Single‐Chain Inherent Elasticity Reveals γ‐Irradiation–Induced Backbone Reconstruction in Poly(Vinylidene Fluoride)

ABSTRACT

γ‐Irradiation significantly alters the mechanical properties and functions of poly(vinylidene fluoride) (PVDF), yet the molecular mechanism underlying its property evolution at high irradiation dose remains unclear. Because the single‐chain inherent elasticity of a polymer directly reflects its backbone structure, single‐molecule force spectroscopy (SMFS) was employed to examine PVDF under different γ‐irradiation doses. The results show a progressive increase in chain flexibility with increasing dose. Fourier‐transform infrared spectroscopy and X‐ray photoelectron spectroscopy reveal the formation of oxygen‐containing groups accompanied by C═C bonds. By quantitatively correlating SMFS measurements with theoretical elasticities derived from quantum mechanical calculations, we provide the first single‐molecule‐level evidence that prolonged high‐dose irradiation (2000 kGy) reconstructs the PVDF backbone into an alternating ether (C─O─C) and double‐bond (C═C) architecture. This work establishes a direct link among irradiation dose, backbone transformation, and mechanical response, offering molecular insight into the irradiation regulation of PVDF for applications in extreme radiation environments.

Through quantitative comparison of the experimentally measured inherent elasticity with theoretical elasticities of plausible post‑irradiation backbone structures, we provide the first single‑molecule‑level evidence that prolonged high‑dose irradiation (2000 kGy) reconstructs the PVDF backbone into an alternating ether (C─O─C) and double‑bond (C═C) architecture.

1. Introduction

Poly(vinylidene fluoride) (PVDF) is widely used in various fields owing to its outstanding chemical resistance, high mechanical strength, and excellent radiation tolerance [1, 2]. In recent years, increasing evidence has shown that controlled irradiation can enhance its mechanical strength and surface properties and even introduce new functionalities such as improved dielectric performance and anti‐aging capability [3]. Consequently, PVDF has found critical applications in aerospace and nuclear engineering, such as radioactive waste containers, reactor seals, and radiation‐resistant coatings, where long‐term stability under high‐dose irradiation is essential [4]. However, prolonged exposure to high‐energy irradiation inevitably alters the chemical structure and physical properties of PVDF, ultimately leading to functional degradation [5]. Although mechanical integrity can be partially maintained at early stages, long‐term high‐dose irradiation significantly accelerates embrittlement and increases failure risk, thereby limiting the reliable use of PVDF in harsh radiation environments.

To improve the reliability of PVDF in nuclear applications and explore its potential in other high‐radiation fields, the effects of irradiation dose on its structure–property relationships have attracted increasing attention. Fan et al. reported that ⁶⁰Co γ‐irradiation induces cleavage of C─H and C─F bonds in PVDF, while radical recombination promotes cross‐linking and enhances its thermal stability by ∼20°C [6]. Tan et al. demonstrated that γ‐irradiation causes bond scission and generates fluorinated C═C double bonds [7]. More recently, Liu and Xing independently suggested that irradiation produces not only double bonds and cross‐links but also complex branching structures [8, 9]. These advances have improved our understanding of the irradiation dose–dependent structure–property relationship in PVDF. However, conventional techniques provide only ensemble‐averaged structural information and cannot unambiguously distinguish between backbone and side‐chain modifications, often leading to inconsistent interpretations of structural evolution and its influence on material performance. Consequently, although irradiation‐induced structural changes have been widely reported, the precise molecular structures and their evolution pathways in irradiated PVDF remain unresolved.

Because polymer materials consist of large ensembles of individual chains, probing structural changes at the single‐chain level provides a direct route to elucidating irradiation‐induced molecular transformations. Atomic force microscope–based single‐molecule force spectroscopy (SMFS) has been widely used to investigate polymer chain elasticity, conformational transitions, melting behavior, and polymer–environment interactions [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Previous studies have demonstrated that when polymer–solvent interactions and side‐chain interactions are negligible, a single polymer chain exhibits an enthalpic elasticity determined solely by its backbone structure, referred to as inherent elasticity [28, 29]. This concept is generally applicable to all types of polymers and thus provides an internal reference for understanding single‐chain mechanical behavior [30, 31, 32, 33]. Importantly, a strict one‐to‐one correspondence exists between backbone architecture and inherent elasticity [34, 35]. Accordingly, direct comparison of experimentally measured single‐chain elasticity from SMFS with theoretically calculated elastic responses of candidate molecular structures enables unambiguous identification of the polymer backbone structure. Using this paradigm, we have resolved long‐standing structural controversies in amorphous boron and red phosphorus [34, 36]. Here, we apply this approach to irradiated PVDF and reveal irradiation‐induced backbone reconstruction through correlating experimental data with theoretical elastic behavior [37].

