Using Ultrafast Infrared Spectroscopy to Study Free Volume in Polymer Materials
Polymers are versatile materials with many industrial applications such as gas separation membranes and dielectric media. They are tolerant to a range of working conditions, and combined with organic synthetic chemistry, their chemical structures are tunable to offer a virtually infinite library of material properties. Free volume is a key component of polymer membranes. Its characteristics are related to, and in some cases dictate, the membrane’s macroscopic properties, such as thermal response, viscosity, gas permeability and dielectric response.
Figure 1. Schematic representation of polymer membrane showing FVEs and vibrational probe, PhSeCN, trapped inside them.
Glass forming polymers above their glass transition temperature, Tg, exist in thermal equilibrium, as they possess enough thermal energy to achieve the most efficient chain packing. As the system crosses below Tg, its viscosity increases rapidly, chain mobility is diminished, and polymer chains become locked in an inefficiently packed, high-energy, non-equilibrium configuration. This leaves scattered across the matrix a series of “pockets” of unoccupied space called free volume elements (FVEs), which span a range of sizes and structures (Fig. 1).
Using poly(methyl methacrylate), PMMA, and polystyrene, PS, we developed an experimental approach called Restricted Orientation Anisotropy Method (ROAM) to measure the size, size distribution, structural dynamics timescales, and size-dependent intrinsic electric fields of polymer FVEs. ROAM uses a polarization-selective pump-probe experiment to measure the orientational dynamics of a small vibrational probe embedded inside FVEs. The vibrational probe is used as a molecular ruler for FVE sizes, and its vibrational frequency is used to extract polymer E-fields.
Figure 2. Population decay (i.e., first excited state lifetime) of PhSeCN in poly(methyl methacrylate) and polystyrene. Decays are characterized by a single exponential decay.
In time-resolved vibrational spectroscopy, the experimental time-window is determined by the excited state lifetime of the observed vibrational mode. Because polymers are slow-moving chemical systems, their molecular dynamics are slow, and a long first excited state lifetime is required. The symmetric CN stretch of phenyl selenocyanate, PhSeCN, has a vibrational lifetime of >400 ps at room temperature, which allows an observation window of over 1 ns (Fig. 2). This property results from the presence of the selenium atom between the CN moiety and the phenyl ring. The heavy atom isolates the CN stretch and inhibits intramolecular vibrational relaxation pathways, thus increasing the CN’s vibrational lifetime.
The orientational dynamics of PhSeCN inside FVEs are characterized by frequency dependent biexponential decays with non-zero final offsets (Fig. 3 A – B). Because the frequency of a particular probe molecule is partly determined by the surrounding local electrostatics (see below), different frequencies correspond to subensembles of probe in distinct chemical environments (FVEs). The non-zero decay offsets indicate that the probe’s reorientation is restricted such that it cannot fully randomize its orientation, and the frequency dependence shows that different probe subensembles have distinct orientational dynamics. Because orientational restriction results from a collision between the probe and the inner walls of the surrounding polymer cage, the extent of decay at each frequency quantifies the level of restriction of the probe. Thus, the PSPP experiment unambiguously shows that different subensembles of probe molecules are trapped in FVEs of different sizes.
Figure 3. Left: Anisotropy decay (orientational dynamics) of PhSeCN in (A) PS and (B) PMMA. Right: Reorientation cone angles and corresponding FVE radii and total radii of (A) PS and (B) PMMA.
The orientational dynamics are modeled as a succession of free diffusion processes inside a hard-walled cone, during which the probe samples a particular range of angular space. Using the wobbling-in-a-cone (WIAC) model, the angle of reorientation is extracted from the anisotropy decays (Fig. 3), resulting in a set of frequency dependent cone angles (Fig. 4). Using the molecular dimensions of PhSeCN, the reorientation angles are converted into the radii of the surrounding polymer FVEs, and the result is a set of frequency dependent FVE radii (Fig. 4). High vibrational frequencies are associated with large radii, whereas low vibrational frequencies result from small radii. There is a linear relation between vibrational frequency and FVE radii in the high frequency regime. This linearity is lost in the low frequency regime, where the FVE radii tend to converge, showing that FVEs with the same radii can result in different probe vibrational frequencies. These observations indicate that there are fewer structural configurations that result in large FVEs compared to small FVE.
