1 Introduction

Polytetrafluoroethylene (PTFE) is a semi-crystalline polymer that has unique properties such as excellent thermal and chemical properties, highest resistivity of any material, very high dielectric strength, low mechanical strength, high specific gravity, low dielectric constant, low melt flow rate and high melt viscosity. It has resistant to almost all acidic and caustic materials, and offers useful properties over the wide temperature range. These properties make it an ideal material for encapsulation of electrical wires, electrical components and exposed to high temperatures and aggressive chemicals. Also, PTFE can be used in the nuclear and aerospace industries, pump valves, pipes, industrial processing technology and as a common engineering material for small high-performance parts [1,2,3]. PTFE fibres have the same features as that of PTFE and these fibres can be applied in the textile technology including fabricating heat insulating and protecting clothes [4].

When polymers are exposed to radiation, the quantum of energy above the covalent bond energy of the main carbon chain can be absorbed. As a result, the long molecular chains will break. Cross-linking or chain scissions in polymers can be induced by exposure to a radiation source, such as electron beam and gamma radiation. These changes in the properties of polymeric materials depend on the induced chain strength, chain re-orientation, and crystallinity. Gamma-irradiation of polymers can modify the geometry of the bond structure and vary the characteristics of the long chains [5]. The extent of modification depends on its structure, dose rate, dose range, temperature, etc.

The cross-linking of PTFE fiber can be occurred when it irradiated at room temperature in air or in vacuum. This results in the dramatic drop of mechanical properties and molecular weight. PTFE is very sensitive to ionizing irradiation because its mechanical properties are only maintained at a high molecular weight of more than few millions [6]. Oshima et al. studied the cross-linking of PTFE when it was irradiated using gamma rays at different temperatures [7]. It is found that the radiation resistance and the mechanical properties have been improved at room temperature. Also, the degradation of irradiated PTFE at room temperature due to the radicals formed has a restriction on the mobility and recombination processes. Oshima et al. found that the crystallinity of PTFE products decreases after irradiation and becomes more transparent [8]. The effects of gamma irradiation on the optical and chemical properties of PTFE sheet were studied with gamma doses up to 12 kGy [9]. Gamma irradiation changes the optical properties, reduces optical dispersion parameters, induces cross-linking and forms free radical PTFE sheet. Ol’khov et al. investigated the effect of gamma irradiation on the molecular-topological structure of PTFE [10]. They revealed that PTFE transformed into amorphous phase, while the molecular mass of interjunction chains in the amorphous block and the low-melting crystalline modification were reduced.

Within the above-mentioned literatures, different techniques such as X-ray diffraction (XRD), differential scanning calorimetry (DSC), and Fourier transform infrared (FTIR) have been applied to study the physical and structural properties of irradiated PTFE materials [7,8,9,10]. These techniques need more time for adjusting the set-up, preparing investigated samples and for evaluating the physical properties.

Interferometry and digital holography (DH) are considered as an effective and sensitive optical technique that can be applied for achieving quantitative phase microscopy [11,12,13]. These techniques are fast and precise tool for determining the optical and structural properties of polymer and optical fibres [14, 15]. The evaluated optical parameters such as refractive indices, refractive index profile and birefringence were used to investigate the microstructure and molecular arrangement inside the polymeric fibres [12, 16]. Digital holographic microscopy (DHM) was recommended for achieving opto-mechanical and opto-thermal properties of fibres [15, 17]. The DHM method depends on recording the hologram intensity and reconstructing the intensity and the phase of the wave field. The phase information is proportional to the optical path difference (OPD) within the test object. Capturing the whole wave field, amplitude and phase, enables digital focusing emulating the manual focusing control of conventional microscopes [18, 19]. Recently, Yassien and El-Bakary applied DHM method for studying the effects of gamma irradiation doses on the physical properties of basalt fibres [20]. It was found that the basalt material has high resistance to gamma radiation. In consequence, no significant effects on the physical properties were indicated.

