On the Mutual Relationships between Molecular Probe Mobility and Free Volume and Polymer Dynamics in Organic Glass Formers: cis-1,4-poly(isoprene)

We report on the reorientation dynamics of small spin probe 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) in cis-1,4-poly(isoprene) (cis-1,4-PIP10k) from electron spin resonance (ESR) and the free volume of cis-1,4-PIP10k from positron annihilation lifetime spectroscopy (PALS) in relation to the high-frequency relaxations of cis-1,4-PIP10k using light scattering (LS) as well as to the slow and fast processes from broadband dielectric spectroscopy (BDS) and neutron scattering (NS). The hyperfine coupling constant, 2Azz′(T), and the correlation times, τc(T), of cis-1,4-PIP10k/TEMPO system as a function of temperature exhibit several regions of the distinct spin probe TEMPO dynamics over a wide temperature range from 100 K up to 350 K. The characteristic ESR temperatures of changes in the spin probe dynamics in cis-1,4-PIP10k/TEMPO system are closely related to the characteristic PALS ones reflecting changes in the free volume expansion from PALS measurement. Finally, the time scales of the slow and fast dynamics of TEMPO in cis-1,4-PIP10k are compared with all of the six known slow and fast relaxation modes from BDS, LS and NS techniques with the aim to discuss the controlling factors of the spin probe reorientation mobility in polymer, oligomer and small molecular organic glass-formers.


Introduction
The structural and dynamic origin of the vitrification i.e., a transition of a glass-forming material from its normal liquid state through the supercooled liquid one into the glassy one is a long-term investigated phenomenon [1][2][3][4]. The structure and dynamics of material can be study via traditional-direct methods such as X-ray and neutron diffraction [5,6], neutron and light scattering [7][8][9][10], nuclear magnetic resonance (NMR) [11] and broadband dielectric spectroscopy (BDS) [12,13].
The main findings in the dynamic behavior of glass-forming organics studied by BDS, including oligo-and polymers, are the deviations of a structural relaxation from the ideal exponential behavior in the time dependence of the relaxation response, the so-called non-Debye behavior, as well as in the temperature dependence of the characteristic time scale of the structural α relaxation, τ α , the so-called non-Arrhenius behavior [1][2][3][4].
The dynamic changes in dipole reorientation given by the cross-over bends in the temperature and time dependences are marked by the characteristic dynamic temperatures T DYN , such as the Arrhenius temperature, T A , in viscosity or BDS data [14,15] and the Stickel temperature, T B ST [16], the Schönhals temperature, T B SCH [17], as well as the Alegría-Colmenero-Ngai temperature, T B ACN = T B βKWW [18][19][20], from BDS measurements. In addition, both slowdown of the structural dynamics accompanied by a broadening of the distribution of relaxation times reflex a development of the dynamic heterogeneity of the glass-formers [1][2][3][4]. These aspects are responsible for the afore-mentioned deviations of the large-scale structural relaxation and the small-scale local secondary relaxations [21]. In addition to the mentioned phenomenological features, there exists only a few theoretical works with inclusion of dynamic heterogeneity, such as recently published the generalized Adam-Gibbs model [22].
The structural-dynamic evolution of glass-form can be also investigated through the extrinsic probes, i.e., an atomic ortho-positronium probe (o-Ps) by positron annihilation lifetime spectroscopy (PALS) [23,24] and stable molecular nitroxide radicals via electron paramagnetic resonance (ESR) [25][26][27]. These external probes are highly sensitive to the local structural-dynamic changes over a broad temperature range. The PALS technique detects the annihilation behavior of o-Ps probe through the o-Ps lifetime, τ 3 (T), reflecting the local free volume changes in a given glass-former over a wide temperature range. In ESR, the rotational dynamics of spin probes, such as 2,2,6,6-tetramethyl-piperidinyl-1oxy (TEMPO), within a diamagnetic glass-former is observed in the ESR spectra. They can be evaluated via two dynamic parameters, the spectral parameter of the probe mobility, 2A zz (T), and the correlation times, τ c (T). In both extrinsic probe techniques, the corresponding PALS and ESR temperature dependences of various glass formers are highly non-monotonic. They exhibit several regions of the different thermal behavior of both probes and their change as are marked by the characteristic PALS temperatures T bi PALS of various bend effects [28] and the characteristic ESR ones of distinct crossover effects: T 50G and T Xi ESR [29,30]. Their mutual coincidences indicate that the changes in the τ 3 and 2A zz quantities with temperatures are controlled or, at least, influenced by the same physical process [31,32].
Moreover, the comparison between the characteristic PALS temperatures with aforementioned dynamic characteristic temperatures, T DYN , and the dynamic time scales, the two bend effects in the PALS response above the glass-to-liquid transition at T b2 L and T b1 L are related to the structural α-relaxation or sometimes, to the secondary βprocess [31][32][33][34][35][36]. On the other hand, concerning the characteristic ESR temperatures, their mutual relationships with dynamic ones appears to be more complicated. However, for some glass formers, the characteristic electron spin resonance (ESR) and dynamic (DYN) temperatures in temperature dependences mutually coincide [31,32] The full interpretation of the spin probe dynamics in a given medium requires to reveal the origin of temperature coincidence(s), i.e., the mutual relationship between relaxation dynamics of the pure substance and the spin probe reorientation (the dynamic response of the spin probe system substance/spin probe) [37,38].
