Restricted Orientation Anisotropy Method for FVE Radii Characterization: Confirmed and Refined via the Study of Six Vibrational Probes

Abstract

The Restricted Orientation Anisotropy Method (ROAM) is a new technique for determining polymer free volume element (FVE) radii using ultrafast infrared (IR) polarization-selective pump−probe (PSPP) spectroscopy. ROAM utilizes small IR vibrational probe molecules as molecular rulers to measure the FVE radii and the radius probability distribution (RPD). Here, we present a rigorous test of the method by performing ROAM experiments on polystyrene using six different probe molecules that have different lengths and shapes. In addition, we enhance the method for determining the length of the molecular ruler, resulting in greater accuracy. ROAM measures the orientational relaxation of the probes. Because the probes are too large to rotate in the FVEs completely, PSPP experiments provide their restricted angular ranges. The FVE radius is determined from the angular range and probe length. The IR measurements are made on the CN stretches of phenyl selenocyanate, phenyl thiocyanate, and four para-substituted benzonitriles (p-XBZN, where X = F, Cl, Br, I). The FVE radius measured using the six probes is the same with a small experimental error. The average of the radii measured at the spectral peaks of the six probes is 2.81 ± 0.02 Å. The RPD is determined and used to obtain the average radius, 2.94 Å, within a few hundredths of an Angstrom to values found with positron annihilation lifetime spectroscopy. The fact that six probes with different lengths and shapes give the same radius proves ROAM's efficacy and confirms the model of the FVEs as cylinders on the probe's length scale.

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“…Six vibrational probes with different shapes and lengths were used to perform ROAM measurements on amorphous polystyrene (PS). The measurements yielded the same FVE radius within a few hundredths of an Å for each of the six probes, demonstrating the method’s accuracy . It is worth noting that the average FVE radius in the PS study agreed with two separate PALS measurements. ,, In addition to demonstrating the ROAM’s accuracy, the studies eliminate the possibility that a small amount of embedded vibrational probe molecules influence the FVE sizes.…”

“…Here, FVEs are treated as cylindrical elements, and the half-cone angles are the half-angles of the largest cone the probe can make inside the cylinder . Detailed experiments have shown that the ensemble-averaged shape of FVEs is a cylinder . The parametrization is given in the following expression r ( t ) = 0.4 S 0 2 ( S 1 2 + false( 1 − S 1 2 false) exp false( prefix− t / τ 1 false) ) ( S 2 2 + false( 1 − S 2 2 false) exp false( prefix− t / τ 2 false) ) S 0 , S 1 , and S 2 are order parameters describing the range of angular sampling, which can be converted to the cone angles using eq S i = 1 2 cos ( θ i ) ( 1 + cos false( θ i false) ) S 0 S 1 is converted to θ fast , which describes the fast diffusive motion that occurs at a time scale <10 ps.…”

“…The cone angles can be converted into FVE radii using the contact geometries and dimensions of the probe molecule, PhSeCN. The following equation gives the conversion from cone angles to radii ( R ) R = 1 2 ( l .25em sin ( θ f a s t ) + normalΔ r 1 + normalΔ r 2 ) l is the length of the PhSeCN from the center of the selenium (Se) atom to the center of the para-hydrogen and Δ r 1 and Δ r 2 are the van der Waal (vdW) radii of the Se atom and the para-hydrogen atom, respectively . The value of l was determined from a density functional theory calculation.…”

“…There are no inherent limitations for the types/sizes of nanoparticles as long as they do not introduce a large amount of scattering. In addition, ROAM measurements utilize the vibrational probe, phenyl selenocyanate; however, other probe molecules can be used . The polymer needs to contain the probe molecules over an extended period.…”

“…Recently, a new technique, the restricted orientation anisotropy method (ROAM), based on ultrafast infrared (IR) spectroscopy, was developed for measuring the free volume element (FVE) radii and radius probability distributions (RPDs) in polymeric materials. − the ROAM combines the measurements of the orientational relaxation of the vibrational probe molecules embedded in the FVEs with the physical dimensions of the probe as a “molecular ruler” to extract the radii of the FVEs. Previously, the ROAM was successfully applied to characterize a variety of pure polymer systems. − The ROAM experiments show high sensitivity to different polymer environments and the modification of polymer end groups. , The ROAM technique was refined recently, and definitive tests were performed . Six vibrational probes with different shapes and lengths were used to perform ROAM measurements on amorphous polystyrene (PS).…”