equation and extracting the temperature at which the relaxation time is 10 4 τ LJ .…”

Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

“…In addition, the standard Mittag-Leffler function is used to account for the fractional diffusion of the free chains. The resulting survivability function is given in Equation (10), where s is the segment index (contour length variable) along the primitive chain that ranges from 0 to L. Here, L is the total contour length of the chain. E is the Mittag-Leffler expression, with α the fractional index.…”

“…The particles are generally treated as rigid objects because the moduli of the filler particles, like carbon black and silica, are much higher than the matrix polymers. The structural and rheological properties of the polymers in and near interfaces can be notably different from those within the bulk of the matrix polymer [10], which can greatly affect the macroscopic properties of the composites [11]. For example, the transition from the melt state to the glass state is significant within the particle-polymer interface.…”