Recently, a combined ESR, PALS and BDS work on oligomer cis-1,4-poly(isoprene) (cis-1,4-PIP0.8k) consisting of twelve monomer units per chain was reported [39]. Here, in the low-T and high-T regions, the unimodal broad or narrow line shape of ESR spectra reflect the slow or fast motion regime of spin probe TEMPO, respectively. In the intermediate-T region, the bimodal EPR spectra imply the dynamic heterogeneity of the spin probe TEMPO. In the comparison of ESR and PALS responses, several coincidences between the acceleration of the spin probe dynamics at T xi and the free volume expansion at T bi were revealed. Finally, some of these changes were tentatively ascribed to certain features of the structural α relaxation [25][26][27]. In spite of the numerous temperature coincidences, the time scales of spin probe reorientation and relaxation dynamics of given matrix are not in agreement. Even at high temperatures, the reorientation time scale of molecular probe is shorter than that of the segmental α process.
On the other hand, for a few small molecular glass formers, such as n-propanol [38] or glycerol [37], the full coupling between the time scales of the spin probe reorientation in the fast motion regime and the reorientation of medium constituents was found. One possible explanation for a decoupling of time scales found in cis-1,4-PIP0.8k may be that some other faster motional process(es) controlling the spin probe reorientation could be detected by an appropriate high-frequency dynamic technique.
Very recently, a preliminary joint ESR and PALS study of polymer cis-1,4-PIP10k revealed the dynamic heterogeneity of the spin probe TEMPO, i.e., slow and fast component in the supercooled state of polymer as well as mutual coincidences between ESR and PALS temperatures [40].
The aim of this investigation is (i) to carry out a detailed joint study of the polymeric cis-1,4-poly(isoprene) (cis-1,4-PIP10k) sample with the higher molecular weight, above the entanglement situation, by PALS, ESR and suitable high-frequency dynamic techniques, namely, broadband dielectric spectroscopy (BDS) and especially, light scattering (LS) (ii) to compare the ESR and PALS findings of oligomeric and polymeric cis-1,4-poly(isoprene) (cis-1,4-PIP0.8k vs. cis-1,4-PIP10k) and finally, (iii) to discuss a role of the free volume from PALS and the fast motional modes obtained from LS and BDS data and to clarify the controlling factors of spin probe reorientation by combining the ESR data with other high-frequency dynamic results from BDS and detailed LS measurements.

Electron Spin Resonance (ESR)
ESR measurement of cis-1,4-PIP10k/TEMPO solution was carried out on the X-band Bruker-ER 200 SRL (Stuttgart, Germany) at constant frequency 9.4 GHz, with a manual control of the heater and the gas flow (Bruker BVT 100). ESR spectra of cis-1,4-PIP10k/TEMPO system were recorded during heating over a wide temperature range from 100 K to 350 K. The temperature stability was ±0.5 K. The sample at each temperature was kept for 15-20 min before starting to accumulate two ESR spectra. The ESR lineshape analysis was in terms of the spectral parameter of 2A zz (T) [25][26][27] and the correlation times in the slow and fast motion regimes, τ c slow (T),τ c fast (T) and the corresponding fractions of the spin probes in the respective motion regime F slow (T), F fast (T) [41].

Positron Annihilation Lifetime Spectroscopy (PALS)
PALS lifetime spectra were obtained by the conventional fast-fast coincidence spectrometer using plastic scintillators coupled to Philips XP 2020 photo-multipliers, Photonis S.A.S., Brive, France. The time resolution of spectrometer was about 320 ps. The cis-1,4-PIP10k sample was measured under vacuum over a wide temperature range from 100 K to 350 K by helium closed-cycle refrigerator Janis CCS-450, Lake Shore Comp., Woburn, MA, USA. The temperature stability was around 1 K. The measuring time per one spectrum at each temperature was at least 2 h. The LifeTime (LT) program (version LT polymers) [42] was applied for the analysis of lifetime spectra into three components. Here, the relative contribution of para-positronium (p-Ps) and ortho-positronium (o-Ps) annihilation to lifetime spectra was 1:3. A short lifetime component from para-positronium annihilation (p-Ps) was fixed at τ 1 = 0.125 ns, an intermediate one τ 2 was attributed to the annihilation of free positrons e + in bulk, small free volumes and defects. Finally, a long component τ 3 originates from the ortho-positronium (o-Ps) annihilation. The o-Ps probe annihilates in organic materials via a pick-off process in which e + from the o-Ps annihilates with the e − of cavity surface, while the o-Ps lifetime is shortened, depending on the size and shape of cavity [43][44][45][46][47][48][49].

Light Scattering
Depolarized light scattering spectra of the pure cis-1,4-PIP10k sample were measured in a back-scattering geometry using the tandem Fabry-Perot interferometer (Sandercock model, Ottawa, ON, Canada) at frequencies below~300 GHz and the Raman spectrometer (Trivista 777, Teledyne Princeton Instruments, Trenton, NJ, USA) at frequencies above~100 GHz.