Because the anisotropy curve is a biexponential decay, two processes are associated with the reorientation of the probe. The first ~10 ps decay process measures the degree of reorientation of probe molecules before any structural changes take place and is associated with the size of the FVE. The second, longer process of ~150 ps, is associated with the FVE structural dynamics and fluctuations. The WIAC model yields two sets of cone angles and radii for each anisotropy decay curve: (1) the size of the FVE at that frequency, and (2) the cumulative radius accessible to the probe before and after structural rearrangements of the FVE. It is important to highlight that even though the total radius is larger than the FVE radius, the FVEs don’t change size during their structural rearrangement.
Figure 4. FVE radius probability distribution (RPD) of PS and PMMA.
Using the frequency dependent FVE radii (Fig. 4) and the linear absorption spectrum of the probe in the membrane (Fig. 6), we apply a maximum entropy mathematical formalism to extract the FVE radius probability distribution (RPD) functions of the polymer (Fig. 5). Polymer RPDs can be highly non-Gaussian with tails to large FVE radii. PS has larger FVEs compared to PMMA, with average FVE radii of 3.4 and 3.0 Å, respectively. Additionally, PS displays a much longer tail that extends to 5.5 Å, whereas PMMA’s tail only extends to 3.9 Å. The RPD curves are important because their characteristics can be related to the membranes’ macroscopic properties, and since ROAM is a highly sensitive technique, it can distinguish very small differences across polymer matrices.
Figure 5. Linear absorption spectrum of the symmetric CN stretch of PhSeCN in (A) PS and (B) PMMA.
The frequency of a vibrational mode is partly determined by the local electrostatics of its surrounding environment. Polymers are highly heterogeneous chemical systems and display a wide range of local chemical environments, which results in a wide range of vibrational frequencies. This is the origin of the inhomogeneously broadened linear absorption spectrum of the probe (Fig. 6). Because there is a non-Gaussian distribution of FVE sizes (Fig. 5) and environments, the FTIR spectra also display non-Gaussian lineshapes, with tails to the low vibrational frequency regime.
Figure 6. Intrinsic electric fields of PS and PMMA as a function of FVE radius.
First-order Stark effect offers a straightforward linear relation between vibrational frequencies and surrounding electric fields. Different local electrostatics result in different vibrational frequencies, and because different frequencies represent subensembles of probe molecules trapped in FVEs of different sizes, each FVE radius can be related to a unique intrinsic polymer electric field magnitude (Fig. 7). Electric fields in PS and PMMA range from 0.35 to 1.1 GV/m, and each is associated with a different FVE size. The fields are linear with respect to radius when the FVEs are large, but plateau to the same value when the FVEs are small.
ROAM has proven to be a highly sensitive and versatile technique capable of detecting sub-angstrom differences in FVE sizes across polymers of different chemical compositions. This method allows for the extraction of a large amount of information about the microscopic structure of polymer membranes from a single experiment and it offers fast time resolution to observe its structural fluctuations. This technique is also minimally perturbative and non-destructive, which will enable the study of changes in polymer membranes as they occur over macroscopic timescales. We are applying this method to understand the role of FVE sizes in determining gas permeation and dielectric breakdown polymer properties, and we continue to develop the technique to understand its full scope in elucidating how the microscopic structure of polymer materials results in their macroscopic properties and industrial performance.
Relevant Publications
492. "Amorphous Polymer Dynamics and Free Volume Element Size Distributions from Ultrafast IR Spectroscopy," David J. Hoffman, Sebastian M. Fica-Contreras, and Michael D. Fayer Proc. Nat. Acad. Sci. U.S.A. 117, 13949-13958 (2020). [SI]
499. "Free Volume Element Sizes and Dynamics in Polystyrene and Poly(methyl methacrylate) Measured with Ultrafast Infrared Spectroscopy," Sebastian M. Fica-Contreras, David J. Hoffman, Junkun Pan, Chungwen Liang, and Michael D. Fayer J. Am. Chem. Soc. 143, 3583-3594 (2021). [SI]
501. "Distinguishing Steric and Electrostatic Molecular Probe Orientational Ordering Via Their Effects on Reorientation-Induced Spectral Diffusion," David J. Hoffman, Sebastian M. Fica-Contreras, Junkun Pan, and Michael D. Fayer J. Chem. Phys. 154, 244104 (2021). [SI]
503. "Long Vibrational Lifetime R-selenocyanate Probes for Ultrafast Infrared Spectroscopy: Properties and Synthesis," Sebastian M. Fica-Contreras, Robert Daniels, Omer Yassin, David J. Hoffman, Junkun Pan, Gregory Sotzing, and Michael D. Fayer J. Phys. Chem. B 125, 8907-8918 (2021) [SI]