The quantification of radical concentration in organic radical polymers: techniques and challenges

Electron paramagnetic resonance

Electron paramagnetic resonance (EPR) spectroscopy, ubiquitous in the investigation of paramagnetic materials, is used to detect unpaired electrons in a variety of materials including ORPs.^{12,13,25–27} This tool is most often used for the qualitative measurement of spins in a solid or solution using the continuous wave (CW) mode of operation. The more powerful quantitative (q-EPR) measurements are widely adopted to the study of biological processes, as they provide a direct measure of the concentration of spins, through the comparison of the double-integral of the unknowns’ absorption, to a standard that consists of a known concentration of spins. q-EPR’s application to materials is more limited, as for many systems (e.g. coordination complexes and stable organic radicals) qualitative data provides the required information, and these measurements are simple to undertake (Fig. 3). Although the quantitative measurements offer extremely high sensitivity (10¹² spins per mT of line width),²⁸ undertaking the measurements present a limitation on accuracy and repeatability as numerous factors affect the signal amplitude, which is key to quantification.^29,30 Examples of systematic errors include: cavity setup, sample size, shape and placement within the instrument, improper calibration of the instrumental variables and any alterations to these variables between analyses, such as an instrument being retuned,³¹ as well as the inability to use an appropriate reference sample. For ORPs the latter is significant as the standard will likely differ to the actual sample.^13,25,31 Specifically, TEMPO-based reference standards are commonly used for ORP systems regardless of the composition of the polymer,^12,13,25 alternatives such as metal salts have also been used.²⁶ Differences between the dielectric constant of the reference standard and ORP are known to reduce the accuracy of the technique, unless an internal standard within the instrumental cavity is used to normalise the signal amplitude.³¹ As with standard qualitative EPR, the presence of dissolved oxygen in the samples can interfere with the EPR signals, adding error to q-EPR measurements.³² Furthermore, spin relaxation must be sufficient for detection; an ORP low concentration or insufficient packing density will provide a further limitation. The opposite case is also problematic for ORPs i.e. a high spin-concentration and small inter-spin distances will cause significant broadening of the EPR spectra.³³ Specialised pulsed EPR or rapid scan CW-EPR are further methods that can be used^28,29,31 to alleviate the artifacts.³⁴

Fig. 3.

An example of qualitative EPR measurements being used to monitor the decomposition of a verdazyl radical (1,5-diethyl-3-(4-aminophenyl)-6-oxoverdazyl), over the course of 1 month. Measurements were performed using a MicroESR Standard benchtop (ver. 3.0, Bruker) EPR spectrometer at 298 K.

To achieve a high degree of accuracy in q-EPR, a nuanced approach is required but seldom detailed for ORPs.^12,13,27 To highlight this, one groups’ efforts to minimise error associated with their q-EPR measurements involved housing their instrument in a glove box and preparing identical shortened capillary tubes so that consistent scans across different samples without detuning of the cavity was achieved.¹³ Furthermore, for calibration, freshly sublimed TEMPO is used as a reference standard, with the g-factor for each sample precisely measured and calibrated using a Mn²⁺ marker located within the instrument’s resonant cavity.^12,13 The highly specialised nature of these measurements restricts their widespread adoption to ORPs.