The experiment with Raman spectrometer was performed in a right-angle scattering geometry by using a solid-state laser with a wavelength of 532 nm (Millennia, Spectra Physics, Santa Clara, CA, USA). An additional monochromator was used to suppress the spurious secondary laser lines in the excitation beam [53]. The spectral resolution of the spectrometer was about 30 GHz. Wavelength calibration of the spectrometer was done by comparing of the measured spectrum of a neon discharge lamp and tabular data. The cis-1,4-PIP10k sample was sealed in a cylindrical glass cuvette. For relatively low-temperature measurements (200-320 K), the sample was attached to a cold finger of an optical closedcycle helium cryostat (Advanced Research Systems, Inc., Macungie, PA, USA) through an indium gasket. In the case of high-temperature measurements (330-380 K), the sample was placed in a home-built oven.
The experiment with tandem Fabry-Perot interferometer (TFPI) was carried out in a back scattering geometry by using a solid-state laser operating at the wavelength of 532 nm (Excelsior, Spectra Physics, Santa Clara, CA, USA). For performed measurements at different temperatures, a hermetically sealed flat cuvette with cis-1,4-PIP10k was placed inside of a liquid nitrogen cryostat (Linkam, Scientific Instruments, Tadworth, UK). In order to cover a wide frequency range, the spectra at four free spectral ranges 5 GHz, 15 GHz, 75 GHz, 300 GHz were measured. The narrow interference filter was used to suppress higher transmission orders of the interferometer [54,55]. For an accurate evaluation of the spectral shape, all spectra were corrected on the transmission function of the interferometer as described in Ref. [56]. In the end, the spectra measured with TFPI were combined with those obtained by Raman spectrometer.
In LS technique, light scattering susceptibility spectra χ"(ν) of cis-1,4-PIP10k were collected at selected temperatures from the T range: 200-380 K. Based on the dynamic susceptibility, the light scattering data are able to directly compare to dielectric loss (ε") obtained from broadband dielectric spectroscopy (BDS). The spectra consist of the tail of the segmental relaxation and the fast dynamics which appears above 30 GHz. Light scattering data extend the segmental relaxation outside of the frequency window accessible to the broadband dielectric spectroscopy (BDS) [50]. Figure 1 shows the spectral evolution of the spin system cis-1,4-PIP10k/TEMPO over a broad temperature range from 100 K to 350 K. The ESR spectra reflect the changes in reorientation dynamics of TEMPO probe from the broad anisotropic spectra of slow spin probe motion at low temperatures through the bimodal spectra to the narrow triplet spectra of fast spin probe reorientation in the high T region. The quite wide region of the bimodal spectra occurred in the temperature range from ca. 155 K up to ca. 245 K, where the slowand fast-moving spin probes are superposed.

ESR Data
1 Figure 1. Spectral evolution of the spin system of cis-1,4-poly(isoprene) and TEMPO (cis-1,4-PIP10k/TEMPO) at selected temperatures over the temperature range from 100 K to 350 K. The experimental data (black) and simulated (green) electron spin resonance (ESR) spectra of cis-1,4-PIP10k/TEMPO system within the slow motion regime at 100 K, 140 K, superimposed slow and fast motion regimes at 170 K up to 245 K and within the fast motion regime at 290 K up to 350 K are shown. The distance of the outer line separation, 2A zz displays the double-sided arrow.
As mentioned in the Experimental section, the obtained ESR spectra can be evaluated in terms of the distance of the outer line separation, 2A zz [25][26][27] and the correlation times, τ c slow (T),τ c fast (T), as well as their related population fractions, F slow (T), F fast (T) [41].
3.1.1. Spectral Parameter of Mobility, 2A zz Figure 2 shows the temperature dependence of the distance of the outer line separation, 2A zz of spectra of TEMPO/cis-1,4-PIP10k system over a wide temperature range from 100 K to 350 K. Five regions of distinct thermal behavior of 2A zz reflecting different spin probe mobility can be distinguished. They are marked as A-E. Two weak decreases at T X1 slow,2Azz~1 60 K and T X2 slow,2Azz~2 05 K within the slow motion regime followed by the main transition of spin probe reorientation from the slow to fast motion regime at T 50G = 232 K and finally, by the onset and crossover effects within the fast regime at T X1 fast,2Azz~2 40 K and T X2 fast,2Azz~2 82 K occur. The glass-to-liquid transition temperature T g DSC is also included by vertical line.
At the lowest temperatures, the broad spectrum reaches the extrema separation value of 2A zz (100 K) = 67.5 ± 0.2 Gauss which lies in the typical range for van der Waals organic compounds [32].
In the low temperature regions A and B of the slow motion regime, the 2A zz parameter of mobility starts to decrease slightly at the first characteristic ESR temperature T X1 slow,2Azz ∼ = 160 K and next, at T X2 slow,2Azz ∼ = 205 K. The second value is situated in the vicinity of the glass-to-liquid temperature of cis-1,4-PIP10k T g DSC = 208 K as detected by DSC technique [50]. This relative closeness of the T X2 slow,2Azz and T g DSC values indicates that the second change, i.e., acceleration in the spin probe TEMPO mobility during heating is closely related to the glass-to-supercooled liquid transition as the basic thermodynamic signature and a descriptor of any amorphous materials.
The most pronounced effect in the 2A zz -T plot is a transition of the spin probe TEMPO reorientation from the slow to fast motion regime within the region C which is usually quantified operationally by the characteristic ESR temperature T 50G . At this temperature, the outermost peaks separation in the triplet signal reaches just 50 Gauss. Its value for the cis-1,4-PIP10k/TEMPO system is T 50G = 232 K.
