Thermodynamic and Dynamic Transitions and Interaction Aspects in Reorientation Dynamics of Molecular Probe in Organic Compounds: A Series of 1-alkanols with TEMPO

The spectral and dynamic properties of 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) in a series of 1-alkanols ranging from methanol to 1-decanol over a temperature range 100–300 K were investigated by electron spin resonance (ESR). The main characteristic ESR temperatures connected with slow to fast motion regime transition; T50G ‘s and TX1fast ‘s are situated above the corresponding glass temperatures, Tg, and for the shorter members, the T50G ‘s lie above or close to melting point, Tm, while the longer ones the T50G < Tm relationship indicates that the TEMPO molecules are in the local disordered regions of the crystalline media. The T50G ‘s and especially TX1fast ‘s are compared with the dynamic crossover temperatures, TXVISC = 8.72M0.66, as obtained by fitting the viscosity data in the liquid n-alkanols with the empirical power law. In particular, for NC > 6, the TX1fast ‘s lie rather close to the TXVISC resembling apolar n-alkanes [PCCP 2018,20,11145-11151], while for NC < 6, they are situated in the vicinity of Tm. The absence of a coincidence for lower1-alkanols indicates that the T50G is significantly influenced by the mutual interaction between the polar TEMPO and the protic polar medium due to the increased polarity and proticity destroyed by the larger-scale melting transition.


Introduction
In general, the dynamics of glass-forming liquids, i.e., organics and inorganics forming the supercooled liquid by their cooling below the melting temperature, T m , and finished via a liquid−to−glass transition to a glass below the glass temperature, T g , is non-monotonous and exhibits a change at the so-called dynamic crossover temperature, T cross = T B or T X , lying between T m and T g [1][2][3][4][5][6][7][8][9][10][11][12].This dynamic crossover phenomenon between the relatively weakly and strongly changing supercooled liquid dynamics is observed using experimental techniques, such as viscosity (VISC) at T B,η or T X [1,2], and dielectric spectroscopy (DS) at T B,DS ST [3,4] or T B,DS MG [5], as well as T B,DS KWW [6] and T B,DS SCH [7].Usually, the crossover temperatures are determined by fitting the supercooled liquid dynamics using a combination of classic phenomenological expressions for viscosity, η, or structural relaxation time, τ, such as the Vogel-Fulcher-Tamman-Hesse (VFTH) equation [1], or using the power law (PL) equation [2].Lately, a special evaluation method using Stickel's temperature-derivative analysis or the more general Martinez-Garcia apparent enthalpy analysis of the relevant dynamic quantities, giving T B,DS ST and T B,DS MG , respectively, was proposed [3][4][5].Other ways of determination of the crossover temperature are based on the onset of the increasing broadening of the frequency dispersion of the structural relaxation time distribution, and on the change in structural relaxation strength, ∆ε α , leading to T B,DS KWW or T B,DS SCH , respectively [6,7].In the case of the PL eq. with T X [2,9], this expression is rationalized theoretically using the idealized mode coupling theory (I−MCT) of liquid dynamics [11] via the derivation of the same form of temperature dependence for viscosity and relaxation time using the so-called critical temperature, T c ≈ T X.
The crossover transition is a very significant feature of the supercooled liquid's behavior, as has been demonstrated by the findings of several empirical correlations of T B or T X with various characteristic temperatures of a variety of structural-dynamic phenomena, such as the decoupling or bifurcation of the primary α relaxation and the secondary β process, T αβ , from DS or dynamic light scattering (DLS) [8].Moreover, the crossover phenomenon is also illustrated by various extrinsic probe techniques, such as FS, ESR and PALS.These have revealed the decoupling of the translation from the rotation of molecular probes and medium dynamics at T decoup , either for the relatively large fluorescence probes via fluorescence spectroscopy (FS) [13] or the decoupling of rotation of the spin probes from the medium dynamics, using electron spin resonance (ESR) [14].Finally, crossover in the supercooled liquid state is also manifested by a bend effect in ortho-positronium lifetime τ 3 vs.T dependence, as detected by positron annihilation lifetime (PALS).This slope change reflects a change in the free volume expansion at the characteristic PALS temperature T b1 L above T g in amorphous glass−formers [15].Evidently, it is increasingly recognized that the dynamic crossover before glass transition temperature plays an essential if not fundamental role in our understanding of the glass transition phenomenon [9].
In contrast to the aforementioned cases of amorphous glass-formers, observations of crossover transition in strongly crystallizing, i.e., relatively hardy supercooled apolar and polar organics, is substantially more difficult.This is connected with the problem of the formation of sufficiently large amorphous domains in the otherwise dominantly ordered material, and subsequently, with their characterization by suitable experimental techniques.Recently, we have proposed one special method for creating such amorphous domains in crystalline materials, consisting of the introduction of an appropriate molecular probe disordering the immediate surroundings of the otherwise ordered medium.This includes the spin probe (2,2,6,6−tetramethyl piperidin−1−yl) oxyl (TEMPO) with V TEMPO vdW = 170 Å 3 in a series of apolar n−alkanes ranging from n-hexane to n−nonadecane using the ESR technique [16].On the basis of the close correlation between one of the characteristic ESR temperatures, namely, T X1 fast , lying a bit above the main slow−to−fast transition at T 50G , and marking the onset of the pure fast motion regime of TEMPO and the crossover temperatures, T X VISC , as obtained from fitting the corresponding viscosity data for a series of n-alkanes using the PL eq., dynamic crossovers in the local disordered regions around the probe molecules in the otherwise dominantly crystalline organics were detected.
One of the most important aspects of extrinsic probe techniques such as ESR is the potential interaction between the probe used and the medium's constituents, which can to a greater or lesser extent influence the corresponding probe response to the investigated organic matrix.In our previous work on a series of apolar crystallizing n-alkanes, we used one of the smallest polar spin probes, TEMPO, where in this interaction aspect is supposed to be small [16].The aim of this work was to test other types of strongly crystallizing organic media consisting of protic polar compounds, such as 1−alkanols, with the potential for an intermolecular H−bonding interaction, not only between its own polar molecules but also between these polar molecules and polar spin probe TEMPO.The spectral and dynamic data obtained for the TEMPO on the family of aliphatic monoalcohols or 1−alkanols H(CH 2 ) N OH with N C = 1-10, i.e., ranging from methanol to 1−decanol, are interpreted using the newly analyzed viscosity data in the literature in order to reveal the roles of the thermodynamic and dynamic transitions, as well as of the interaction aspect, in the main slow-to-fast transition behavior of the spin probe TEMPO used.