2. Results and Discussion

For PVDF, no specific noncovalent interactions exist between side chains, and only very weak van der Waals interactions occur between PVDF and nonpolar organic solvents, which can be neglected under liquid‐phase SMFS conditions [38]. Therefore, nonane was chosen as the experimental medium to probe the single‐chain inherent elasticity of PVDF. To ensure the reliability of the force‐extension (F–E) curves and minimize random variations from individual measurements, multiple F–E curves were collected from independent experiments (Table S1). Figure 1a shows three representative F–E curves of PVDF. The initial adhesion peak arises from nonspecific interactions between the AFM tip and the sample surface when the tip is just lifted, and the polymer chain has not yet been fully stretched. Therefore, it does not affect the subsequent measurement of single‐chain elasticity. As the tip continues to retract, the polymer chain is gradually stretched until the bridging interaction ruptures, giving rise to the final peak in the curves.

FIGURE 1.

(a) Representative F–E curves of PVDF acquired in nonane. (b) Representative normalized F–E curves shown in panel (a). (c) Comparison of the experimental curve of PVDF and the QM‐FRC curve of PE.

Due to polymer polydispersity and the stochastic nature of AFM tip–molecule pickup, the original F–E curves exhibit varying contour lengths [39]. To enable meaningful comparison, the curves were normalized by linearly scaling the extension axis, while keeping the force axis unchanged. This procedure removes the influence of polydispersity while preserving the relative shape of the F–E curves. Since the samples were prepared by physical adsorption, rupture forces are broadly distributed, making the maximum rupture force unsuitable as a normalization reference. Thus, a force of 500 pN within the stable mid‐force elastic regime was selected for normalization, as it is reliably achievable in most experiments and offers both feasibility and representativeness [40]. After normalization, the F–E curves overlap well (Figure 1b and Figure S1a), indicating that they reflect the single‐chain elasticity of PVDF in nonane.

It is worth noting that the effect of pulling geometry typically manifests in two distinct ways: either as a continuous change in the F–E response or as angle‐independent behavior [41, 42, 43]. In this study, the pulling angle was not deliberately controlled and should be randomly distributed. All experimental F–E curves obtained in nonane showed good coincidence after normalization (Figure 1b and Figure S1a), indicating that the pulling geometry does not significantly affect the single‐chain elastic response of PVDF.

To verify that the single‐chain elasticity of PVDF measured in nonane reflects its backbone‐determined inherent elasticity, polyethylene (PE) with the same C─C backbone structure was selected as a reference system. The theoretical elastic parameters of PE have been previously determined by quantum mechanical (QM) calculations (Table 1), and the relationship between applied force and extension of PE can be expressed as:

$$F={\mathrm{\Sigma }}_{\mathrm{i}=1}^n{\gamma }_i{\left(\frac{L\left[F\right]}{L_0}-1\right)}^i$$ (1)

where γ₁ is the linear elastic modulus, γ₂ and γ₃ are nonlinear correction terms, L ₀ is the contour length at zero force, and L[F] is the contour length under an applied force F.

TABLE 1.

Theoretical elastic coefficients of PE and three candidate backbones of PVDF after γ‐irradiation at 2000 kGy. The optimal l _b values used in the QM‐FRC model fitting are also shown.

Structure	γ1 [nN]	γ2 [nN]	γ3 [nN]	l b [nm]
PE	28.7	−42	16.9	0.154 ± 0.002
I	32.2	−43.2	7.2	—
II	34.5	121.1	−657.4	—
III	8.4	8.5	−26.2	0.60 ± 0.01

Based on earlier foundational work, the single‐chain mechanical behavior of polymers can be described by several theoretical models, among which the freely rotating chain (FRC) model has been demonstrated to be suitable for flexible chains [34, 44, 45, 46, 47]. By incorporating the QM‐derived elastic parameters of PE into the FRC model, a QM‐FRC model was constructed to describe the inherent elasticity of a C─C backbone (see Supporting Information for details). The QM‐FRC model does not rely on specific atom types but instead derives elastic parameters directly from the potential energy surface of the model. Therefore, it is equally applicable to main‐chain structures containing heteroatoms [48, 49]. By introducing theoretical elastic parameters corresponding to different backbone structures, this model can generate structure‐specific theoretical elasticity curves, providing a quantitative basis for identifying experimental F–E curves. The QM‐FRC model is given by:

$$\frac{R}{L_0}=\left(\frac{L\left[F\right]}{L_0}\right)\left[1-\frac{k_{B}T}{\left(2F{l}_{\mathrm{b}}\right)}\right]$$ (2)

where R/L ₀ is the normalized extension, T is the absolute temperature, l _b is the length of the rotating unit, and k _B is the Boltzmann constant.