Finally, within the fast regime of the spin probe TEMPO reorientation, two regions D and E are observed which are marked by the characteristic ESR temperature, i.e., an onset to the fast regime at T X1 fast,2Azz~2 40 K and further acceleration of TEMPO mobility at T X2 fast,2Azz lying at around 282 K. This simple measure of the spin probe mobility in relation to free volume findings and the origin of all characteristic ESR temperatures will be discussed later.

Spectral Simulations
The rotational dynamics of TEMPO in cis-1,4-PIP10k can be also evaluated by the more sophistic approach via spectral simulations. The advantageous program is represented by the Non-linear Least Squares Line (NLSL) code based on the isotropic Brownian model of the spin probe reorientation and provides the time scales of slow and fast moving components τ c slow (T), τ c fast (T) as well as their population fractions F slow (T), F fast (T) [41]. Figure 1 represents a comparison between the experimental and simulated one-or two-component ESR spectra over a wide temperature range. The unimodal ESR spectra were found in the low-T range from 100 K to 150 K as well as in the high-T one from 250 K to 350 K. Bimodal ESR spectra from the superimposed slow and fast components were appeared in the intermediate-T range between 155 K and 245 K as documented by the good quality of fits ranging between 0.994 and 0.998. Figure 3 displays the time scale, τ c slow , τ c fast of the corresponding slow and fast spectral components as a function of the inverse temperature 1/T. The three basic regions of the distinct mobility of the TEMPO probes in cis-1,4-PIP10k can be clearly distinguished and subsequently marked as A, B and C. The one-component broad spectra from slow spin probe motion occur in the low temperature region A slow from 100 K to 150 K. On increase the temperature within region B, the bimodal spectra appear at T X1 slow = T X,ini fast = 155 K and persist up to T c~2 50 K. Moreover, in this region of the so-called dynamic heterogeneity of TEMPO mobility, two slow (B slow,1 , B slow,2 ) and fast (B fast,1 , B fast,2 ) sub-regions are observed at T X2 slow or T X1 fast , respectively. Within this superposed region B, the sensitivity of both the slow-and fast-motion components to T g DSC is evident compared to cis-1,4-PIP0.8k [39] as well as 1-PrOH [38] which exhibit only a phase change at T g in the slow component. Note that the differences between polymeric cis-1,4-PIP10k and oligomeric cis-1,4-PIP0.8k will be compared in detail below in separate part of the Discussion section. Finally, the ESR spectra in region C simulated as the singlet narrow spectra reveal the occurrence of two fast sub-regimes at T X2 fast = 295 K. The six slow and fast regions can be described by the Arrhenius equation τ c,i (T) = τ ∞,i exp[E i */RT] with the pre-exponential factor, τ ∞,i , the activation energy, E i * and the regression coefficient given in Table 1. However, for experimental data of the highest-Tregion C fast,2 , the Vogel-Fulcher-Tamman- [57][58][59], worked very well. Here, τ ∞ is the pre-exponent, B VFTH is the VFTH parameter and T 0 VFTH is the divergence temperature. This formula gives more realistic description than the Arrhenius one that provides the unrealistically low pre-exponent 3.3 × 10 −17 s.  Table 1.
The temperature dependences of the relative fractions of the individual spectral components F slow and F fast are given in Figure 4. In general, they exhibit the changes at the characteristic ESR temperatures T X1 F , T X2 F and T c F which are consistent with the characteristic ESR temperatures from the τ c vs. 1/T plot: T X1 slow = T x,ini fast , T X2 slow = T X1 fast and T c . Figure 5 displays the temperature dependence of the mean o-Ps lifetime, τ 3 , in the pure cis-1,4-PIP10k sample in the temperature range from 100 K to 350 K. The PALS measurements were performed in slow heating mode with 5-10 K steps. The PALS response exhibits five regions of distinct thermal behavior of the o-Ps annihilation which are characterized by four characteristic PALS temperatures, i.e., T b1 G~1 58 K, T g PALS~1 96 K, T b1 L = 246 K, T b2 L = 291 K. On the right axis of Figure 5, the mean equivalent free volume, V h = (4π/3)R h 3 , determined by the standard quantum-mechanical model of o-Ps in a spherical hole, relates to the observed mean o-Ps lifetime, τ 3 , and the mean sphere size of free volume entity R h [23,24,[43][44][45]:

PALS Data
where τ 3,0 = 0.5 ns is the spin averaged lifetime of p-Ps and o-Ps and ∆R = R 0 − R h = 1.66 Å is the thickness of the electron layer around the free volume hole which was obtained for well known cavities in molecular crystals and zeolites [43][44][45]. In general, in poly-mers as complex chain-like systems, one can expect rather the aspherical shape of the intersegmental space and its anisotropic thermal expansion as demonstrated for several model oligomeric and polymeric substances [46][47][48][49]. However, the equivalent free volume V h sph = (4π/3)R h 3 is commonly used as an approximate measure of the free volume hole size [23,24].  As in Figures 2 and 3 the glass-to-liquid transition temperature, T g DSC , is also included. In the τ 3 -T plot, in the lower-T region, the first bend temperatures at T b1 G~0 .76T g DSC or (~0.81 T g PALS ) and the most pronounced effect are situated in the glassy state below T g DSC . This effect lying a bit lower than T g DSC is designated as T g PALS . This shift of T g is due to the different rates of the temperatures change during the DSC and PALS experiments.