Thermodynamic and Crossover Transition Behaviors in 1−alkanols
It is well known that 1−alkanols, similarly to n−alkanes, belong to the class of relatively easily crystalizing organic compounds.For this strong ordering tendency, they must have special means of preparation of the totally or partially amorphous samples, with the one exception of 1−propanol (C3OH), which is a very good glass−former [17].

Thermodynamic Transitions in 1−alkanols
Figures 1 and 2 and Table 1 summarize the data from the literature on the three basic thermodynamic transitions of condensed materials, i.e., the glass−to−liquid (devitrification) transition of the amorphous phase, the solid-to-liquid (melting) transition of the crystalline phase, as well as the liquid−to−gas (evaporation) transition of the liquid phase to gas.In general, the corresponding transition temperatures, i.e., glass temperature T g and melting temperature T m , for 1−alkanols, exhibit a non-monotonous characteristic as a function of their molecular, size expressed by the number of carbon atoms in the chain, N c , or molecular weight, M, while the boiling temperature, T b , shows a monotonous type of dependence over the whole molecular size interval.In contrast to the melting with well-defined T m values [18], the T g values measured so far exhibit a scatter up to 10 K, which depends on both the preparation procedure and the measuring technique, such as dynamic-mechanical spectroscopy (DMS), differential thermal analysis (DTA) or differential scanning calorimetry (DSC), and dielectric spectroscopy (DS) [19][20][21][22][23][24][25][26][27][28], with this value apparently diminishing with increasing molecular size.In spite of this fact, the T g value for the shortest 1−alkanols decreases from methanol (C1OH) to ethanol (C2OH), followed by a monotonous increasing trend, starting from C2OH in the DMS data [26], or from 1−propanol (C3OH) in the CAL data [17].As originally proposed by Faucher and Koleske [26], the DMS results could be described by the power law (PL)-type expression as a function of molecular weight, M: where A and α are empirical parameters of a given homologous series of compounds.As seen in Figure 1A, they exhibit similar trends depending relatively strongly on the method of generation of the amorphous material and the set up used in DMS or DTA, respectively.The latter values of T g DTA coinciding with T g CAL in cases of lower 1-alkanols, such as ethanol, 1−propanol and 1−butanol, as studied by the special CAL technique, i.e., quasiadiabatic calorimetry (QADC) [17,28], are considered to be more reliable, mainly because of the experimental complexity of DMS.
special means of preparation of the totally or partially amorphous samples, with the one e ception of 1−propanol (C3OH), which is a very good glass−former [17].

Thermodynamic Transitions in 1−alkanols
Figures 1 and 2 and Table 1 summarize the data from the literature on the three bas thermodynamic transitions of condensed materials, i.e., the glass−to−liquid (devitrificatio transition of the amorphous phase, the solid-to-liquid (melting) transition of the crystalli phase, as well as the liquid−to−gas (evaporation) transition of the liquid phase to gas.general, the corresponding transition temperatures, i.e., glass temperature Tg and meltin temperature Tm, for 1−alkanols, exhibit a non-monotonous characteristic as a function of the molecular, size expressed by the number of carbon atoms in the chain, Nc, or molecul weight, M, while the boiling temperature, Tb, shows a monotonous type of dependence ov the whole molecular size interval.In contrast to the melting with well-defined Tm valu [18], the Tg values measured so far exhibit a scatter up to 10 K, which depends on both t preparation procedure and the measuring technique, such as dynamic-mechanical spectro copy (DMS), differential thermal analysis (DTA) or differential scanning calorimetry (DSC), an dielectric spectroscopy (DS) [19][20][21][22][23][24][25][26][27][28], with this value apparently diminishing with increasin molecular size.In spite of this fact, the Tg value for the shortest 1−alkanols decreases fro methanol (C1OH) to ethanol (C2OH), followed by a monotonous increasing trend, startin from C2OH in the DMS data [26], or from 1−propanol (C3OH) in the CAL data [17].A originally proposed by Faucher and Koleske [26], the DMS results could be described by t power law (PL)-type expression as a function of molecular weight, M: where A and α are empirical parameters of a given homologous series of compounds.A seen in Figure 1A, they exhibit similar trends depending relatively strongly on the metho of generation of the amorphous material and the set up used in DMS or DTA, respective The latter values of Tg DTA coinciding with Tg CAL in cases of lower 1-alkanols, such as ethan 1−propanol and 1−butanol, as studied by the special CAL technique, i.e., quasi-adiabatic c orimetry (QADC) [17,28], are considered to be more reliable, mainly because of the expe imental complexity of DMS.Finally, in Figure 1B, the estimated values of glass transition, Tg*, calculated according to the well-known empirical rule for many organic and inorganic glass-formers (Tg* = (2/3) × Tm -see e.g., Refs.[29][30][31][32]), are also listed.Given their comparison with the measured Tg data from DTA or DMS, it follows that this rule is not valid for our series of the first ten 1-alkanols, with the one exception of C3OH.Alternatively, the measured Tm CAL /Tg DTA ratios fulfill the rather different empirical rule of ~1.70, instead of Tm/Tg* = (3/2) = 1.50, which is valid again for C3OH only-see Figure 3.As for the melting transition of 1−alkanols, the same expression can be approximately used for the melting points: where C = 8.41 and γ = 0.705 are empirical parameters of the melting of a given homologous series of compounds, as derived mainly from the calorimetric data [18] in Figure 2. A similar approach has recently been applied for n−alkanes and monoalcohols in spite of the very pronounced zig-zag effect for the former, with a similar γ value of 0.7, as given by Novikov and Rössler [29].Finally, in Figure 1B, the estimated values of glass transition, T g *, calculated according to the well-known empirical rule for many organic and inorganic glass-formers (T g * = (2/3) × T m -see e.g., Refs.[29][30][31][32]), are also listed.Given their comparison with the measured T g data from DTA or DMS, it follows that this rule is not valid for our series of the first ten 1-alkanols, with the one exception of C3OH.Alternatively, the measured T m CAL /T g DTA ratios fulfill the rather different empirical rule of ~1.70, instead of T m /T g * = (3/2) = 1.50, which is valid again for C3OH only-see Figure 3.
As for the melting transition of 1−alkanols, the same expression can be approximatel used for the melting points: where C = 8.41 and γ = 0.705 are empirical parameters of the melting of a given homolo gous series of compounds, as derived mainly from the calorimetric data [18] in Figure 2. A similar approach has recently been applied for n−alkanes and monoalcohols in spite of th very pronounced zig-zag effect for the former, with a similar γ value of 0.7, as given b Novikov and Rössler [29].Finally, in Figure 1B, the estimated values of glass transition, Tg*, calculated accord ing to the well-known empirical rule for many organic and inorganic glass-formers (Tg* (2/3) × Tm -see e.g., Refs.[29][30][31][32]), are also listed.Given their comparison with the meas ured Tg data from DTA or DMS, it follows that this rule is not valid for our series of th first ten 1-alkanols, with the one exception of C3OH.Alternatively, the measured Tm CAL /T DTA ratios fulfill the rather different empirical rule of ~1.70, instead of Tm/Tg* = (3/2) = 1.50 which is valid again for C3OH only-see Figure 3.In the case of T m , the full horizontal lines represent the constant value of T m /T g = 1.5 derived from the empirical rule, and the dotted line represents T m /T g ~1.68 for our series of 1-alkanols, whereas in the case T X , with one exception for C1OH, an increasing linear trend of T X /T g is found.Finally, T X /T m ~0.81.