In this work, for the first time, the effect of gamma irradiation doses on the optical and structural properties of polytetrafluoroethylene (PTFE) fibres was determined using a modified method that depends on DHM. The PTFE samples were subjected to gamma radiation doses from 3 to 40 kGy. The method was applied to extract the phase from single shot captured holograms of the irradiated fibres. The obtained phase gives quantitative information about the physical thickness and index of refraction of the fibres which are functions of physical density and crystallinity. The refractive indices, birefringence, orientation function, 3D refractive index profile and crystallinity are determined for the irradiated PTFE fibres.

2 Theoretical considerations

2.1 Digital holographic microscopy (DHM)

DHM is a technique, analogy to standard interferometry, which is based on the coherent superposition of light transmitted and/or diffracted from a test object with a known, e.g., plane wave, reference wave generating an interference pattern. Within the resulting interference pattern, the phase of the light field which is transmitted or diffracted from a test object is encoded. Hence, the lateral phase distribution can be recovered from the intensity of the resulting interference pattern which can be directly recorded using a camera sensor such as a charge-coupled device (CCD). The phase distributions comprise the optical path difference (OPD) of light passed through or diffracted from the test object. Thus, many properties of the test object such as the 3-D form, the refractive index and birefringence among others, can be measured. The OPD is measured with high precision which is reached, in the case of investigating smooth light fields, few nanometers. In many cases where the spatial carrier frequency method is used to recover the phase information, only one camera image is needed for recovering the phase distribution [21]. This makes the method very fast compared to other methods such as X-ray diffraction (XRD), differential scanning calorimetry (DSC).

In the following, the formalization of hologram recording and the phase recovery process will be briefly introduced. A simplified scheme for illustrating the mechanism of producing the interference between the object wave and the reference wave is shown in Fig. 1.

Fig. 1
figure 1

A simplified scheme for illustrating the interference between the light diffracted from a test object, object wave, and a plane reference wave. λ is the wavelength of light, θ is the angle between the object and the reference waves, d is the distance between the object and recording planes and CCD refers to as a camera sensor which is used to capture the interference pattern or the hologram

Since test object is not located across the recording plane, the generated interference pattern is called a hologram. It is noted that the scheme shown in Fig. 1 is called off-axis holography scheme. To generate a hologram, a coherent light with a wavelength λ is divided into two parts using a beam splitter or a 1 × 2 fiber splitter. One part is used to illuminate the object. The light diffracted from the object is referred to as object wave (O). The object wave is directed to the recording plane using, e.g., relays optics. Across the recoding plane, the object wave can be given in the form:

$$O\left( {x,y} \right) = \left| {O\left( {x,y} \right)} \right|\exp \left[ { - i\varphi \left( {x,y} \right)} \right],$$
(1)

where x and y represent positions across the recording plane and |O(x,y)| is the object wave amplitude and φ is the phase of the object wave. The second part is the reference wave (R) and commonly, a tilted plane wave is generated which can be written at the recoding plane in the form:

$$R\left( {x,y} \right) = \left| {R\left( {x,y} \right)} \right|\exp \left[ {i2\pi \left( {\sigma x + \beta y} \right)} \right],$$
(2)

Here, |R(x,y)| is the amplitude of the reference wave and α and β are the spatial carrier frequencies given by:

$$\alpha = \sin \theta_{x} /\lambda {\text{ and }}\beta = \sin \theta_{y} /\lambda .$$
(3)

In Eq. (3), θx and θy are tilt angles between the object and the reference waves in x and y directions. The intensity of the resulting interference pattern across the hologram, i.e., the recoding, plane can be written as:

$$I = \left| {R + O} \right|^{2} = \left| R \right|^{2} + \left| O \right|^{2} + 2\left| R \right|\left| O \right|\cos \left[ {\varphi + 2\pi \left( {\alpha x + \beta y} \right)} \right].$$
(4)

The explicit dependence on positions across spatial or frequencies domains will be omitted in the following for reasons of simplicity. To recover the object phase information φ, the spatial carrier frequency approach is used. Within this method, the intensity captured by the camera sensor and represented by Eq. (4) is Fourier transformed using the fast Fourier transform. Accordingly, Eq. (4) can be written in the frequency domain as:

$$\widehat{I} = A + \widehat{O}\left( {\alpha - \xi ,\beta - v} \right) + \widehat{O}^{*} \left( {\alpha - \xi ,\beta - v} \right).$$
(5)