In addition, in the liquid state above T g PALS ≈ T g DSC , further two bend effects are observed at T b1 L = 1.18T g DSC (1.26T g PALS ) and T b2 L = 1.40T g DSC (1.48T g PALS ). Again as in the ESR case, the origins of these changes in the free volume expansion with increasing temperature remain to be revealed.  At the highest temperatures 370 K, 375 K and 380 K, the segmental α relaxation peak in the susceptibility spectra can be seen. In order to extract the α relaxation time,τ α , the susceptibility spectra at these temperatures were fitted by the Cole-Davidson (CD) function defined as [60]: where ν is the frequency, A, τ CD , and β CD are fitting parameters characterizing the amplitude, the weight maximum position and the high frequency asymptotic power law behavior of the α relaxation peak, respectively. The characteristic α relaxation time τ α was determined from the equation τ α = τ CD. β CD [12,13,51,52,61]. In the susceptibility spectra at lower temperatures, the maximum of the structural α relaxation, τ α , was obtained from a master plot for the α relaxation peak. To construct this master plot, the susceptibility spectra at three temperatures 370 K, 375 K and 380 K as a function of the reduced frequency ντ α were plotted. Next, the data for lower temperatures were added. For each temperature, a value of τ α was found out to reach the best overlap of the high-frequency parts of the α relaxation peaks for different temperatures from 270 K to 380 K. Figure 7 shows the obtained segmental α relaxation times as evaluated from the present LS measurements together with those from the BDS ones including three points from very restricted LS study [50]. Arrhenius plot of the segmental α relaxation time, τ α , for cis-1,4-PIP10k as obtained from the present Light Scattering LS work together with those from a combined BDS and LS study of the same cis-1,4-PIP10k in Ref. [50]. Fit curves of the Power Law (PL) function or the Mode Coupling theory (MCT) model (Equation (10)) over intermediate-and high-T region as well as the TOP model (Equation (11)) over the whole T range are included and commented in the text in detail.

Analysis of the Fast Dynamics
In Figure 6, the wing of the LS spectra in cis-1,4-PIP10k can be described by a power law expression: χ" wing (ν) = C/ν The fast motion relaxation on shorter time scales than the slow segmental α relaxation time is well described by the Gilroy-Phillips (GP) model of thermally activated jumps in asymmetric double-well potentials [62,63]. This GP model was used in the temperature range up to 310 K, where the wing is still dominating the relaxation at lower frequencies. This model assumes the exponential distribution of the barrier heights V, exp(−V/V 0 ), with some typical barrier V 0 . The susceptibility has a low-frequency power-law tail with the slope b = T/V 0 at T << V 0 that goes to 1 at higher T. From the right side of the peak, the slope is as for the Debye relaxation, −1. For simplicity, we approximated this behavior by the function with correct asymptotes.
In Figure 9, the boson peak frequency, ν BP , decreases with increasing temperature, while the relaxation frequency of fast motion maximum, ν 0 , is more or less constant within the error bars interval. However, it is difficult to separate the fraction of the fast relaxation motions at T > 310 K due to too smooth LS spectrum, many unknown parameters in the individual components and unknown shape of the right slope of the α relaxation that exceeds the wing at T > 310 K. At these high temperatures, the Mode Coupling theory (MCT) analysis appears to be more suitable approach.

MCT Analysis
The idealized mode coupling theory (I-MCT) gives some prediction about the temperature evolution of the susceptibility minimum between the slow structural α process and the fast dynamics [65,66], which can be summarized as in the equation: where ν min and χ" min are the frequency or amplitude of minimum, respectively. The exponents a and b describe the low-frequency part of the fast dynamics and the high frequency part of the segmental α process. In Figure 10, the linearized scaling law amplitudes (SLA) provide the critical temperature of the MCT model: The SLA for ν min and χ" min give the values for T c I-MCT = 180 K or 262 K, respectively, by taking into account all the data range. In this case, a significant discrepancy between T c I-MCT values as obtained from the analysis of ν min and χ" min exists. For resolving this problem, the fact was took into account that even at low temperatures, a minimum in the susceptibility spectra (see Figure 6) formed by some additional relaxation with a bump near 1 GHz was seen, while within the MCT, a minimum near T g was not observed. In this case, the value (ν min ) 2*0.34 near 200 K as a low-temperature limit and to see the crossing of (ν min ) 2*0.34 (T) with this value was taken into account. This way of analysis gives also T c I-MCT ≈ 262 K (see Figure 10). So, from the analysis can be concluded that the analysis of the temperature dependence of the position and amplitude of the susceptibility minimum gives for T c I-MCT ≈ 262 K. Note that the onset of the SLA enhancements starts already somewhat above 240 K.