Dynamic Crossovers in 1-alkanols
As mentioned in the introduction, the crossover temperature in the supercooled liquid state of many organic compounds can be obtained using the power law (PL) equation, connecting the viscosity of liquids, η, with temperature T in the normal liquid and weakly supercooled liquid states [2,9,16].Figures 4-6, as well as Table 1, give the results of this method of determination of the crossover temperature, T X .Thus, Figure 4 presents compilations of the viscosity data for a series of ten 1-alkanols ranging from methanol (C1OH) up to 1-decanol (C10OH) as a function of temperature, mostly derived from the two large summarizing literature sources [33,34].Most viscosity data of 1-alkanols fall into the normal liquid state between the melting temperature, T m , and the boiling temperature, T b .For the two lower members of this series, namely, ethanol (C2OH) and 1-propa nol (C3OH), the viscosities were also measured in the supercooled liquid state below the corresponding T m 's; these values were only slightly lower for C2OH [35], but in C3OH they almost reached down to the corresponding T g, because of its very good glass-forming ability [17,[35][36][37].Moreover, the additional liquid data from ref. [38] are included.

Int. J. Mol. Sci. 2023, 24, x FOR PEER REVIEW
In the case of Tm, the full horizontal lines represent the constant value of Tm/Tg = rived from the empirical rule, and the dotted line represents Tm/Tg ~ 1.68 for our 1-alkanols, whereas in the case TX, with one exception for C1OH, an increasing line of TX/Tg is found.Finally, TX/Tm ~ 0.81.