Here, A is the Fourier transformation of the non-coherent term which is represented by the sum of the intensities of the object and the reference waves. This term is referred to as the DC-term or 0-order. The second and the third terms of Eq. (5) represent the object wave field and its conjugation (+ 1 and − 1 orders), where both of them are displaced by the carrier frequencies α and β into different positions across the Fourier domain. Thus, the total separation of the DC-term, object and its conjugation depends on the tilt angle θ. Thus, the minimum carrier frequencies which can be applied to separate the three terms are correlated with the highest frequency ξmax and \(v_{\rm{max} }\)of the object wave in the frequency domain and can be given by:

$$\alpha \ge 3\xi_{\rm{max} } {\text{ and }}\beta \ge 3v_{\rm{max} } .$$
(6)

Across the Fourier domain, the object wave field frequencies (+ 1 order) are selected using a mask and the two other terms are filtered out. Then, the selected frequencies are shifted to the center of the spectrum compensating the displacement caused by the carrier frequency. Hereafter, an inverse fast Fourier transform is applied. Thus, a filtered version of the object wave field (\(\dot{O}\)) is obtained:

$$\dot{O}\left( {x,y} \right) = \left| {\dot{O}\left( {x,y} \right)} \right|\exp \left[ { - i\dot{\varphi }\left( {x,y} \right)} \right],$$
(7)

from the recovered phase information, the OPD is determined and thus parameters such as the refractive index and the birefringence are calculated.

2.2 Refractive index and birefringence

Using the extracted phase, the index of refraction (n||  and n) for light polarized parallel and perpendicular to the fibre axis can be evaluated with the aid of the following equation which presented by Barakat and Hamza [11]:

$$n^{i} = n_{L} \pm \frac{{\varphi_{0}^{i} }}{D}\frac{\lambda }{2\pi }.$$
(8)

Symbol \(i\) denotes the state of light polarization (parallel || or perpendicular ⊥ to the fiber axis), nL is the refractive index of the used immersion liquid, \(\lambda\) is the wavelength of the monochromatic light used and D is the fibre thickness.

Using the obtained values of the refractive indices (n||  and n), the mean birefringence, B = n|| n, can be evaluated directly.

2.3 Polarizability per unit volume

The polarizability per unit volume for light polarizing parallel P||  and perpendicular P to the fiber axis can be directly evaluated using the calculated values of the refractive indices n||  and n and by applying the Lorentz–Lorenz equation [22]:

$$\frac{{n^{2} - 1}}{{n^{2} + 2}} = \frac{4\pi }{3}P.$$
(9)

2.4 Refractive index profile

The refractive index variations in a transparent material result in a change in the optical path length and the phase difference between two light waves passing through the medium before and after the change. Consequently, the refractive index profile reflects the changes of index of refraction across the fibre diameter. These profiles can be calculated using the following equation [14]:

$$\begin{aligned} \frac{{\lambda \varphi_{Q} }}{2\pi } = \sum\limits_{j = 1}^{Q - 1} \begin{aligned} 2n_{j} \bigg[\sqrt {[R - (j - 1)t]^{2} - (d_{Q} n_{L} /n_{j} )^{2} } - \sqrt {(R - jt)^{2} - (d_{Q} n_{L} /n_{j} )^{2} } \bigg]^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} \hfill \\ \hfill \\ \end{aligned} \hfill \\ + 2n_{Q} \sqrt {[R - (Q - 1)t]^{2} - (d_{Q} n_{L} /n_{Q} )^{2} } - n_{L} \sqrt {R^{2} - d_{Q}^{2} } + \sqrt {R^{2} - X_{Q}^{2} } , \hfill \\ \end{aligned}$$
(10)

where R is the fibre radius, nj is the refractive index of the fibre layer j, t is thickness of the layer (t = R/Q), Q is the number of layers, dQ is the distance between the incident beam and the fibre center and XQ is the distance between the emerging beam and the fibre center.

2.5 Orientation function

The orientation is a phenomenon unique to polymers that provides valuable information about the relationships between various properties such as mechanical, dielectric and molecular orientation. This phenomenon of the polymer shows the extent to which the chains are aligned in any particular direction. The molecular orientation of polymers can be frequently characterized by Hermans’s orientation function (ƒ) which relates with the optical birefringence B using the following equation [23]:

$$f = \frac{B}{{B_{\rm{max}} }}.$$
(11)

Here, Bmax is the maximum (intrinsic) birefringence of polymer fibres and its value for a PTFE fibre was evaluated and it equals 0.045 [24].