The QM‐FRC theoretical curve of PE (see Supporting Information for details) overlaps well with the experimental F–E curve of PVDF after normalization (Figure 1c), demonstrating that the single‐chain elasticity of PVDF measured in nonane corresponds to its inherent elasticity [36, 50]. Because the QM‐FRC curve of PE is smoother and free of experimental noise compared with the measured curves, it was adopted as the reference curve for subsequent comparative analysis (denoted as 0 kGy).

After establishing the single‐chain inherent elasticity of PVDF, we next examined the effect of γ‐irradiation dose (100, 500, 1000, 1500, and 2000 kGy) on its single‐chain mechanical behavior (Table S1 and Figure S1b–f). The normalized representative F–E curves measured at each irradiation dose exhibit good overlap (Figure 2a–e), indicating that the single‐chain mechanics of PVDF at different doses are well defined.

FIGURE 2.

Representative normalized F–E curves of PVDF obtained in nonane after γ‐irradiation at (a) 100, (b) 500, (c) 1000, (d) 1500, and (e) 2000 kGy. (f) Comparison of representative normalized F–E curves of PVDF after γ‐irradiation at various doses and the QM‐FRC fitting curve of PE (0 kGy).

A single polymer chain can be regarded as an entropic spring. To quantitatively compare the trend of changes in mechanical elasticity under different irradiation doses, the normalized extension R/L ₀ of the F–E curves under the same external force was analyzed relative to the QM‐FRC reference curve (0 kGy). The results show that above 100 pN, all irradiated samples deviate from the inherent elasticity of PVDF, with the deviation increasing progressively with irradiation dose (Figure 2f). Notably, at 2000 kGy, PVDF exhibits a significantly more flexible chain behavior compared to the pristine C─C backbone‐determined elasticity, indicating that γ‐irradiation progressively reconstructs the polymer backbone and alters single‐chain flexibility.

To validate this hypothesis, Fourier transform infrared spectroscopy (FT‐IR) and X‐ray photoelectron spectroscopy (XPS) analyses were used to characterize irradiation‐induced chemical changes in PVDF. As shown in Figure 3a, the FT‐IR spectra display new absorption bands at 1275, 1633, and 1740 cm⁻¹, corresponding to C─O─C, C═C, and C═O stretching vibrations, respectively, suggesting irradiation‐induced oxidation and backbone bond cleavage in PVDF [5, 51, 52, 53, 54, 55, 56]. Additionally, a new broad band near 3300 cm⁻¹ is attributed to O─H stretching, likely arising from reactions between backbone radicals and oxygen‐ or water‐derived species under high‐energy irradiation [57]. These results suggest that high‐energy irradiation induces oxidation, double‐bond formation, and structural reconstruction of the PVDF [8, 9, 58].

FIGURE 3.

(a) FT‐IR spectra of PVDF after γ‐irradiation at various doses. (b) XPS survey spectra and (c) high‐resolution C 1s spectra of PVDF after γ‐irradiation at various doses.

XPS analysis further confirms the irradiation‐induced structural evolution of PVDF (Figure 3b). The appearance of the O 1s signal in the survey spectrum indicates the incorporation of oxygen, which likely leads to the formation of side‐chain groups such as C═O and ─OH, as well as C─O─C linkages along the backbone, consistent with the FT‐IR results. High‐resolution C 1s spectra (Figure 3c) show new peaks at 286.1 and 288.4 eV after irradiation, which are assigned to C─O─C bonds and C═O groups, respectively [5, 51, 59, 60]. Notably, within 0–100 kGy, the C─F binding energy shifts from 289.3 to 290.5 eV, mainly due to the electron‐withdrawing effect from newly formed oxygen‐containing groups [61, 62, 63]. At higher irradiation doses (> 100 kGy), the contents of C─O─C and C═O groups stabilize while the overall C─F content decreases, resulting in an almost constant C─F binding energy.