Dynamic Crossovers in 1-alkanols
As mentioned in the introduction, the crossover temperature in the supercoo uid state of many organic compounds can be obtained using the power law (PL) eq connecting the viscosity of liquids, η, with temperature T in the normal liquid and supercooled liquid states [2,9,16].Figures 4-6, as well as Table 1, give the result method of determination of the crossover temperature, TX.Thus, Figure 4 presen pilations of the viscosity data for a series of ten 1-alkanols ranging from methanol up to 1-decanol (C10OH) as a function of temperature, mostly derived from the tw summarizing literature sources [33,34].Most viscosity data of 1-alkanols fall Viscosities for a series of 1-alkanols as a function of temperature together with th tive power law (PL) fittings given by Equation (3).The vertical lines in the same colors as t sponding experimental points for each member of a series of 1-alkanols mark the melting tures (on the left) and the boiling points (on the right), with two extrema demonstrations for (black points and lines) and 1-decanol (orange points and lines).Trends in Tm and Tb are s the two arrows at the bottom of the plot.into the normal liquid state between the melting temperature, Tm, and the boili perature, Tb.For the two lower members of this series, namely, ethanol (C2OH) and nol (C3OH), the viscosities were also measured in the supercooled liquid state be corresponding Tm's; these values were only slightly lower for C2OH [35], but in they almost reached down to the corresponding Tg, because of its very good glassability [17,[35][36][37].Moreover, the additional liquid data from ref. 38    Viscosity of a good glass-former 1-propanol over (A) a restricted temperature range from Tb down to slightly below Tm using the data sets summarized in Ref. [33] (Landolt-Börnstein Table data) and Ref. [34] (DIPPR data), and (B) an extraordinarily wide temperature range from Tb down almost to Tg with the addition data from Refs.[35][36][37] in the strongly supercooled liquid state, as well as from Ref. [38] in the liquid one, together with the best PL equation fitting.The original references marked, such as 1891T1 and 26M2, can be found in Ref. [33].
All the viscosity data for the series of the first ten 1-alkanols can be described by the power law (PL) equation: (3) where η∞ is the pre-exponential factor, TX is the empirical characteristic dynamic PL temperature or the theoretical critical MCT temperature Tc, and µ is a non-universal coefficient.The corresponding fitting curves are plotted in Figure 4 and the obtained crossover temperatures TX are listed in Table 1 and Figure 6.In the above-mentioned case of 1-alkanols for which viscosity data in the supercooled liquid state also exist [35][36][37], the TX values for, e.g., C2OH, extracted from fitting over the usual normal liquid state ranging Tb−Tm = 192 K, and over the whole accessible temperature range of 227 K [35] (Tb−Tmin = 227 K), change by 4 K only.Similarly, for the very good glass-former C3OH, this difference reaches 3 K, which is towards the lower value, as it also includes the strongly supercooled liquid range data from Ref. [35]-see Figure 5A,B.Thus, the PL equation fit over the normal liquid state appears to be a very good approximation only for obtaining the TX values lying in the supercooled liquid state below the corresponding Tm values in strongly crystallizing Viscosity of a good glass-former 1-propanol over (A) a restricted temperature range from T b down to slightly below T m using the data sets summarized in Ref. [33] (Landolt-Börnstein Table data) and Ref. [34] (DIPPR data), and (B) an extraordinarily wide temperature range from T b down almost to T g with the addition data from Refs.[35][36][37] in the strongly supercooled liquid state, as well as from Ref. [38] in the liquid one, together with the best PL equation fitting.The original references marked, such as 1891T1 and 26M2, can be found in Ref. [33].Finally, returning to Figure 3, a comparison of TX/Tg vs. Tm/Tg dependencies as a function of molecular size NC starting from C2OH shows a diametrically different trend for the former quantity with respect to the latter one, i.e., the increasing distance of the particular TX from the respective Tg with the increasing molecular size of 1−alkanol.This finding, All the viscosity data for the series of the first ten 1-alkanols can be described by the power law (PL) equation: where η ∞ is the pre-exponential factor, T X is the empirical characteristic dynamic PL temperature or the theoretical critical MCT temperature T c , and µ is a non-universal coefficient.The corresponding fitting curves are plotted in Figure 4 and the obtained crossover temperatures T X are listed in Table 1 and Figure 6.In the above-mentioned case of 1-alkanols for which viscosity data in the supercooled liquid state also exist [35][36][37], the T X values for, e.Similarly, for the very good glass-former C3OH, this difference reaches 3 K, which is towards the lower value, as it also includes the strongly supercooled liquid range data from Ref. [35]-see Figure 5A,B.Thus, the PL equation fit over the normal liquid state appears to be a very good approximation only for obtaining the T X values lying in the supercooled liquid state below the corresponding T m values in strongly crystallizing organics, such as 1-alkanols.These are also listed in Table 1, together with the few determinations based on the first three members, namely, C1OH, C2OH and C3OH, as given by other authors [2,5,9].
Table 1.Basic physical properties of investigated 1-alkanols.It is shown that the PL equation is valid for a large number of organic molecular glassformers over rather higher temperature range [2,5,9] It is also known that the I-MCT also works very well for the relatively lower viscosity regime [11].In reality, although the viscosity does not diverge at T X ≈ T c , several analyses of the slightly supercooled and normal liquid dynamics in various organic glass-formers in terms of the extended mode coupling theory (E-MCT), which removes this singularity, provide the same crossover temperature in the supercooled liquid phase [11,40].Thus, the T X parameter marks two distinct regimes of the strongly and weakly supercooled liquid dynamics [11].In particular, it corresponds to the onset of dynamic heterogeneities, i.e., regions with slower dynamics embedded into regions of higher dynamics, when the decoupling of translation from rotation of the molecular tracers and the decoupling of rotation of the molecular tracer from that of the medium constituents occur, and the classic Stokes−Einstein or Debye−Stokes−Einstein laws, respectively, are violated [9,14].
Figure 6 displays the molecular size dependence of the extracted dynamic crossover temperature T X for 1−alkanols, together with its fitting curve, with a similar form to that of T g and T m .Similar to the quantities of T g and T m , after the initial decrease to the second lowest member the series of nine 1−alkanols, the power law formula below is followed: with the β exponent, equaling 0.656, lying in between those for the glass temperature, T g (α = 0.503), and melting point, T m (γ = 0.705).
Finally, returning to Figure 3, a comparison of T X /T g vs. T m /T g dependencies as a function of molecular size N C starting from C2OH shows a diametrically different trend for the former quantity with respect to the latter one, i.e., the increasing distance of the particular T X from the respective T g with the increasing molecular size of 1−alkanol.This finding, together with the almost identical relative distance of T X from T m (ca.0.81 × T m ), indicates that the larger the molecule of 1−alkanol, the larger the temperature range of the strongly (or deeply) (and correspondingly, the shorter the weakly (slightly)) supercooled liquid state.On the other hand, upon cooling the smaller 1−alkanols, the weakly supercooled liquid state persists for longer, with a correspondingly shorter deeply supercooled liquid range.

ESR Data 2.2.1. General Spectral and Dynamic Features
Figure 7 presents the 2A zz' vs. T dependencies for our series of spin systems: TEMPO/1alkanols.In all cases, the quasi-sigmoidal courses of these plots are found, with higher 2A zz' values in a slow motional regime at relatively lower temperatures and the lower 2A zz' ones in a fast motion regime in relatively higher temperature regions.The most pronounced feature of 2A zz' vs. T dependencies is a more or less sharp change at the main characteristic ESR temperature, T 50G at which the 2A zz' (T 50G ) value reaches just 50 Gauss, corresponding to the correlation time of the TEMPO in a typical organic medium around a few ns.Note that the detailed spectral simulations of the TEMPO dynamics in several organics, including one of the investigated 1−alkanols, namely, 1−propanol [41], reveal that the spin probe population even at T 50G is not completely situated in the fast motion regime, which occurs at a slightly higher temperature, T X1 fast .In addition to these main characteristic ESR temperatures, T 50G and T X1 fast , other effects appear at T X1 slow and T X2 fast , a discussion of which goes beyond the scope of this work, and will therefore be addressed elsewhere.All the 2A zz' vs. T plots also include the afore-mentioned thermodynamic and dynamic temperatures: T g , T m or T X , respectively.The mutual relationships of these three basic characteristic thermodynamic and dynamic temperatures with T 50G and T X1 fast in a series of 1−alkanols will be discussed below, in Section 2.2.2.
In principle, the main slow-to-fast motion transition of the TEMPO in any organics is related not only to these thermodynamic and dynamic transitions, but it may also be influenced by further factors, such as the potential mutual interaction of a polar spin probe with organic media, especially polar ones.The values of anisotropic hyperfine constants A zz' (100 K) at the lowest measured temperature of 100 K, and of isotropic ones A iso (RT) at room temperature, are summarized in Table 1.Their dependencies on N C, as well as on some relevant bulk properties of the media, such as the bulk polarity of media, through their dielectric constant, ε r , will be discussed in the Section 2.2.3.
room temperature, are summarized in Table 1.Their dependencies on NC, as well as on some relevant bulk properties of the media, such as the bulk polarity of media, through their dielectric constant, εr, will be discussed in the Section 2.2.3.
Finally, the mutual connections between the temperature parameters of the slow-tofast transition, and the thermodynamic as well as dynamic ones, in relation to the polarization interaction of the polar TEMPO probe with a series of polar 1−alkanols, are discussed in Section 2.2.4.Finally, the mutual connections between the temperature parameters of the slowto-fast transition, and the thermodynamic as well as dynamic ones, in relation to the polarization interaction of the polar TEMPO probe with a series of polar 1−alkanols, are discussed in Section 2.2.4.