2.6 Density of fibres

The density of the polymer fibre is an important factor for determining its mechanical properties and the potential for lightweight construction [25]. Also, the density study provides quantitative information for the quality control in the fibre production and determines the presented defects or the completed production processes [26]. The density (ρ) of the PTFE fibre can be evaluated using the density gradient column or interferometrically with the aid of the following equation [27, 28]:

$$\rho = \frac{{\left( {n^{2} - 1} \right)}}{{k\left( {n^{2} + 1} \right)}},$$
(12)

where n is the average refractive index of the fibre (n = (n||  + 2n)/3). K is a constant referred to as the specific refractivity and equals 0.119 cm3/g for PTFE materials [28].

2.7 Degree of crystallinity

Crystallinity measurement of semicrystalline polymers is an important structural parameter which affects various physical properties such as refractive indices, density (ρ), mechanical, chemical, and thermal properties of a fibre [29]. The density of the polymers related to the percent or degree of crystallinity χ by the following equation [30]:

$$\chi = \left( {\frac{{\rho - \rho_{a} }}{{\rho_{c} - \rho_{a} }}} \right) \times 100.$$
(13)

Here, ρa and ρc are the density of the pure amorphous and pure crystalline phases, respectively. The values of these densities are (2.04 ± 0.03) and (2.30 ± 0.01) g/cm3 for PTFE polymer, respectively [31].

3 Experimental techniques

3.1 Digital holographic microscopy set-up

Figure 2 shows the configuration of the DHM-based Michelson interferometer used to realize the measurements. In contrast to Mach–Zehnder-based techniques, the proposed DHM is robust since the separated optical paths of both the reference and the object waves are minimal. The spatial carrier is adjusted by tilting one of the mirrors by the angle β.

Fig. 2
figure 2

Michelson interferometer-based digital holographic microscopy: f is the front focal plane of a microscope objective MO and behind or at the focal plane a piece of the tested fibre is located. BS refers to a beam splitter, M refers to mirrors, β is the angle of a tilted mirror and CCD denotes the recording camera

As shown in Fig. 2, a pigtailed laser diode with a central wavelength of 637 nm emits a spherical wave from the fibre tip which is used to illuminate the test object. The test wave front passes through a 5X Plan APO infinity corrected microscope objective with a long working distance of 37.5 mm and a numerical aperture of 0.14. The magnified test wave front is then divided by a beam-splitter BS into two waves, which are back reflected from the two mirrors M towards a camera sensor (AVT Pike). The sensor has a resolution of 2452 × 2048 pixels, where the pixel pitch is 3.45 µm. A tilt angle of β = 1.65° is selected to separate the two copies of the test wave front showing the interference of one copy with a reference background. The PTEF samples are immersed in an immersion liquid with a refractive index of nL = 1.438 measured at room temperature (25°). According to the direction of the fringe shift within the fibre, the ± sign is selected to be − in Eq. (8).

3.2 Material and irradiation

PTFE fibres are man-made fibres identified as Teflon fibres in which the fibre substance is polytetrafluoroethylene. PTFE fibres can be stitched, woven, and spun into any form. PTFE fibres can be produced by different methods such as: extruding a mixture of viscose and an aqueous dispersion containing PTFE components into a setting medium through a shaped nozzle and subsequently sintered to get dark brown fibres. Another one by drawing monofilament of PTFE material formed by paste extrusion at a temperature higher than the crystal melting point of PTFE [4]. In this study, the PTFE fibres were manufactured and produced using the fibre extrusion technology (FET) machine in the Department of Textiles Industries at Leeds University [24]. This machine has pilot plant spinning unit’s extruder which consists of three heating zones, and the temperature of each zone was 235 °C, 245 °C, and 245 °C, respectively. The temperature of the metering pump is 245 °C and the die head was kept at the same temperature. The spinneret consisted of 20 holes; each hole has diameter 0.8 mm and length 3.2 mm. The used PTFE fibres have circular cross-sectional shapes and have the diameters of 80 μm. Comment physical, thermal and mechanical properties of PTEF fibres are summarized in Table 1.