Based on the FT‐IR and XPS results, it can be inferred that γ‐irradiation generates radicals on the repeating units of PVDF, while trace oxygen or water in air accelerates irradiation‐induced degradation, leading to partial bond cleavage [64, 65, 66]. Specifically, the FT‐IR spectrum shows characteristic peaks of C─O─C stretching (1275 cm⁻¹) and C═C stretching (1633 cm⁻¹), while the C 1s XPS spectrum reveals corresponding signals of C─O─C (286.1 eV) and C═O (288.4 eV) groups. These results confirm that irradiation induces the formation of oxygen‐containing functionalities (e.g., C═O and ─OH) as well as new bonding motifs such as C─O─C and C═C. Such structural changes are likely associated with the reconstruction of polymer backbones, side chains, or interchain connections (Figure S2). In this study, we focus on the reconstruction of the PVDF backbone that governs its inherent elasticity, and therefore propose three plausible post‐irradiation backbone structures: ether‐containing (I), double‐bond‐containing (II), and alternating ether/double‐bond (III) structures (Figure 4).

FIGURE 4.

Schematic illustration of three plausible backbone structures of PVDF after γ‐irradiation at 2000 kGy in the presence of O₂/H₂O: (I) a C─O─C–containing structure, (II) a C═C–containing structure, and (III) an alternating C−O−C/C═C structure.

Because backbone structure and inherent elasticity exhibit a strict one‐to‐one correspondence, these three plausible structures are expected to display distinct single‐chain elastic behaviors. QM calculations were therefore performed on oligomers representing structures I–III (Figure S3), and their elastic parameters were obtained (Figure S4 and Table 1, see Supporting Information for details).

For candidate structure I, QM‐FRC fitting curves generated with l _b values of 0.1, 0.3, 0.5, 0.7, 0.9, and 1.0 nm show no agreement with the experimental F–E curve of PVDF irradiated at 2000 kGy (Figure S5a), indicating that structure I is not the dominant repeating unit at high γ‐irradiation dose. Similarly, for structure II, none of the theoretical curves obtained with different l _b values overlap with the experimental curve (Figure S5b), excluding structure II as the major backbone motif after irradiation.

In contrast, for structure III, the experimental curve of PVDF irradiated at 2000 kGy lies between the theoretical curves with l _b = 0.5 and 0.7 nm (Figure 5a), suggesting that the optimal l _b falls within this range.

FIGURE 5.

(a) Comparison of the QM‐FRC fitting curves (dotted lines) for structure III with different l _b values and the representative F–E curve of PVDF after γ‐irradiation at 2000 kGy (solid line). (b) Average force deviation value between the representative F–E curve and QM‐FRC fitting curves as a function of l _b. (c) Optimal QM‐FRC fitting curve for Structure III with l _b = 0.60 ± 0.014 nm (dotted line) overlaid with the representative F–E curves (solid line).

To determine the best‐fit value, the mean force deviation between QM‐FRC and experimental curves was calculated (see Supporting Information for details). As shown in Figure 5b, the minimum deviation occurs at l _b = 0.60 ± 0.014 nm, which is consistent with the repeating unit length of structure III (∼0.6 nm). Using this optimal parameter, four representative F–E curves are well described by the QM‐FRC model (Figure 5c and Figure S6). These findings demonstrate that long‐term high γ‐irradiation dose (2000 kGy) transforms the PVDF backbone from the original C─C sequence into a new structure featuring alternating C─O─C and C═C units.

3. Conclusion

In summary, this study demonstrates that increasing the irradiation dose from 0 to 2000 kGy induces a systematic evolution in the single‐chain mechanical response of PVDF. At stretching forces above 100 pN, the normalized extension at a given force increases markedly with irradiation dose, indicating a continuous enhancement in chain flexibility relative to the inherent elasticity of the pristine sample. FT‐IR and XPS analyses attribute this mechanical evolution to irradiation‐induced chemical reconstruction, whereby γ‐irradiation induces bond scission, oxidation, and reorganization of both the PVDF backbone and side groups, leading to the formation of oxygen‐containing functionalities and C═C units.