The Mutual Relationships of T 50G and T X1 fast with Thermodynamic and Dynamic Transitions
In Figure 8, global comparisons of the characteristic ESR temperatures T 50G and T X1 fast with the aforementioned thermodynamic and dynamic temperatures T g , T X and T m are presented.In all the cases, the slow-to-fast transition in all 1−alkanols occurs above the corresponding glass−to−liquid transition, T g , i.e., in the amorphous phase of liquid sample or in the local amorphous liquid zones of partially crystalline matrices, at least. Figure 9 expresses these comparisons in terms of the corresponding ratios: T 50G /T m , T 50G /T X and T X1 fast /T m , T X1 fast /T X .We can approximately distinguish two distinct regions of these ratios with a boundary at around C5OH low M region: C1OH-C5OH with T 50G /T m ≈ 1 (5) high M region: C6OH-C10OH with T 50G /T X ≈ 1 ( 6)

The Mutual Relationships of T50G and TX1 fast with Thermodynamic and Dynamic Transitions
In Figure 8, global comparisons of the characteristic ESR temperatures T50G and TX with the aforementioned thermodynamic and dynamic temperatures Tg, TX and Tm presented.In all the cases, the slow-to-fast transition in all 1−alkanols occurs above corresponding glass−to−liquid transition, Tg, i.e., in the amorphous phase of liquid sam or in the local amorphous liquid zones of partially crystalline matrices, at least. Figure 9 presses these comparisons in terms of the corresponding ratios: T50G/Tm, T50G/TX a TX1 fast /Tm, TX1 fast /TX.We can approximately distinguish two distinct regions of these rat with a boundary at around C5OH So, for higher members starting at C6OH to C10OH, with a relatively longer aliphatic part, we observe a plausible closeness between the characteristic ESR temperatures and the T X 's, indicating that the main ESR transition is related to the dynamic crossover between the deeply and slightly supercooled liquid state.This basic finding is similar to the previous one for a series of n−alkanes [16], with the fact that the T X 's of 1−alkanols are higher than the T X values for the corresponding n-alkanes with the same number of C atoms in the molecule.This difference indicates that the spin probe TEMPO is not fully surrounded by the apolar aliphatic parts of the 1−alkanol molecules, and that the polar -OH groups influence its dynamics, as will be discussed later in Section 2.2.3.This indicates that the immediate environment of the molecular-sized spin probe TEMPO is locally disordered, and subsequently, sensitive to the crossover transition in this local amorphous phase.On the other hand, for low M members from C1OH to C5OH, the T 50G and T X1 fast values lie significantly above the corresponding T X values, and they are situated in the vicinity of the corresponding melting temperatures, T m .This indicates that the slow-to−fast transition of TEMPO appears to be related to the global disordering process connected with the solid−to−liquid state phase transition in the otherwise partially crystallized samples.So, for higher members starting at C6OH to C10OH, with a relatively longer aliphati part, we observe a plausible closeness between the characteristic ESR temperatures an the TX's, indicating that the main ESR transition is related to the dynamic crossover be tween the deeply and slightly supercooled liquid state.This basic finding is similar to th previous one for a series of n−alkanes [16], with the fact that the TX's of 1−alkanols are highe than the TX values for the corresponding n-alkanes with the same number of C atoms in th molecule.This difference indicates that the spin probe TEMPO is not fully surrounded b the apolar aliphatic parts of the 1−alkanol molecules, and that the polar -OH groups influenc its dynamics, as will be discussed later in Section 2.2.3.This indicates that the immediat environment of the molecular-sized spin probe TEMPO is locally disordered, and subse quently, sensitive to the crossover transition in this local amorphous phase.On the othe hand, for low M members from C1OH to C5OH, the T50G and TX1 fast values lie significantl above the corresponding TX values, and they are situated in the vicinity of the correspond ing melting temperatures, Tm.This indicates that the slow-to−fast transition of TEMPO appears to be related to the global disordering process connected with the solid−to−liqui state phase transition in the otherwise partially crystallized samples.