Table 1 General physical, thermal and mechanical properties of PTEF [28]

PTFE samples were irradiated by gamma rays using a cobalt source (Co-60) source of Russian irradiator (model ISSLEDOVATEL). The temperature in the cavity during irradiation was about 40 °C. The samples were irradiated with the following doses: 3 kGy, 10 kGy, 25 kGy and 40 kGy, in air and at room temperature (30 °C). The radiation dose rate was 10 kGy/100 min.

4 Results and discussions

Figure 3 shows examples of such interference patterns for un-irradiated (pristine) PTFE samples and PTFE irradiated with dose of 40 kGy, respectively. From the recorded holograms, it can be observed that the fringe shift within the fibre is changed. This means that the irradiation affects the optical and structure properties of the fibre. Consequently, the fibre properties can be modified and/or improved. This modification will be in the following quantitatively evaluated and discussed.

Fig. 3
figure 3

The intensity of two captured digital holograms recorded for pristine (a) and irradiated PTFE sample with a dose of 40 kGy (b). Dynamic range of the two images is adapted to vary between 0 and 1. Both images are recorded for light polarizing parallel to the fibre axis

Starting from the carrier frequency captured intensity holograms of the test samples, the adaptive spatial carrier frequency method is applied to recover the phase information [21, 32, 33].

To achieve this, the following steps summarized in Fig. 4 are implemented:

Fig. 4
figure 4

Example of the filtering process for recovering the phase information: a recorded digital hologram for irradiated PTFE sample with a dose of 40 kGy. Applying a FFT gives the spectrum b which shows the + 1 (to be selected), − 1 and the 0 diffraction orders. After filtering out the − 1 and 0 orders and shifting the + 1 order to the center of the spectrum, an inverse FFT is applied to obtain the complex amplitude across the object plane. From that complex amplitude the phase is extracted and shown in (c). This wrapped phase is then unwrapped using Goldstein unwrapping approach and the resulting unwrapped phase is shown in (d). The scale bar shown in a, c and d has a size of 75 μm

  1. 1.

    The fast Fourier transform is applied on the recorded intensity hologram.

  2. 2.

    Across the frequency domain, the spectrum which contains the three diffraction orders as described by Eq. (5) is masked to select only the + 1 diffraction order. All other frequencies are then removed.

  3. 3.

    The selected + 1 diffraction is shifted to the center of the spectrum. This is achieved by numerically determining the center of the + 1 order. This center represents as a Dirac delta function, i.e., the impulse function. By convolving the + 1 order with the negative of the Dirac delta function using the fast Fourier transform, the + 1 order is translated to the center of the spectrum.

  4. 4.

    Now, an inverse fast Fourier transform is applied to recover the phase distribution φ’ at the hologram plane by taking the argument of the resulting complex amplitude. Thus, the phase information across the object plane is recovered. The results are shown in Fig. 4 for one sample as an example.

Steps 2–4 are repeated for all captured holograms to recover the associated phase information.

These phase information represent a wrapped phase information having values within the interval [− π, π]. The distribution has to be unwrapped to obtain a continuous phase distribution. This is done using Goldstein phase unwrapping technique and the result is shown in Fig. 4d. Substituting the reconstructed unwrapped phase information into Eq. (10), the 3D refractive index profiles along the fibre samples are obtained for light polarizing parallel (n|| ) to the fibre axis for pristine and irradiated PTFE fibre with a dose of 40 kGy. The results are shown in Fig. 5. According to our previous study, the DHM phase measurements lead to measure the refractive index with accuracy up to 4 × 10−4 [15].

Fig. 5
figure 5

3D refractive index profiles measured for light polarized parallel to the fibre axis for pristine (a) and PTFE irradiated with a dose of 40 kGy (b)

These profiles show the variation of the refractive index in 3D by gamma irradiation. To clarify this effect, the mean refractive index across the center of the investigated samples was used in the following discussing.