Magnetic susceptibility measurements

Magnetic susceptibility measurements are excellent for quantification of spin concentration in an ORP solid sample. These measurements are non-destructive and allow the effective magnetic moment to be directly measured, and degree of polymer functionalisation to be determined. Magnetometers such as superconducting quantum interference devices (SQuID),^25,26,35,36 and vibrating sample magnetometers (VSMs),³⁷ not only offer quantification at room temperature but also allow for in-depth analysis of temperature and field-dependent properties. For conducting polymers,³⁸ magnetic exchange interactions are not often evident at room temperature or without application of a bias field, the latter is not accessible with EPR.³⁹ The spin concentration in the ORP is often found directly from the slope of the Curie–Weiss plot (Fig. 4).²⁵ Unlike q-EPR, which requires a specialised setup to minimise the significant errors, these instruments offer a simple setup and use standardised methodologies that greatly reduce the complexity of the measurement. Accessibility is the only major hindrance in their use for ORP characterisation. For example, in the Australian research landscape, there are only a handful of institutions maintaining magnetometers. In the absence of this instrumentation, room temperature susceptibility can still be determined with a number of modest and commonly available methods such as Gouy⁴⁰ and Faraday balances,⁴¹ or even using nuclear magnetic resonance (NMR) spectroscopy through the Evans method.⁴² The Evans method is a technique that utilises the observed change in chemical shift of a ¹H NMR peak when in the presence of a known quantity of a paramagnetic species. The change in chemical shift is proportional to the magnetic susceptibility of the compound, allowing the number of unpaired electrons per repeating unit of polymer to be calculated. Although some of these methods have decreased sensitivity and capability when compared to magnetometers, their accessibility makes them possible alternatives well suited to ORP characterisation.

Fig. 4.

A Curie–Weiss plot from a PTMA sample, figure adapted from Nishide et al.,³⁵ with permission. Construction of a Curie–Weiss plot is achieved by plotting the inverse of the magnetic susceptibility as a function of temperature. The gradient of the slope is equal to the inverse of the Curie constant (C⁻¹) and the number of unpaired electrons per repeating unit (n) is calculated. To calculate n, the effective magnetic moment (µ_eff) can be calculated (µ_eff = 800 Cµ_B), and the number of unpaired electrons can be determined (n = –1 + μ eff2+1).³⁸ χ_g⁻¹, inverse mass susceptibility; emu, electromagnetic unit.

Ultraviolet–visible absorbance spectroscopy

Ease of use, high accuracy and cost effectiveness have ensured that ultraviolet–visible absorbance spectroscopy (UV-Vis) is one of the most widely adopted methods for the determination of unknown radical concentrations in ORPs.^{8,11,13,23,43} Degree of polymer functionalisation can be determined by construction of a Beer–Lambert plot using an absorption that is common to the ORP and a standard, often the unbound radical (Fig. 5). An essential requirement is that the electronic transition chosen for the analysis is a characteristic absorption from the radical, which does not overlap with other absorbances associated with the polymer backbone or precursor. Nitroxide-based systems are known to be subject to significant changes in peak intensity and wavelength given the polarity of the solvent used,⁴⁴ and peak intensities and wavelengths can vary following attachment to the ORP. Therefore, the commonly unbound radical reference standard is not well suited to this analysis. Any compounds with significant electronic differences (e.g. the presence of additional electron-withdrawing or electron-donating groups) to the ORP are unsuitable for use as a reference standard. The molar absorptivity must be as close as possible between the ORP and reference standard. Ideally the reference would consist of an ORP with standardised radical concentration, but the difficulties in synthesising such a system make it unviable. The limited solubility of some ORPs is a further restriction to quantification using UV-Vis.^10,13

Fig. 5.

(a) Representative UV-Vis spectra of PTMA at three concentrations. The peak maxima are used to determine radical concentration using a Beer–Lambert plot (inset), constructed with a similar monomer species (tBu-TEMPO). Figure illustrative of work from Bertrand et al.²³ (b) The decomposition of TEMPO upon addition of 1-hexanethiol, monitored using UV-Vis. Figure adapted from Zhang et al.⁴⁵ with permission.

