Disentangling the Secondary Relaxations in the Orientationally

J. Phys. Chem. B 2010, 114, 6099–6106

6099

Disentangling the Secondary Relaxations in the Orientationally Disordered Mixed Crystals: Cycloheptanol + Cyclooctanol Two-Component System Julio C. Martıńez-Garcıá,† Josep Ll. Tamarit,*,† Luis C. Pardo,† Marıá Barrio,† Sylwester J. Rzoska,‡ and Aleksandra Droz-Rzoska‡ Group de Caracteritzacio´ de Materials, Department de Fı´sica I Enginyeria Nuclear, ETSEIB, Diagonal 647, UniVersitat Polite`cnica de Catalunya, 08028 Barcelona, Catalonia, Spain, and Institute of Physics, UniVersity of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland ReceiVed: January 11, 2010; ReVised Manuscript ReceiVed: March 10, 2010

The dynamics of the pure compounds and mixed crystals formed between cycloheptanol (cC7-ol) and cyclooctanol (cC8-ol) has been studied by means of broadband dielectric spectroscopy at temperatures near and above the orientational glass transition temperature. Both compounds are known to display at least one orientationally disordered (OD) phase of simple cubic symmetry, and within this phase, a continuous formation of mixed crystals was demonstrated in the past (Rute, M. A. et al. J. Phys. Chem. B 2003, 107, 5914). The dielectric loss spectra of cC7-ol and cC8-ol show, in addition to the well-pronounced R-relaxation peaks with a continuous temperature shift (characteristic of the freezing of the molecular dynamics), secondary relaxations (β and γ for cC8-ol and γ for cC7-ol) which are intramolecular in nature. The dynamics of several OD mixed crystals was recently studied (Singh, L. P.; Murthy, S. S. N. J. Phys. Chem. B 2008, 112, 2606), and surprisingly enough one of the secondary relaxations was not evidenced. We show here by means of a careful set of measurements for several mixed crystals and of a detailed analysis procedure the existence of the secondary relaxations for the mixed crystals. The results, moreover, doubtless reinforce the physical origin of each of the secondary relaxations. 1. Introduction Thermodynamic and relaxational properties of glass-forming materials are of fundamental importance for the understanding of molecular dynamics of diffusion and relaxation phenomena emerging from high above and below the glass transition temperature.1–4 Probably the most challenging duty for condensed matter physics concerns the understanding of the microscopic dynamics underlying the glass formation with the concomitant impressive increase of the time scale of molecular motions when lowering (increasing) the temperature (pressure). Such microscopic dynamics related with the cooperative rotational and translational motions can be characterized by means of dielectric spectroscopy due to the broad available dynamic range through the well-known R-relaxation appearing in the imaginarypartofthedielectricresponse,ε′′(ν),atlow-frequencies.3,4 Preceding the structural R-relaxation, faster processes are commonly found. Regardless of the high-frequency processes as that related to local (nonpropagating) vibrations and appearing as an excess in the vibrational density of states at around 1 THz (Boson peak)5,6 or the predicted (by the mode-coupling theory, MCT) β-fast relaxation process associated with a rattling motion of a particle in a cage formed by the surrounding particles,7 one of the most typical processes appearing at frequencies above the structural R-relaxation is the commonly referred to as Johari-Goldstein (JG) β-relaxation (or slow β-relaxation).8–14 This process has been shown to occur even in single rigid molecules, and it is generally ascribed to the notion of small angle restricted reorientations of all entities; according to the * Corresponding author. Phone: +34 934016564. Fax: +34 93401 18 3. E-mail address: [email protected]. † Universitat Polite`cnica de Catalunya. ‡ University of Silesia.

