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

Abstract

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; T_50G ‘s and T_X1^fast ‘s are situated above the corresponding glass temperatures, T_g, and for the shorter members, the T_50G ‘s lie above or close to melting point, T_m, while the longer ones the T_50G < T_m relationship indicates that the TEMPO molecules are in the local disordered regions of the crystalline media. The T_50G ‘s and especially T_X1^fast ‘s are compared with the dynamic crossover temperatures, T_X^VISC = 8.72M^0.66, as obtained by fitting the viscosity data in the liquid n-alkanols with the empirical power law. In particular, for N_C > 6, the T_X1^fast ‘s lie rather close to the T_X^VISC resembling apolar n-alkanes [PCCP 2018,20,11145-11151], while for N_C < 6, they are situated in the vicinity of T_m. The absence of a coincidence for lower1-alkanols indicates that the T_50G 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.

1. 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, Δε_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 τ₃ 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 ų 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(CH₂)_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.

2. Results and Discussion

2.1. 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].

2.1.1. Thermodynamic Transitions in 1−alkanols

Figure 1 and Figure 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:

T_g = AM ^α

(1)

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., quasi-adiabatic calorimetry (QADC) [17,28], are considered to be more reliable, mainly because of the experimental complexity of DMS.

As for the melting transition of 1−alkanols, the same expression can be approximately used for the melting points:

T_m = CM ^γ

(2)

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.

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.

2.1.2. 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]. Figure 4, Figure 5 and Figure 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.

All the viscosity data for the series of the first ten 1-alkanols can be described by the power law (PL) equation:

$${\eta }_{}\left(T\right)={\eta }_{\infty }{\left[\frac{\left(T-T_X\right)}{T_X}\right]}^{-\mu }$$

(3)

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.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. 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.

1-alkanol	M g/mol	Tg K	TX K	Tma K	Tba K	Azz’ (100K) b G	Aiso (RT) c G	μgd D	μle D	εrd -
MeOH	32.04	108.2 f 110.2 g 103 h 104.2 i	135.8 1352	175.2	338	37.87	16.46	1.70	2.70	33
EtOH	46.07	103.2 f 100.2 g 98.4 i 96 j 97 k	111 1115	158.9	351	36.81	16.30	1.69	2.81	25.3
1-PrOH	60.10	108 f 98 j 109 g 100 i 103 l 110 m	126.5 1399	146.8	371	36.15	16.23	1.68	2.87	20.8
1-BuOH	74.12	119 f 111.7 i 113.6 n 111 o 119 m	142	183.7	391	35.95	16.16	1.66	2.88	17.8
1-PentOH	88.15	120.1 f 124 g 120 i 126.1 l 127.4 m	168	194.8	411	35.9	16.05	1.70	2.97	15.1
1-HxOH	102.18	125 f 138 g 129.9 i 135 m	178	224.4	430	35.75	15.91	1.65	2.87	13.0
1-HptOH	116.20	123 f 143 g 141.2 i 141.9 m	199.7	239	449	35.60	15.88	1.71	2.99	11.75
1-OctOH	130.23	149 g 149.9 i 148.3 m	225.4	258.1	468	35.45	15.83	1.68	2.90	10.30
1-NonOH	144.25	153 i 154.4 m	236	268	487	35.25	15.75	1.60	2.73	8.83
1-DecOH	158.28	(160.1) m	239	279	501	35.15	15.70	1.60	2.70	7.93

^a Ref. [18]; ^b uncertainty = 0.05 G; ^c uncertainty = 0.03 G; ^d Ref. [33]; ^e Ref. [39]; ^f Ref. [19]; ^g Ref. [20]; ^h Ref. [21]; ⁱ Ref. [22]; ^j Ref. [23]; ^k Ref. [24]; ^l Ref. [25]; ^m Ref. [26]; ⁿ Ref. [27]; ^o Ref. [28].

Table 1. Basic physical properties of investigated 1-alkanols.

1-alkanol	M g/mol	Tg K	TX K	Tma K	Tba K	Azz’ (100K) b G	Aiso (RT) c G	μgd D	μle D	εrd -
MeOH	32.04	108.2 f 110.2 g 103 h 104.2 i	135.8 1352	175.2	338	37.87	16.46	1.70	2.70	33
EtOH	46.07	103.2 f 100.2 g 98.4 i 96 j 97 k	111 1115	158.9	351	36.81	16.30	1.69	2.81	25.3
1-PrOH	60.10	108 f 98 j 109 g 100 i 103 l 110 m	126.5 1399	146.8	371	36.15	16.23	1.68	2.87	20.8
1-BuOH	74.12	119 f 111.7 i 113.6 n 111 o 119 m	142	183.7	391	35.95	16.16	1.66	2.88	17.8
1-PentOH	88.15	120.1 f 124 g 120 i 126.1 l 127.4 m	168	194.8	411	35.9	16.05	1.70	2.97	15.1
1-HxOH	102.18	125 f 138 g 129.9 i 135 m	178	224.4	430	35.75	15.91	1.65	2.87	13.0
1-HptOH	116.20	123 f 143 g 141.2 i 141.9 m	199.7	239	449	35.60	15.88	1.71	2.99	11.75
1-OctOH	130.23	149 g 149.9 i 148.3 m	225.4	258.1	468	35.45	15.83	1.68	2.90	10.30
1-NonOH	144.25	153 i 154.4 m	236	268	487	35.25	15.75	1.60	2.73	8.83
1-DecOH	158.28	(160.1) m	239	279	501	35.15	15.70	1.60	2.70	7.93