Segmental α Relaxation of cis-1,4-PIP10k in Terms of the Power Law (PL) Function or Mode Coupling Theory (MCT) Model and the Two-Order Parameter (TOP) Model
The extracted time scales of the structural (segmental) relaxation as a function of temperature in Figure 7 can be described by various expressions, such as the power law (PL) function [67] or equivalently the afore-mentioned idealized mode coupling theory (I-MCT) model [65,66] and the two-order parameter (TOP) model [68][69][70]. Returning to Figure 7, both types of dynamic models of the segmental α relaxation time data of cis-1,4-PIP10k are tested. The PL function which is related to the prediction of the I-MCT are expressed by the following formula: where τ ∞,α is the pre-exponential factor, T X is the characteristic temperature of PL function and MCT model and µ is the coefficient. Both are valid at rather intermediate and higher temperatures in relatively lower viscosity of materials [71,72]. In our case of cis-1,4 PIP10k, the relaxation data above T = 271 K (from the first LS point in Figure 7 up to the final 380 K) can be satisfactorily described by Equation (10) which provides the characteristic dynamic crossover temperature of T x PL = T c I-MCT = 245.8 K and µ = 3.1. Alternative description and the related solid-like and liquid-like domain picture interpretation of the segmental dynamics in cis-1,4-PIP10k over the whole measured temperature range can be provided by the two-order parameter (TOP) model [68][69][70]. This model is based on the modified VFTH (M-VFTH) formula: where τ(T) is the structural relaxation time, τ ∞ is the pre-exponent factor, E * τ is the activation energy above T * m ≈ T A , T 0 is the divergence temperature, B is the coefficient and F(T)is a probability function for solid-like domains. The latter quantity is defined as: where κ describes the sharpness of the probability function between solid-like and liquidlike domains and T c m is the characteristic TOP temperature, i.e., the critical temperature where the free energy of a crystallizing liquid is equal to that of the crystal ∆G lq = ∆G cr or, in the general case of non-crystallizing glass-formers, the free energy of a liquid is equal to that of a solid: ∆G lq = ∆G sol . In the present case, the parameters are as follows: log τ α,∞ = −14.3, E * τ = 37.7 J/mol, B = 525.1 K, κ = 0.054 1/K, T c m = 237.5 K and T 0 = 169.7 K. Both the characteristic model temperatures T X PL = T c I-MCT and T m c,TOP are rather close to each other and they will be discussed in a connection with the obtained ESR and PALS data.  In the ESR response, the first weak decrease in 2A zz at T X1 slow,2Azz~1 60 K lies close to the slight bend effect at T b1 G~1 58 K in the τ 3 vs. T plot within the glassy state of cis-1,4-PIP10k. As already mentioned above, in the Results section, the second decrease at T X2 slow,2Azz~2 05 K lies in the vicinity of the glass-to-liquid temperature T g DSC = 208 K. The most pronounced effect in the 2A zz vs. T dependence marking a transition of the spin probe TEMPO between its slow and fast motion regimes at conventionally defined T 50G = 232 K does not have any direct counterpart in the τ 3 -T plot, although it is not very distant from T b1 L . Here, τ 3 (T 50G )~2.07 ns and the corresponding equivalent spherical free volume size V h sph (T 50G )~110 Å 3 falls into the first empirical rule: τ 3 (T 50G ) = 2.17 ± 0.12 ns and V h sph (T 50G ) = 114 ± 15 Å 3 [32]. On further increasing temperature in the supercooled liquid state of cis-1,4-PIP10k, the onset to the fast motion regime occurs at T X1 fast,2Azz~2 40 K in 2A zz -T plot in the vicinity of the mild bend effect in the PALS response at T b1 L = 246 K. Finally, in the normal liquid state of cis-1,4-PIP10k, the TEMPO probes exhibit further acceleration at roughly T X2 fast,2Azz~2 82 K within the fast motion regime accompanied by the further narrowing of the triplet spectrum which is in plausible agreement with the onset to the quasi-plateau effect at T b2 L~2 91 K. Here, τ 3 (T X2 fast )~2.75 ns corresponding to the equivalent spherical free volume V h sph (T X2 fast )~180 Å 3 are in a good agreement with the second rule, i.e.,  In the low temperature region, an appearance of the fast component in the ESR spectrum is observed at T X1 slow =T X,in fast close to T b1 G at which a small increase in the o-Ps lifetime and related free volume expansion also occur. The second acceleration in the slow and simultaneously the slight first one in the fast component are found at T x2 slow and T x1 fast which lie in the vicinity of the T g PALS and T g DSC values.The full disappearance of the slow component at T c = 250 K can be related to T b1 L = 246 K. Finally, the crossover effect between two fast motion sub-regimes at T X2 fast is in a good accord with an onset to the quasi-plateau effect in the normal liquid state around T b2 L . The observed mutual PALS and ESR coincidences at a level of the changes of the respective time scales can be summarized as follows: T X1 slow = T X,in fast = T b1 G , T X2 slow = T X1 fast ∼ = T g PALS ≈ T g DSC , T c ∼ = T b1 L and finally, T X2 fast ∼ = T b2 L . The mutual temperature coincidences of the various effects in the ESR and PALS responses indicate that the changes in the free volume expansion at the characteristic PALS temperatures are closely related to the changes in the dynamic state of the small molecular probe TEMPO. This strongly suggests the common physical origin of these mutually coinciding changes. The natural question arises: What physical processes are behind the various crossover effects in the atomic probe annihilation and the molecular mobility in cis-1,4-PIP10k?