Using the results of the unwrapping phase for pristine and irradiated PTFE fibres with doses 3 kGy, 10 kGy, 25 kGy and 40 kGy, the refractive indices for light polarizing parallel and perpendicular were calculated with the aid of Eq. (8). Figure 6 shows the relationship between the refractive indices and gamma irradiation doses. This figure indicates that the refractive indices in parallel (n|| ) and perpendicular (n) directions increase with increasing gamma doses. However, at a high dose of 40 kGy, the mean refractive indices decreased. The increase of the values of refractive indices reflects the loss of PTFE transmission with the formation of cross-linking by gamma irradiation [8]. This behavior may be due to that the crystallite size increases with the increasing of gamma doses, so the light scattering by large crystals disturbs the light transmission. While, the decreasing in refractive indices at 40 kGy dose results in the improvement of the transmittance of PTFE material with the increasing cross-linking density. This is because the crystallite size becomes small at high gamma doses and therefore, the light scattering decreases [8].

Fig. 6
figure 6

The relationship between the refractive indices (n||  and n) and gamma irradiation doses

Using the evaluated values of refractive indices (n||  and n) and Eq. (9), the polarizabilities per unit volume P||  and P for the pristine and the irradiated PTFE fibres at different irradiation doses were determined and are shown in Fig. 7. It is clear from this figure that the behavior of the variations of P||  and P with gamma doses is similar to that obtained for n||  and n. Other physical parameters such as birefringence B, orientation function f and density ρ were evaluated using Eqs. 11, 12 and 13, respectively, and the results are given in Table 2. The table indicates that the values of B, f and ρ have been changed by gamma irradiation. The changing of these physical properties upon irradiation is due to the variations of the molecular weight which results from the chain scission and the cross-linking [7,8,9]. Also, density increases with gamma irradiation up to a dose of 25 kGy and decreases at a dose of 40 kGy. This behavior reflects the variations of refractive indices with gamma doses and the cross-linking induced in irradiated PTFE materials. Briskman and Tlebaev explained the increasing of the polymer density upon irradiation due to its conductivity related with phonon transfer, and the density of the crystalline phase is higher than that of the amorphous phase [34]. Also the decreasing of density at high doses results from the decreasing of crystallinity and the generation of macrostructural defects. The evaluated values of the density and refractive indices of PTFE fibres are found to be in agreement with those obtained by other authors [24, 28, 35].

Fig. 7
figure 7

The relationship between the polarizabilities (P||  and P) and gamma irradiation doses

Table 2 Results of birefringence B, orientation function ƒ and density ρ for pristine and irradiated PTFE fibres using DHI method

The obtained density of PTFE was used to determine the degree of crystallinity with the aid of Eq. (13). Figure 8 illustrates the relationship between crystallinity and irradiation doses of PTFE fibres. This figure indicates that the crystallinity improves by irradiation up to 25 kGy and decreases at a dose of 40 kGy. This behavior of the crystallinity of the PTFE fibres with gamma irradiation was found and explained previously by other authors [8, 36]. The increased of the crystallinity degree of PTFE with irradiation is due to the increasing of the cross-linking and PTFE mobility at certain irradiation doses which leads to form additionally small crystallites. It is noted that the loss of crystallinity at a high dose of 40 kGy is due to the chain cession, the generation of free radicals and the formation of the macrostructural defects. These effects result in the disordering of the crystallite chains which indicates an increase in the amorphous structure of PTFE by irradiation.

Fig. 8
figure 8

The relationship between crystallinity and irradiation doses of PTFE fibres

5 Conclusions

A modified method that depends on digital holographic microscopy was used to study the effect of gamma irradiation doses on some optical and structural properties of PTFE fibres. The phase information was extracted from a single shot captured hologram of irradiated fibre samples. The refractive indices, birefringence, orientation function, 3D refractive index profile and crystallinity were determined for the irradiated samples. The obtained results showed the improvement of the optical parameters and crystallinity by gamma irradiation with dose up to 25 kGy. This behavior reflects the cross-linking of PTFE structure by irradiation. Measured optical parameters and crystallinity were found to decrease at a dose of 40 kGy. This reflects the amorphization of the PTFE material at the high radiation dose. DHM method gives fast and precise quantitative results for investigating physical as well as optical properties of irradiated PTFE fibres compared to XRD and DSC analysis.