Isotropic and Anisotropic Hyperfine Constants
A iso (RT) and A zz' (100 K) as a Function of the N C , Polarity and Proticity of 1−alkanols Figure 10 displays the anisotropic hyperfine constant, A zz' (100K), and the isotropic.hyperfine constant, A iso (RT), of the TEMPO as a function of the chain length in the series of 1-alkanols studied.Our values of A iso (RT) for TEMPO are quite consistent with the few obtained for lower members of our series, namely, C1OH-C4OH [42][43][44].Although both the quantities decrease with increasing chain size, a significant difference can be found in the corresponding trends.The former quantity shows two clear regions of distinct behavior: a sharper decreasing trend for low-M members, and a weaker one for higher M members above N C ~4.On the other hand, the A iso (RT) parameter is slightly reduced with a suggestion of a slight change at N C ~6 as the number of C atoms in the molecule, N C , increases.
These basic empirical findings can be discussed in relation to the polarity of a set of polar media, with the dissolved polar spin probe TEMPO µ TEMPO ~3 D [45], from both the phenomenological and theoretical viewpoints.First, the A iso (RT) values can be related to various measures of the polarity of the medium, e.g., the dipole moment of the medium's molecule, µ entity,x , as a measure of the polarity of the individual entity in a given phase state x = gaseous or liquid state or the static dielectric constant of the medium, ε r (RT), as a measure of the polarity of the bulk liquid medium, as listed in Table 1.In the first case, evidently, no relationship can be found due to the quasi-constant values of the gaseousphase µ g = 1.66 ± 0.05 D [34] or the liquid-phase µ l = 2.84 ± 0.15 D dipole moments [39].On the other hand, Figure 11 displays the mutual relationships between the isotropic hyperfine constant, A iso (RT), and the dielectric constant, ε r (RT), of 1−alkanols [34], together with those of the latter quantity at RT as a function of the number of C atoms in the chain inserted.Both the quantities decrease with N C , resulting in an A iso (RT) vs. ε r (RT) relationship, with approximately two regions showing distinct behavior: (i) for the lower polar 1−alkanols (C10OH-C5OH) with ε r < ~17, with a strong sensitivity of A iso (RT) to polarity and a weak one to proticity, and (ii) for higher polar 1−alkanols (C3OH-C1OH) with ε r > ~17, with the weak sensitivity of A iso (RT) to polarity and a stronger sensitivity to proticity, due to the increased population of HO-groups potentially interacting with the spin probe TEMPO molecule.The apparent boundary between both regions occurs at N C = 4-5, i.e., for 1−butanol or 1−pentanol, where the ε r (RT) vs. N C (RT) plot changes rather notably from a sharply decreasing dependence to a slightly decreasing one, and where, at the same time, conformational degrees of freedom and related enhanced alignments of the apolar parts of the molecules start to occur.Interestingly, in spite of the absence of ε r (100 K) data facilitating their direct comparison with A zz' (100K), the boundary for this quantity seems to be consistent with that for A iso (RT), suggesting a significant role of polarity and proticity in both the mobility states of the spin probe TEMPO.These findings of the solvent dependence of the different ESR parameters are consistent with the previous ones for A iso (RT) [46,47], as well as for A zz' (77 K) [48,49].
of the latter quantity at RT as a function of the number of C atoms in the chain Both the quantities decrease with NC, resulting in an Aiso (RT) vs. εr (RT) relation approximately two regions showing distinct behavior: (i) for the lower polar (C10OH-C5OH) with εr < ~ 17, with a strong sensitivity of Aiso (RT) to polarity an one to proticity, and (ii) for higher polar 1−alkanols (C3OH-C1OH) with εr > ~ 17 weak sensitivity of Aiso (RT) to polarity and a stronger sensitivity to proticity, d increased population of HO-groups potentially interacting with the spin probe TE ecule.The apparent boundary between both regions occurs at NC = 4-5, i.e., for or 1−pentanol, where the εr (RT) vs. NC (RT) plot changes rather notably from decreasing dependence to a slightly decreasing one, and where, at the same tim mational degrees of freedom and related enhanced alignments of the apolar pa molecules start to occur.Interestingly, in spite of the absence of εr (100K) data f their direct comparison with Azz' (100K), the boundary for this quantity seems sistent with that for Aiso (RT), suggesting a significant role of polarity and protici the mobility states of the spin probe TEMPO.These findings of the solvent depe the different ESR parameters are consistent with the previous ones for Aiso (RT) well as for Azz' (77 K) [48,49].Our basic finding is similar to that derived for another larger nitroxide spin probe, 1−oxyl−2,2,5,5−tetramethyl pyrroline−3−methyl)methanethiosulfonate (MTSSL), in a series of 17 solvents ranging from apolar methylbenzene (toluene) (ε r (RT) = 2.4) to highly polar water (ε r (RT) = 80.4) and even more polar formamid (ε r (RT) = 109), including most of the members of our 1−alkanol series, with one exception for 1−pentanol [50].These authors similarly distinguished the following two regions, i.e., an "apolar"region for ε r (RT) < 25, where the sensitivity of A iso (RT) and A zz' (77K) to the polarity expressed by ε r (RT) is large, and a "polar" region for ε r (RT) > 25, where the sensitivity of A iso (RT) and A zz' (77 K) to the polarity is small, and the change is ascribed to the medium proticity.