In Figure 13, the relationships between the mean o-Ps lifetimes at the characteristic PALS temperature in the liquid state and the mean characteristic segmental α relaxation times, τ α , and the mean secondary relaxation, τ β are showed [68][69][70]. In the former case it can be seen that the so-called equivalent α temperature, T α,eq , i.e., the temperature at which the PALS time scale equals to LS and BDS [33][34][35][36][37][38], being 303 K is not too distant from the second characteristic PALS temperature, T b2 L = 291 K. This plausible match of T findings suggests that an onset of the quasi-plateau effect in the PALS response is related to the segmental α dynamics of cis-1,4-PIP10k sample. Moreover, this is fully consistent with the generally accepted bubble concept of the o-Ps annihilation in low viscous organic media [73].  [50] data and the secondary β process, τ β , from DS study on 1,4-PIP500k in Ref. [73].
Next, based on the finding of the relation T X2 fast~T b2 L , the second acceleration in the TEMPO reorientation within the fast motion regime is at least influenced by the segmental process. As for the first characteristic PALS temperature at T b1 L , being close to the T c from Figure 3, the situation is a bit more complicated. At T b1 L , the mean time scale of the segmental α relaxation reaches a few µs, i.e., about three orders of magnitude longer than the o-Ps lifetime τ 3 (T b1 L ) = 2.1 ns. On the other hand, after a commonly used linear extrapolation of the secondary β scale [74] into the liquid state, one can estimate the so-called αβ merging temperature, T αβ ≈ 245 K, at which both the relaxation processes should merge and further continue as a unified αβ process. This mutual temperature coincidence T c~Tb1 L~T αβ seems to suggest that the first slight change in the free volume expansion between deeply and slightly supercooled liquid state as well as the appearance of the pure fast reorientation regime of the TEMPO molecules could be related to the occurrence of the potentially unified αβ process in cis-1,4-PIP10k.
Next, these mutual phenomenological relationships between the characteristic PALS and ESR temperatures will be further discussed in the context of both models applied for the segmental dynamics in Section 3.3.4. As presented in Figure 7, the MCT model equivalent to the empirical PL function and the TOP model provide satisfactory fits with the corresponding model temperatures: T X PL = T c I-MCT = 245.8 K or T m c,TOP = 237.5 K, respectively. These quite close values are in plausible agreement with the characteristic PALS and ESR temperatures T c~Tb1 L . Thus, both models offer the corresponding interpretations in terms of the apparent divergence of the density fluctuation or the crossover between the solid-like and liquid-like domains. In the former case, the unphysical divergence might be removed by adding of the hopping term in the extended version of the mode coupling theory (E-MCT) that provides the same T c E-MCT as its idealized version T c I-MCT [63]. On the other hand, Figure 14 represents the probability function of the solid-like domains extracted from Equation (11) of the TOP model together with all the characteristic PALS and ESR temperatures as well as the afore-mentioned merging temperature T αβ from DS study [74].  (11) with the characteristic PALS and ESR (from spectral simulations) temperatures together with the characteristic TOP temperatures as well as with the glass-to-liquid temperature T g DSC and the αβ merging temperature T αβ DS [74].
The quite satisfactory closeness between the characteristic PALS and ESR temperatures in the glassy state with an onset of the liquid-like domains at around T 0 TOP was observed. Further, as given above, the first characteristic ESR and PALS temperatures in the supercooled liquid state lie in the vicinity of the crossover temperature where the liquid-like domains begin to dominate over the solid-like ones, i.e., in the vicinity of a transition between the strongly supercooled to the weakly supercooled liquid. Finally, the high-T characteristic PALS and ESR temperatures T b2 L and T X2 fast appear close to the third characteristic TOP temperature, namely, the Arrhenius one T A = 300 K. Here, the liquid-like domains are substantially predominant over the solid-like ones and cis-1,4-PIP10k behaves as a normal low viscosity liquid.

Comparison of ESR and PALS Responses for Polymeric cis-1,4-PIP10k vs. Oligomeric cis-1,4-PIP0.8k
It is of interest to compare the present PALS and ESR data on polymeric cis-1,4-PIP10k with its oligomeric cis-1,4-PIP0.8k counterpart [39] and to reveal the size effect of the corresponding chains on both free volume microstructure and spin probe TEMPO dynamics. The former glass former contains about 140 basic structural units~[CH 2 -CH=C(CH 3 )-CH 2 ]~per chain, while the later one is essentially shorter with ca. only 12 monomers/chain. Figure 15a,b demonstrate that with the increasing chain length and thus, the increasing strength of inter-and intra-segmental interactions, the free volume reduces and consequently, the molecular reorientation dynamics slows down. The difference in the TEMPO mobility, as expressed by the respective correlation times, appears to be larger within the slow motion regime in the glassy state as well as above T g DSC in the strongly supercooled liquid one, where the free volume difference is not so large. On the other hand, in the slightly supercooled liquid state, this free volume difference becomes larger up to the corresponding T b2 L , while the difference in the rotation dynamics of TEMPO within the fast motion region is smaller. At higher temperatures, i.e., in the quasi-plateau region above T b2 L , due to the well-known artefact nature of the o-Ps response in low viscosity media mentioned above, such a comparison cannot be performed. The observed trends in the spin probe TEMPO dynamics could be ascribed to the different degrees of the local perturbation of the respective oligomeric or polymeric medium by the molecular probe TEMPO.