For PTMA, high accuracy has been reported when determining the radical concentration using UV-Vis.⁸ The absorbance of PTMA and 4-acetoxy-2,2,6,6-tetramethylpiperidine-N-oxyl at ~460 nm was measured at concentrations of 5 and 10 g L⁻¹ in dichloromethane for both samples. The calculated molar extinction coefficient for PTMA and the monomer radical samples, when compared, gave a reported value of 100.26% functionalisation of the PTMA. Given that this ORP was synthesised using a direct polymerisation method (Fig. 2(i)), the monomer sample used as the standard is structurally similar to the ORP being analysed. Therefore, the monomer is an adequate reference for a system where known concentrations cannot be used. The good solubility exhibited by the PTMA sample also ensured suitability to UV-Vis analysis. The availability of UV-Vis makes it an attractive method for the characterisation of ORP radical concentration; however, the correct precautions must be taken to ensure validity of the obtained data. Given this technique does not directly measure the spin concentration, ideally it should be reported validated alongside other techniques for radical concentration quantification.

Alternative quantification techniques

There are a wide range of alternative methods that can be used to determine the radical concentration in an ORP. A variety of analytical techniques including iodometric titration,⁴⁶ Kjeldahl nitrogen analysis²² and elemental analysis (EA) have been used.^22,26,47,48 The two former methods require significant sample preparation and handling, and have only been applied to nitroxide-based ORPs. Kjeldahl nitrogen analysis has not been widely used, and may not be applied to pendant groups with significant nitrogen content, given radical concentration must be inferred from the nitrogen content found in the ORP. Using EA, the functionalisation can be calculated by comparing the observed composition with the theoretical composition with 100% functionalisation. This technique was used to confirm the quantitative functionalisation of a nitroxide-based ORP.⁴⁸ However, using EA for ORP characterisation involves non-standard application of the technique with the potential for result anomalies. Usually, the acceptable difference between the calculated and experimental values in EA is ±0.4%, but in ORP analysis the difference between the calculated and experimental values is the metric for determining polymer radical content. For this reason, it is assumed that differences between the calculated and experimentally determined elemental values are due to the functionalisation of the polymer, but impurities can unknowingly alter the results. Impurities such as residual solvent may be indistinguishable from radical molecules in the experimental sample, and as such the composition of elements may be misleading if purity has not been confirmed with an alternative method such as ¹H NMR analysis.

Fourier Transform–infrared (FT-IR) spectroscopy has also been used to quantify the concentration of radicals in ORPs. For PTMA, the relative intensity of the carbonyl stretches is examined and used to determine the degree of functionalisation within the polymer (Fig. 6).¹⁰ In polymer samples, broadening of FT-IR signals is often observed, meaning peak area is often more suitable than peak intensity for this calculation. As both solid and solution analysis is available, this method is also applicable for insoluble ORPs. For this to be useful, vibrations of interest in the base polymer cannot overlap with those from the newly formed bonds from radical attachment. This limits this semi-quantitative method to certain polymer types, such as acrylate-based ORPs, and only to PPM (Fig. 2(iii)) prepared ORPs. FTI-R quantification will not be useful to ORP systems with transient radical pendant groups. Like UV-Vis spectroscopy, FT-IR instruments are widely available and offer an alternative to more specialised techniques, but ideally results obtained would be supported through a direct measurement of unpaired spin concentration using q-EPR or magnetometry. FT-IR spectroscopy also has the potential to be developed for the in situ monitoring of PPM reactions used to prepare ORPs.

Fig. 6.

The FT-IR spectra of poly(pentafluorophenyl methacrylate) (PPFPMA) and PTMA, used to determine the relative concentration of TEMPO in PTMA, after post-polymerisation modification of PPFPMA with 4-hydroxy-TEMPO.¹⁰ Figure adapted from Xue et al.,¹⁰ with permission.

