3
|
Vogiatzis GG, van Breemen LCA, Hütter M. Response of Elementary Structural Transitions in Glassy Atactic Polystyrene to Temperature and Deformation. J Phys Chem B 2022; 126:7731-7744. [PMID: 36129780 PMCID: PMC9549470 DOI: 10.1021/acs.jpcb.2c04199] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The effects of temperature, pressure, and imposed strain on the structural transition pathways of glassy atactic polystyrene (aPS) are studied for a wide range of conditions. By employing an atomistic description of the system, we systematically explore its free energy landscape, emphasizing connections between local free energy minima. A triplet of two minima connected to each other via a first-order saddle point provides the full description of each elementary structural relaxation event. The basis of the analysis is the potential energy landscape (PEL), where efficient methods for finding saddle points and exploring transition pathways have been developed. We then translate the stationary points of the PEL to stationary points of the proper free energy landscape that obeys the macroscopically imposed constraints (either stress- or strain-controlled). By changing the temperature under isobaric conditions (i.e., Gibbs energy landscape), we probe the temperature dependence of the transition rates of the subglass relaxations of aPS, thus obtaining their activation energies by fitting to the Arrhenius equation. The imposition of different strain levels under isothermic conditions allows us to estimate the apparent activation volume of every elementary transition. Our findings are in good agreement with experimental observations for the same system, indicating that both length- and time-scales of the structural transitions of glassy aPS can be obtained by proper free energy minimization of atomistically detailed configurations.
Collapse
Affiliation(s)
- Georgios G Vogiatzis
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Dutch Polymer Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Lambèrt C A van Breemen
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Markus Hütter
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| |
Collapse
|
4
|
McKenzie I, Fujimoto D, Karner VL, Li R, MacFarlane WA, McFadden RML, Morris GD, Pearson MR, Raegen AN, Stachura M, Ticknor JO, Forrest JA. A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy–enthalpy compensation and dynamic gradients near the free surface. J Chem Phys 2022; 156:084903. [DOI: 10.1063/5.0081185] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin–lattice relaxation time [Formula: see text] was measured near the free surface and in the bulk. Spin–lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence [Formula: see text]. There is no clear correlation of the average entropy of activation [Formula: see text] and enthalpy of activation [Formula: see text] with MW, but there is a clear correlation between [Formula: see text] and [Formula: see text], i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, [Formula: see text], being approximately independent of MW. Measurements of the temperature dependence of [Formula: see text] as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to [Formula: see text] = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in [Formula: see text] near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a “double-exponential” depth dependence. This model can explain the depth dependence of [Formula: see text] in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.
Collapse
Affiliation(s)
- Iain McKenzie
- TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
- Department of Chemistry, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Derek Fujimoto
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Victoria L. Karner
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Ruohong Li
- TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
| | - W. Andrew MacFarlane
- TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Ryan M. L. McFadden
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | | | - Matthew R. Pearson
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
| | - Adam N. Raegen
- TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | | | - John O. Ticknor
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - James A. Forrest
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| |
Collapse
|