^a Ref. [18]; ^b uncertainty = 0.05 G; ^c uncertainty = 0.03 G; ^d Ref. [33]; ^e Ref. [39]; ^f Ref. [19]; ^g Ref. [20]; ^h Ref. [21]; ⁱ Ref. [22]; ^j Ref. [23]; ^k Ref. [24]; ^l Ref. [25]; ^m Ref. [26]; ⁿ Ref. [27]; ^o Ref. [28].

It is shown that the PL equation is valid for a large number of organic molecular glass-formers 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:

T_X = BM ^β

(4)

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.

2.2. 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/1-alkanols. 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.

Finally, the mutual connections between the temperature parameters of the slow-to-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.

2.2.2. 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)

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.

2.2.3. 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 gaseous-phase 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].

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.

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_D²)], 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.

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 Figure 8 and Figure 9 in Section 2.2.2, we compare the characteristic ESR temperatures T_50G and T_X1^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 Figure 10, Figure 11 and Figure 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 step-like 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.

3. Experimental

3.1. Materials and Methods

A series of 1−alkanols ranging from methanol to 1−decanol, received from Sigma-Aldrich, Inc., St. Louis, MO, USA, was used as the model protic polar media. Our choice of this series stems from the fact that all of the used 1−alkanols are in the liquid state at room temperature, making spin probe system preparation easier. As an extrinsic particle, the spin probe 2,2,6,6−tetramethyl−1−piperidinyloxy (TEMPO) with a quasi-spherical shape and a relatively high dipole moment of μ_TEMPO = 3 D [45] was applied in the deoxygenated 1−alkanols at a very low concentration of ~5 × 10⁻⁴ M.

3.2. ESR

ESR measurements of the very diluted spin systems 1-alkanol/TEMPO were performed on the X-band Bruker–ER 200 SRL spectrometer operating at 9.4 GHz with a Bruker BVT 100 temperature variation controller unit. ESR spectra were recorded after cooling at a rate ~− 4 K/min in a heating mode over a wide temperature range from 100 K up to 300 K, with steps of 5–10 K. To reach the thermal equilibrium, the sample was kept at a given temperature for 10 min before starting three spectra collections. The temperature stability was ± 0.5 K. The microwave power and the amplitude of field modulation were optimized to avoid signal distortion. The ESR spectra were evaluated in terms of the spectral parameter of mobility, 2A_zz’ (T), i.e., the z-component of the anisotropic tensor of the hyperfine interaction A(T), corresponding to the outermost peak separation of the triplet spectra of the spin probe of nitroxide type in a given medium, as a function of temperature and the subsequent determination of the spectral T_50G parameter [50,54]. This is the characteristic ESR temperature, at which 2A_zz’ reaches the conventional value of 50 Gauss (G). Additional characteristic ESR temperatures can be obtained, and used to describe in detail the slow-to-fast regime transition zones over more or less wide temperature intervals around T_50G, as well as in both slow and fast motion regimes: T_Xi ^slow, T_Xi ^fast [55,56,57]. In addition to the anisotropic hyperfine splitting parameter, A_zz’ (100 K), the isotropic hyperfine constant values, A_iso (RT), of the spin probe TEMPO, as a measure of its interaction with a given medium, were determined at room temperature under the fast motion condition in a low-viscosity media [50].

4. Conclusions

The spectral and dynamic behaviors of the spin probe TEMPO in a series of 1−alkanols ranging from methanol to 1−decanol, over a wide temperature range from 100 K up to 300 K, using electron spin resonance (ESR) are reported. For all of the alkanols, the main characteristic ESR temperatures connected with slow-to-fast motion regime transition, namely, T₅₀ and T_X1^fast, are situated above the corresponding glass temperatures, T_g, and for the first five shorter members, the T_50G values lie in the vicinity of the melting point, T_m, while for the longer ones, the T_50G < T_m relationship indicates that the TEMPO molecules are in the local disordered regions of the crystalline media. The T_X1^fast values are compared with the dynamic crossover temperatures, parametrized as T_X^VISC = 8.72M^0.66, which were obtained by fitting the viscosity data for the liquid 1−alkanols with the empirical power law. In particular, for N_C = 6–10, the T_X1^fast values lie relatively close to the T_X^VISC seen for apolar n-alkanes, while for N_C = 1–5, they are situated above the respective T_X^VISC values in the vicinity of T_m. The absence of such a coincidence for lower 1−alkanols indicates that the slow-to-fast motion transition is significantly influenced by the mutual interaction between the polar TEMPO and the protic polar medium, due to the increased polarity and proticity, which are destroyed at higher temperatures associated with the larger-scale solid-to-liquid transition.