Based on spectroscopic analysis, three plausible post‐irradiation backbone structures were constructed, and their theoretical single‐chain elasticities were generated using the QM‐FRC model and compared with the experimental curve at 2000 kGy. Only the alternating C─O─C/C═C structure yields a theoretical curve (l _b  =  0.60 ± 0.014 nm) that quantitatively matches the experimental data. This l _b value is nearly identical to the theoretical length of one repeating unit of the alternating C─O─C/C═C structure (∼0.60 nm), providing direct molecular‐level evidence that long‐term high γ‐irradiation dose reconstructs the PVDF backbone from a C─C sequence into a hybrid structure with alternating C─O─C and C═C units. These findings establish a molecular basis for understanding irradiation‐induced performance degradation of the PVDF backbone and offer a theoretical framework for tuning its properties via controlled irradiation. It should be noted that this study is restricted to backbone reconstruction and does not consider side‐chain modifications and cross‐linking architectures. Future studies will address their roles to achieve a more complete picture of irradiation‐driven structure–property relationships.

4. Experimental Section

4.1. Materials

PVDF (M_w = 4.0 × 10⁵ g mol⁻¹) was purchased from Macklin. Ammonium persulfate (APS, ≥ 98%) was obtained from Aladdin. N‐Nonane (≥ 98%) and N, N‐dimethylformamide (DMF, ≥ 99.5%) were purchased from Adamas. Ethanol (≥ 99.7%, anhydrous) and hydrogen peroxide (H₂O₂, 30 wt.%) were supplied by Jinsan Chemical Reagent Co., Ltd. All reagents were used as received without further purification. Deionized water (resistivity ≥ 18 MΩ·cm) was used throughout the experiments.

4.2. γ‐Ray Irradiation Treatment

PVDF samples were irradiated with γ‐rays at Sichuan Jinhe Nuclear Irradiation Technology Co., Ltd., using a ⁶⁰Co source with an average dose rate of 0.75 kGy h⁻¹. To simulate the actual service environment, the irradiation was carried out under ambient atmospheric conditions. Five irradiation doses were applied: 100, 500, 1000, 1500, and 2000 kGy, corresponding to irradiation times of 134, 667, 1334, 2000, and 2667 h, respectively.

4.3. Sample Preparation and SMFS Measurements

Pristine PVDF and γ‐irradiated PVDF samples were individually dissolved in DMF to obtain solutions with a concentration of 0.1 g L⁻¹. Hydroxylated glass slides serve as substrates. Surface modification was performed by immersing the slides in a saturated APS aqueous solution mixed with 30% H₂O₂ (v/v = 4:3) and reacting at 90°C for 4 h to remove surface contaminants. Afterward, the slides were thoroughly rinsed with deionized water and dried under ambient conditions. Subsequently, 100 µL of each PVDF solution was deposited onto the hydroxylated glass surface and allowed to adsorb for 30 min. Unbound polymer chains were removed by sequential rinsing with deionized water and anhydrous ethanol. The substrates were then dried under ambient conditions before SMFS measurements.

SMFS experiments were performed using a Nanowizard II AFM (JPK instruments, Germany). Before each measurement, a drop of nonane was introduced between the V‐shaped Si₃N₄ AFM tips (Bruker, MLCT model) and the sample surface. The spring constants of the cantilevers (30–50 pN nm⁻¹) were calibrated using the thermos excitation method. Unless otherwise specified, the stretching velocity was set to 2.0 µm s⁻¹. All experiments were conducted at approximately 24°C. To ensure reproducibility, measurements were repeated under identical conditions using different cantilevers of the same model. The obtained force‐extension (F–E) curves were processed and analyzed using Igor Pro software (version 6.05).

4.4. FT‐IR Testing

FT‐IR spectra were recorded using a Thermo Nicolet iS50 spectrometer in the range of 4000–400 cm⁻¹ with a spectral resolution of 4 cm⁻¹. Samples were prepared by the KBr pellet method. Briefly, approximately 1 mg of sample was thoroughly mixed with 100 mg of dried KBr, ground in an agate mortar, and pressed into transparent pellets under vacuum for analysis.

4.5. XPS Measurements

XPS measurements were performed on a Thermo Scientific ESCALAB 250Xi spectrometer using monochromatic Al Kα radiation (hν = 1486.6 eV). The base pressure in the analysis chamber was maintained below 5 × 10⁻⁹ mbar. Elemental compositions were obtained from survey scans, and high‐resolution spectra of the C 1s region were collected for peak deconvolution. All binding energies were calibrated with respect to the adventitious carbon C 1s peak at 284.8 eV. Data analysis and peak fitting were carried out using CasaXPS software.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: marc70322‐sup‐0001‐SuppMat.pdf.

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.