1-alkanols
Figure 11.Empirical relationship between the isotropic hyperfine constant, Aiso (RT), and the relative permitivity, εr (RT), of 1−alkanols.Insert contains the latter quantity at RT from Table 1 as a function of NC.
However, it is evident that this division is rather arbitrary and very rough, because the former "apolar" region also includes many of our polar 1−alkanols.In connection with the aforementioned empirical relation between spectral parameters and bulk polarity, more elaborate theoretical approaches, based on models using the medium as a dielectric continuum with dielectric constant, εr, and the molecular solute, e.g., polar spin probe, as a molecular entity localized in a spherical cavity [47,51], can be discussed.Within the reaction field concept of the polarization of the continuum medium by the polar solute, one obtains for the Onsager's reaction field [52] and Böttcher's reaction field [53] the following functional relations: Aiso = f [(εr − 1)/(εr + 1)] [47], or Aiso = f [(2εr + 1)/(2εr + nD 2 )], where nD is the refraction index of the pure nitroxide [51].Figure 12 displays a test of the validity of the first functional dependence for two basic groups of organic compounds at RT doped by TEMPO.The first is represented by a series of apolar and aprotic polar solvents, which range from apolar benzene (BZ) with εr (RT) = 2.3, to a highly polar but aprotic dimethyl sulfoxide (DMSO) with εr (RT) = 48.9, as taken from Ref. [50].The other group, including our series of ten 1−alkanols from methanol with εr (RT) = 33 to 1−decanol with εr(RT) = 7.9, differs significantly from the predicted linear trend due to the specific protic character of the molecules, allowing for H-bond formation between the polar spin probe TEMPO molecule and the alkanol's one.This is quite consistent with the maximal value of Aiso (RT) = 17 Gauss [44] for highly polar and protic water, where εr (RT) = 80.4 [50].The relatively large difference between water and the first member of the alkanol family is determined on the basis of theoretical calculations using density functional theory (DFT) interpreted in terms of the com-Figure 11.Empirical relationship between the isotropic hyperfine constant, A iso (RT), and the relative permitivity, ε r (RT), of 1−alkanols.Insert contains the latter quantity at RT from Table 1 as a function of N C .However, it is evident that this division is rather arbitrary and very rough, because the former "apolar" region also includes many of our polar 1−alkanols.In connection with the aforementioned empirical relation between spectral parameters and bulk polarity, more elaborate theoretical approaches, based on models using the medium as a dielectric continuum with dielectric constant, ε r , and the molecular solute, e.g., polar spin probe, as a molecular entity localized in a spherical cavity [47,51], can be discussed.Within the reaction field concept of the polarization of the continuum medium by the polar solute, one obtains for the Onsager's reaction field [52] and Böttcher's reaction field [53] the following functional relations: A iso = f [(ε r − 1)/(ε r + 1)] [47], or A iso = f [(2ε r + 1)/(2ε r + n D 2 )], where n D is the refraction index of the pure nitroxide [51].Figure 12 displays a test of the validity of the first functional dependence for two basic groups of organic compounds at RT doped by TEMPO.The first is represented by a series of apolar and aprotic polar solvents, which range from apolar benzene (BZ) with ε r (RT) = 2.3, to a highly polar but aprotic dimethyl sulfoxide (DMSO) with ε r (RT) = 48.9, as taken from Ref. [50].The other group, including our series of ten 1−alkanols from methanol with ε r (RT) = 33 to 1−decanol with ε r (RT) = 7.9, differs significantly from the predicted linear trend due to the specific protic character of the molecules, allowing for H-bond formation between the polar spin probe TEMPO molecule and the alkanol's one.This is quite consistent with the maximal value of A iso (RT) = 17 Gauss [44] for highly polar and protic water, where ε r (RT) = 80.4 [50].The relatively large difference between water and the first member of the alkanol family is determined on the basis of theoretical calculations using density functional theory (DFT) interpreted in terms of the complexation of nitroxide with two water or one methanol molecules, respectively [45,50].Moreover, a closer inspection of this group of protic polar compounds confirms the distinction of a series of 1−alkanols into two subgroups, with distinct slopes of A iso (RT) as a function of the corresponding dielectric function: (i) weaker for higher members from C10OH to C6OH, and (ii) stronger for shorter ones from C5OH to C1OH, with an approximate boundary between C5OH and C6OH, i.e., for ε r (RT)~16.5.A similar situation can be found for the Böttcher reaction field due to the linearity between the respective functional forms.Both these findings appear to be consistent with the empirically determined boundary at C4OH-C5OH, as seen from the A iso (RT) vs. ε r (RT) plot without the inclusion of the polarization interaction between the polar solute and the solvent, as shown in Figure 11.
the corresponding dielectric function: (i) weaker for higher members from C10OH to C6OH, and (ii) stronger for shorter ones from C5OH to C1OH, with an approximate boundary between C5OH and C6OH, i.e., for εr (RT) ~ 16.5.A similar situation can be found for the Böttcher reaction field due to the linearity between the respective functional forms.Both these findings appear to be consistent with the empirically determined boundary at C4OH-C5OH, as seen from the Aiso (RT) vs. εr (RT) plot without the inclusion of the polarization interaction between the polar solute and the solvent, as shown in Figure 11 [44]; aprotic polar, such as dimethylsulfoxide (DMSO) [44]' and protic polar compounds, such as water [44] and our series of ten 1−alkanols.In Figures 8 and 9 in Section 2.2.2, we compare the characteristic ESR temperatures T50G and TX1 fast of the slow-to-fast transition of TEMPO in a series of 1−alkanols with the dynamic crossover TX and thermodynamic transition temperatures Tm, and also shown their mutual ratios as a function of the molecular size, NC, of the media.In particular, we revealed a step-like change in the main spin probe TEMPO transition from that seen at the dynamic crossovers at around TX for the longer chains, to that related to thermodynamic transitions at around Tm for the shorter molecules, at NC ~ 5.
Next, in Figures 10-12 in Section 2.2.3, we present the relations of spectral parameters Aiso (RT) and Azz' (100 K) to NC, as well as their phenomenological and theoretical relationships, especially for that of Aiso (RT) to the polarity properties of a set of 1−alkanols.Here, we have observed a change in the trend of hyperfine interactions with the polarity and proticity of 1-alkanol media at NC ~ 4. Now, a combination of these findings indicates that the slow−to-fast transition in the mobility of TEMPO in a series of 1-alkanols is relatively strongly dependent on the strength of intermolecular interactions between the polar constituents of the polar media, and between the polar spin probe and the polarity and proticity of the 1−alkanols investigated.In the longer members of the 1-alkanol family, with the relatively higher population of apolar aliphatic methylene groups related to a weakly changing Figure 12.Test of the Griffith−Onsanger model for isotropic hyperfine constant, A iso (RT), as a function of the polarization expression ε r (RT) -1)/(ε r (RT) + 1) of the Onsanger reaction field model for three types of media: apolar, such as benzene (BZ) [44]; aprotic polar, such as dimethylsulfoxide (DMSO) [44]' and protic polar compounds, such as water [44] and our series of ten 1−alkanols.fast of the slow-to-fast transition of TEMPO in a series of 1−alkanols with the dynamic crossover T X and thermodynamic transition temperatures T m , and also shown their mutual ratios as a function of the molecular size, N C , of the media.In particular, we revealed a step-like change in the main spin probe TEMPO transition from that seen at the dynamic crossovers at around T X for the longer chains, to that related to thermodynamic transitions at around T m for the shorter molecules, at N C ~5.
Next, in Figures 10-12 in Section 2.2.3, we present the relations of spectral parameters A iso (RT) and A zz' (100 K) to N C , as well as their phenomenological and theoretical relationships, especially for that of A iso (RT) to the polarity properties of a set of 1−alkanols.Here, we have observed a change in the trend of hyperfine interactions with the polarity and proticity of 1-alkanol media at N C ~4. Now, a combination of these findings indicates that the slow−to-fast transition in the mobility of TEMPO in a series of 1-alkanols is relatively strongly dependent on the strength of intermolecular interactions between the polar constituents of the polar media, and between the polar spin probe and the polarity and proticity of the 1−alkanols investigated.In the longer members of the 1-alkanol family, with the relatively higher population of apolar aliphatic methylene groups related to a weakly changing polarity, the slow-to-fast transition is related mainly to the dynamic crossover process around T X , similar to what is seen for the apolar n−alkanes [16].On the other hand, in the shorter members with relatively higher dielectric constants and proticity due to the relatively higher populations in the polar hydroxyl groups, a larger-scale disorder process connected with the solid-to-liquid phase transition around T m is needed in order to destroy not only the dense H-bonding network between the medium's molecules, but also to destroy the clustering of polar TEMPO molecules with them, and subsequently, and the appearance of slow−to−fast transition in the mobility of TEMPO.The critical molecular size of 1−alkanol for this steplike change in the slow-to-fast transition of TEMPO lies at N C ~5, below which the polarity and proticity aspects of the media become dominating factors.

Figure 1 .
Figure 1.(A) Glass−to−liquid transition temperature Tg of 1−alkanols as a function of the molecu size expressed by the number of C atoms in the chain, NC.Two fits of the Tg values from the DM [20,26] and DTA data sets [22] via the PL equation (Tg = AM α ) are included, (B) Comparison of t Tg DTA values with the empirical rule: Tg* = (2/3) Tm.

Figure 1 .
Figure 1.(A) Glass−to−liquid transition temperature T g of 1−alkanols as a function of the molecular size expressed by the number of C atoms in the chain, N C .Two fits of the T g values from the DMS [20,26] and DTA data sets [22] via the PL equation (T g = AM α ) are included, (B) Comparison of the T g DTA values with the empirical rule: T g * = (2/3) T m .
number of C atoms in chain T m = CM γ = 8.41M 0.705 r = 0.991

Figure 3 .
Figure 3.The Tm/Tg, TX/Tg and Tm/TX ratios of 1-alkanols as a function of the molecular size expressed by the number of C atoms in the chain, NC.

