Long Wavelength Thermal Density Fluctuations in Molecular and Polymer Glass-Forming Liquids: Experimental and Theoretical Analysis under Isobaric Conditions

Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids

Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains

Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.

Penetrant shape effects on activated dynamics and selectivity in polymer melts and networks based on self-consistent cooperative hopping theory

We generalize and apply the microscopic self-consistent cooperative hopping theory for activated penetrant dynamics in polymer melts and crosslinked networks to address the role of highly variable non-spherical molecular shape. The focus is on vastly different shaped penetrants that have identical space filling volume in order to isolate how non-spherical shape explicitly modifies dynamics over a wide range of temperature down to the kinetic glass transition temperature. The theory relates intramolecular and intermolecular structure and kinetic constraints, and reveals how different solvation packing of polymer monomers around variable shaped penetrants impact penetrant hopping. A highly shape-dependent penetrant activated relaxation, including alpha time decoupling and trajectory level cooperativity of the hopping process, is predicted in the deeply supercooled regime for relatively larger penetrants which is sensitive to whether the polymer matrix is a melt or heavily crosslinked network. In contrast, for smaller size penetrants or at high/medium temperatures the effect of isochoric penetrant shape is relatively weak. We propose an aspect ratio variable that organizes how penetrant shape influences the activated relaxation times, leading to a (near) collapse or master curve. The relative absolute values of the penetrant relaxation time (inverse hopping rate) in polymer melts versus in crosslinked networks are found to be opposite when compared at a common absolute temperature versus when they are compared at a fixed value of distance from the glass transition based on the variable Tg/T with Tg the glass transition temperature. Quantitative comparison with recent diffusion experiments on chemically complex molecular penetrants of variable shape but fixed volume in crosslinked networks reveals good agreement, and testable new predictions are made. Extension of the theoretical approach to more complex systems of high experimental interest are discussed, including applications to realize selective transport in membrane separation applications.

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S₀(T) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S₀(T) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S₀(T) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.