Future directions

There exists a variety of potentially useful techniques for ORP characterisation that are yet to be fully realised. Cyclic voltammetry and NMR spectroscopy are two unexpected examples, as they are routinely associated with other parts of ORP characterisation. Although cyclic voltammetry is not commonly used for quantification, the peak–current response is directly proportional to the concentration of the redox-active species, as explained by the Randles–Ševčík equation.⁴⁹ By determining the concentration of radical using the peak–current response in a voltammogram of an ORP sample, the degree of functionalisation of an ORP could feasibly be calculated as part of the standard electron transfer investigations undertaken for ORPs. Surprisingly, although NMR spectroscopy is routinely used to characterise polymers and monitor PPM reactions to determine the degree of functionalisation in non-radical systems it has not been used to quantify the functionalisation of an ORP.⁵⁰ Examples of the use of NMR spectroscopy on stable organic radicals can be found. These include monitoring of reactions,⁵¹ determining paramagnetic susceptibility using the Evans method⁵² and decomposition studies⁵³; however, no examples are found of the application of NMR spectroscopy to elucidate radical concentration in ORPs. This may be a result of the expectation that the radicals’ unpaired spins produce paramagnetic line-broadening. As the unpaired electron only resides in specific molecular orbitals, it may still be possible to monitor reactions for specific atoms not involved in this molecular orbital. For example, ¹⁹F NMR spectroscopy could be used to determine the degree of functionalisation in a poly(pentafluorophenyl methacrylate) polymer used for PPM with the TEMPO radical.¹⁰

To demonstrate the usefulness of the less conventional methods for ORP characterisation, we synthesised a common nitroxide-based ORP, poly(TEMPO methacrylamide) (PTMAM), using PPM (see the ‘Experimental details’ section in the Supplementary material). The EPR spectrum of the product is shown below (Fig. 7). We have employed FT-IR spectroscopy (Supplementary Fig. S1), the Evans method (Fig. 8) and quantitative ¹⁹F NMR spectroscopy (Supplementary Fig. S2) to determine the TEMPO concentration in the ORP (Table 1). Detailed calculations are provided in the Supplementary material as a guide. Using the Evans method, the magnetic susceptibility could be calculated by measuring the change in frequency of a standard peak upon addition of a known amount of ORP (Fig. 8). Quantitative ¹⁹F NMR spectroscopy can be used to monitor the reaction and indirectly determine the functionalisation of the ORP by measuring the amount of free pentafluorophenol in solution, which is formed following radical attachment to the initial polymer backbone. Using a trifluorotoluene standard, the concentration of pentafluorophenol was determined, and assumed to be directly proportional to the concentration of TEMPO attached to the polymer.

Fig. 7.

The EPR of a dilute solution of PTMAM in degassed chloroform. Inset shows the solid-state EPR spectrum of the same sample. Measurements were recorded using a MicroESR Standard benchtop (ver. 3.0, Bruker) EPR spectrometer at 298 K.

Fig. 8.

A demonstration of the peak shift observed when using the Evans method to determine the paramagnetic susceptibility of the synthesised polymer, using acetone as a reference standard.

Each of the three methods are not without their limitations,⁵⁴ and they must be reported together to gain confidence in the obtained values of attachment. Quantitative ¹⁹F NMR spectroscopy is a valuable tool for the in situ monitoring of the specific PPM reaction reported, however, its uses are limited for other reactions involving alternative polymers or pendant groups. This technique is further hindered by the presence of catalysts such as triethylamine, which are often used in the PPM attachment of hydroxides, as they can cause hydrolysis and detachment of pentafluorophenol. Under these conditions, the concentration of pentafluorophenol cannot be assumed to be directly proportional to the radical amount on the polymer backbone. The Evans method is effective for room-temperature and solution-state magnetic susceptibility measurements. However, it is less versatile than other magnetometers, particularly for obtaining temperature-dependent magnetic susceptibility data. This limitation arises from the need for significant corrections due to changes in solvent density at different temperatures when constructing a Curie–Weiss plot. Additionally, the Evans method is restricted to solution-state compounds and is therefore unsuitable for insoluble ORPs. As previously mentioned, the use of FT-IR spectroscopy is limited to PPM preparation of ORPs and cannot be employed in PPM reactions where the vibrations of interest overlap with new vibrations resulting from the radical attachment.