Figure 2 .
Figure 2. The melting temperature T m of 1-alkanols as a function of the molecular size expressed by the number of C atoms in the chain, N C .Fit of the T m 's from the CAL data set from Ref. [18] via the PL equation T m = CM γ is included.

Figure 2 .Figure 3 .
Figure 2. The melting temperature Tm of 1-alkanols as a function of the molecular size expressed by the number of C atoms in the chain, NC.Fit of the Tm's from the CAL data set from Ref. [18] via the PL equation Tm = CM γ is included.

Figure 3 .
Figure 3.The T m /T g , T X /T g and T m /T X ratios of 1-alkanols as a function of the molecular size expressed by the number of C atoms in the chain, N C .
are included.

Figure 4 .
Figure 4.Viscosities for a series of 1-alkanols as a function of temperature together with the respective power law (PL) fittings given by Equation (3).The vertical lines in the same colors as the corresponding experimental points for each member of a series of 1-alkanols mark the melting temperatures (on the left) and the boiling points (on the right), with two extrema demonstrations for methanol (black points and lines) and 1-decanol (orange points and lines).Trends in T m and T b are shown by the two arrows at the bottom of the plot.

Figure 5 .
Figure5.Viscosity of a good glass-former 1-propanol over (A) a restricted temperature range from Tb down to slightly below Tm using the data sets summarized in Ref.[33] (Landolt-Börnstein Tabledata) and Ref.[34] (DIPPR data), and (B) an extraordinarily wide temperature range from Tb down almost to Tg with the addition data from Refs.[35][36][37] in the strongly supercooled liquid state, as well as from Ref.[38] in the liquid one, together with the best PL equation fitting.The original references marked, such as 1891T1 and 26M2, can be found in Ref.[33].

Figure 6 .
Figure 6.Dynamic crossover temperature TX of 1−alkanols as a function of the molecular size expressed by the number of C atoms in the chain NC.The fit of the TX values from VISC data via the PL equation of the form TX = BM β is included.

Figure 6 .
Figure 6.Dynamic crossover temperature T X of 1−alkanols as a function of the molecular size expressed by the number of C atoms in the chain N C .The fit of the T X values from VISC data via the PL equation of the form T X = BM β is included.
g., C2OH, extracted from fitting over the usual normal liquid state ranging T b −T m = 192 K, and over the whole accessible temperature range of 227 K [35] (T b −T min = 227 K), change by 4 K only.

Figure 7 .
Figure 7. Spectral parameter 2Azz' in a series of 1−alkanols as a function of temperature.The colors for the ESR data for the individual 1−alkanols are the same as for their viscosity data in Figure 4.The

Figure 7 .
Figure 7. Spectral parameter 2A zz' in a series of 1−alkanols as a function of temperature.The colors for the ESR data for the individual 1−alkanols are the same as for their viscosity data in Figure 4.The characteristic ESR temperatures T Xi slow , T 50G and T Xi fast are marked, and the thermodynamic temperatures T g DTA and T m CAL , as well as the dynamic one, T X , are depicted by the black, olive and blue lines, consistently with Figures 1, 2 and 6 and are discussed in the text in detail.

Figure 8 .Figure 8 .
Figure 8.Comparison of the characteristic ESR temperatures, T50G and TX1 fast , with the thermo namic and dynamic temperatures Tg DTA , TX VISC and Tm CAL , together with their corresponding PL Figure 8.Comparison of the characteristic ESR temperatures, T 50G and T X1 fast , with the thermodynamic and dynamic temperatures T g DTA , T X VISC and T m CAL , together with their corresponding PL fits.

Figure 9 .
Figure 9.Comparison of the ratios of the characteristic ESR temperatures, T50G and TX1 fast , with th dynamic and thermodynamic temperatures, TX or Tm, respectively, as a function of NC.
Figure10displays the anisotropic hyperfine constant, Azz' (100K), and the isotropic hyperfine constant, Aiso(RT), of the TEMPO as a function of the chain length in the serie of 1-alkanols studied.Our values of Aiso (RT) for TEMPO are quite consistent with the few

Figure 9 .
Figure 9.Comparison of the ratios of the characteristic ESR temperatures, T 50G and T X1 fast , with the dynamic and thermodynamic temperatures, T X or T m , respectively, as a function of N C .

Figure 10 .
Figure 10.Hyperfine constants of TEMPO Azz'(100 K) and Aiso (RT) in a series of ten 1−a function of NC.

Figure 10 .
Figure 10.Hyperfine constants of TEMPO A zz' (100 K) and A iso (RT) in a series of ten 1−alkanols as a function of N C .

2. 2 . 4 .
Connection of the Main Slow-to-Fast Motion Transition of the Spin Probe TEMPO with the Polarity, Proticity and Thermodynamic and Dynamic Transition Behaviors of 1−alkanols

2. 2 . 4 .
Connection of the Main Slow-to-Fast Motion Transition of the Spin Probe TEMPO with the Polarity, Proticity and Thermodynamic and Dynamic Transition Behaviors of 1−alkanols In Figures 8 and 9 in Section 2.2.2, we compare the characteristic ESR temperatures T 50G and T X1

1-alkanols Figure 2. The
[18]ing temperature Tm of 1-alkanols as a function of the molecular size expressed by the number of C atoms in the chain, NC.Fit of the Tm's from the CAL data set from Ref.[18]via the PL equation Tm = CM γ is included.
. J. Mol.Sci.2023, 24, x FOR PEER REVIEW 10 o characteristic ESR temperatures TXi slow , T50G and TXi fast are marked, and the thermodynamic temp atures Tg DTA and Tm CAL , as well as the dynamic one, TX, are depicted by the black, olive and blue lin consistently with Figs.1,2 and 6 and are discussed in the text in detail.

2 O Organic liquid media/TEMPO Onsanger reaction field model
. Test of the Griffith−Onsanger model for isotropic hyperfine constant, Aiso (RT), as a function of the polarization expression εr (RT) -1)/(εr (RT) + 1) of the Onsanger reaction field model for three types of media: apolar, such as benzene(BZ) H−donors, i.e., H