According to Figure 5, the temperature dependence of the mean equivalent spherical free volume V h sph estimated from Equation (1) is also included. We can see that the V h sph values of cis-1,4-PIP10k are smaller than the vdW volume of the spin probe TEMPO up to ca. 280 K. Consequently, the slow dynamics of TEMPO in the glassy and deeply supercooled liquid state of cis-1,4-PIP10k is slower than that in cis-1,4-PIP0.8k due to somewhat tighter surroundings around the TEMPO molecules. In both the cis-1,4-PIP glassformers the mean o-Ps lifetime at the corresponding transition temperatures T c 's,τ 3 (T c ), reaches the same value around 2.1 ns corresponding to the V h sph (T c ) ∼ = 115 Å 3 , being smaller than V TEMPO vdW = 170 Å 3 . It seems to imply a local deformation of the immediate surroundings of the TEMPO molecules in cis-1,4-PIP/TEMPO system in comparison to the pure bulk cis-1,4-PIP medium. On further increase of the temperature, this local perturbation of the respective medium should be weaken which results in the closer rotation dynamics of TEMPO within the fast motion regime among both the cis-1,4-PIP media. This hypothesis is further discussed in the next sub-section. Figure 15. Comparison of the ESR and PALS data for cis-1,4-PIP10k vs. cis-1,4-PIP0.8k [39] in terms of (a) τ 3 vs. T and (b) log τ c vs.1/T plots.

Relationships between the Time Scales from ESR and BDS, LS and Further Dynamic Techniques
The local deformation concept of the molecular probe in organic medium, outlined in the previous sub-section, implies that the TEMPO molecule responds to some local dynamics in its immediate surroundings which should be similar or different to the local dynamics of the bulk medium. This would correspond to the full coupled or the decoupled situations, respectively. As already mentioned, in the case small molecular glass formers with the spin probe TEMPO in the fast motion regime, the former situation is observed due to very tight coupling of the spin probe dynamics and the structural relaxation of small molecules that are more compactly arranged around TEMPO [37,38]. On the other hand, in chain media such as cis-1,4-PIP0.8k, the local structural situation is not so favorable partly due to the connectivity aspect of the medium constituents which do not allow compacted microstructure of the spin probe surroundings [39]. In this connection, the time scales of the spin probe TEMPO reorientation with those of numerous motional modes in cis-1,4-PIP10k were suitable to compare. Figure 16 presents the correlation time of TEMPO probe and the characteristic time scales of all the known six motional modes in cis-1,4-PIP10k detected by BDS [50,74] and NS [75] techniques as well as LS over a wide temperature range from 180 K to 380 K. These include relatively slow motional modes, such as the normal [50] and the primary α relaxations [50] from BDS and the present LS study. The secondary β relaxation [74] and relatively fast ones, such as the fast motion and the boson process, reveal LS investigation as well as the methyl group jump rotation [75]. By comparison with the ESR data, in contrast to the small molecular glass formers [37,38], the TEMPO time scales for polymeric cis-1,4-PIP10k in all the three, i.e., slow-, co-existing slow-and fast-and fast motion regimes between 0.75T g and 1.15T g do not follow any of the time scales of molecular motions. Indeed, they lie in between the relatively slow segmental α relaxation and the local fast motion dynamics. Thus, by considering the afore-mentioned PALS finding about the local deformation of the medium by the applied molecular probe, leading the different local potential field around it, this causes the modified local dynamics of the surrounding molecules of medium around the reporter's molecular probe governing its rotation reorientation. Figure 16. Relaxation map of cis-1,4-PIP10k sample consisting of BDS, light scattering (LS) and neutron scattering (NS) time scales together with those for the spin probe TEMPO correlation times in cis-1,4-PIP10k, τ c , obtained in the temperature range 100 K up to 400 K. Dynamic data include the chain relaxation time, τ n , from BDS [50], the segmental relaxation, τ α , from BDS [50] and LS and the secondary β relaxation, τ β , in 1,4-PIP500k over 180 K-205 K from BDS [74], the fast motion relaxation, τ fast , and boson peak, τ boson , from LS as well as CH 3 -jump rotation over 110-240 K from NS [75].

Conclusions
The rotation dynamics of small spin probe 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) in amorphous polymeric glass former, namely, cis-1,4-poly(isoprene) (cis-1,4-PIP10k) was investigated over a wide temperature range from 100 K to 360 K by means of electron spin resonance (ESR). Several regions of distinct spectral and related dynamic behavior of TEMPO were revealed via two parameters of spin probe mobility, i.e., the extrema separation of the spectra and the correlation time. A set of the changes in both parameters, characterized by ESR temperatures, were consistent with the free volume changes in the pure cis-1,4-PIP10k sample detected by PALS technique.
In order to identify the physical process responsible for the spin probe dynamics in the fast regime, the detailed dynamic study of cis-1,4-PIP10k medium was carried out by light scattering techniques focusing on the high-frequency relaxations of the medium constituents. Finally, a comparison of the time scales of both slow and fast motion regimes of TEMPO in cis-1,4-PIP10k with the found six motional modes in cis-1,4-PIP10k, i.e., a series of slow and fast relaxation modes from LS and BDS as well as NS techniques, strongly suggests the controlling factor of the spin probe mobility over a wide temperature region which consists in the local dynamics of the modified local surrounding of the molecular probe TEMPO.