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In this paper we model the segmental relaxation in poly(2-chlorostyrene) 18 nm freestanding films, using only data on bulk samples to characterize the system, and predict film relaxation times ( τ ) as a function of temperature that are in semi-quantitative agreement with film data. The ability to translate bulk characterization into film predictions is a direct result of our previous work connecting the effects of free surfaces in films with those of changing pressure in the bulk. Our approach combines the Locally Correlated Lattice (LCL) equation of state for prediction of free volume values ( V free ) at any given density ( ρ ), which are then used in the Cooperative Free Volume (CFV) rate model to predict τ ( T , V free ). A key feature of this work is that we calculate the locally averaged density profile as a function of distance from the surface, ρ av ( z ), using the CFV-predicted lengthscale, L coop ( z ), over which rearranging molecular segments cooperate. As we have shown in the past, ρ av ( z ) is significantly broader than the localized profile, ρ ( z ), which translates into a relaxation profile, τ ( z ), exhibiting a breadth that mirrors experimental and simulated results. In addition, we discuss the importance of averaging the log of position dependent relaxation times across a film sample (〈log τ ( z )〉), as opposed to averaging the relaxation times, themselves, in order to best approximate a whole sample-averaged value that can be directly compared to experiment.
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This content will become publicly available on January 15, 2026
Modeling the structure and relaxation in glycerol-silica nanocomposites
The relationship between the dynamics and structure of amorphous thin films and nanocomposites near their glass transition is an important problem in soft-matter physics. Here, we develop a simple theoretical approach to describe the density profile and the a-relaxation time of a glycerol-silica nanocomposite (S. Cheng et al., J. Chem. Phys., 2015, 143, 194704). We begin by applying the Derjaguin approximation, where we replace the curved surface of the particle with the planar one; thus, modeling the nanocomposite is reduced to that of a confined thin film. Subsequently, by employing the molecular dynamics (MD) simulation data of Cheng et al., we approximate the density profile of a supported liquid thin film as a stationary solution of a fourth-order partial differential equation (PDE). We then construct an appropriate density functional, from which the density profile emerges through the minimization of free energy. Our final assumption is that of a consistent, temperature-independent scaled density profile, ensuring that the free volume throughout the entire nanocomposite increases with temperature in a smooth, monotonic fashion. Considering the established relationship between glycerol relaxation time and temperature, we can employ Doolittle-type analysis (‘‘naı ¨ ve’’ free-volume model), to calculate the relaxation time based on temperature and film thickness. We then convert the film thickness into the interparticle distance and subsequently the filler volume fraction for the nanocomposites and compare our model predictions with experimental data, resulting in a good agreement. The proposed approach can be easily extended to other nanocomposite and film systems.
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- Award ID(s):
- 2205553
- PAR ID:
- 10617083
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 21
- Issue:
- 3
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 376 to 388
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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