coupling model (CM), it is considered as the primitive relaxation.15,16 The JG β-relaxation can appear as a wing on the high-frequency side of the main R-relaxation, the so-called “excess wing” or simply as a pronounced and well-separated additional relaxation.17,18 Such a difference even gave rise to a controversial classification of glass-forming materials.12,19 In some glass-formers, additional loss peaks in the dielectric response show up because of the intramolecular degrees of freedom which can modify the dipole moment of the molecule.12,20,21 Such secondary relaxations ascribed to internal changes of molecular conformations can be merged with the concomitant and inherent relaxations previously described, and disentangling their origin is not an easy task but absolutely necessary if general theoretical approaches should or should not be ruled out.14,17,22,23 To reduce the degree of complexity of the glass transition, plastic crystals play a crucial role. Plastic crystalline or orientationally disordered (OD) phases, formed by pseudoglobular shaped molecules, are characterized by the existence of a regular lattice formed by the center of mass of the molecules which are disordered with respect to the orientational degrees of freedom.20,24–27 These materials give rise to an orientational glass (OG) on cooling in which only the orientational degrees of freedom are frozen. This is a unique situation, since supercooled liquids giving rise to structural glasses (SGs), which can be considered as canonical glassy systems regarding the number of experimental studies carried out so far, are influenced by both translational and orientational degrees of freedom. In this way, OGs are often considered as model systems for SG formers because of the appearance of many common features concerning the dynamics.25,26 It should be noted that an OG is an unstable state obtained by further cooling the supercooled (metastable) OD phase. It means then that a more stable ordered crystal exists, a scenario completely similar to that of SG.

10.1021/jp100270z  2010 American Chemical Society Published on Web 04/20/2010

6100

J. Phys. Chem. B, Vol. 114, No. 18, 2010

Low-molecular weight cycloalcohols are prototypical materials displaying OD phases.20,28–32 In particular, cyclooctanol (C8H16O, hereinafter referred to as cC8-ol) is a wellknown material displaying an OD phase for which dielectric relaxation phenomena have deserved great attention.28–38 Because of the appearance of several secondary relaxations (β and γ), in addition to the R-relaxation process, it was even considered as an “ideal model system” for studies of the glass transition and, consequently universal scaling relationships were applied to rationalize the excess wing.33,35,37,39 Nevertheless, it has been later demonstrated that the β- and γ-secondary relaxations do not obey such scaling and that the microscopic origin is purely intramolecular, hence losing their JG character.28,37,40 As far as the polymorphic behavior of cC8-ol is concerned, it exhibits a transition from the liquid state to the simple cubic (sc) OD phase I.29,32,37 On further slow cooling the OD phase transforms to an orientationally ordered state (phase II), in which the R-relaxation corresponding to the dipolar disorder is absent. Such a transition can be bypassed by a relatively fast cooling from the OD phase, which enables us to obtain the corresponding OG state below Tg (between 142 and 172 K).27–30,32–38 On heating up above the glass transition, the supercooled OD phase remains (metastable) until about 200 K, where cC8-ol transforms to the orientationally ordered phase II. Details of the polymorphic behavior of cC8-ol have been largely discussed.29 As for the additional β- and γ-relaxation processes in cC8-ol, it has been demonstrated that they also show up in the lowtemperature ordered phase II, with the same relaxation time for a given temperature, and thus they have been ascribed to the conformations of the ring (β-relaxation) and to those (axial and equatorial, γ-relaxation) adopted by the polar OH group with respect to the carbon atom on which the group is bonded.32,37 It is worth noting that the existence of such a conformational disorder has been claimed as the origin of the difficulty to reach the low-temperature ordered phase for many OD phases formed by molecules with intrinsic conformational degrees of freedom.41,42 Cycloheptanol (cC7-ol) attracted far less attention probably because of the existence of two OD and two low-temperature ordered phases.29,31,38,43,44 On cooling from the liquid state the simple cubic OD phase I appears and can be readily supercooled, giving rise to an OG. On the contrary, the tetragonal OD phase II can be hardly supercooled, although some authors reported a glass transition temperature of the corresponding glass state from an extrapolation of the dielectric data.31,38 One of the striking differences between cC7-ol and cC8-ol concerning the relaxation processes appearing in their simple cubic OD phases is that the former shows, in addition to the R-relaxation, only one secondary fast process, which according to the molecular conformational disorder is ascribed to the axial and equatorial orientations of the -OH group and by analogy with cC8-ol is called γ-relaxation.30,31,38 It has been reported that cC7-ol and cC8-ol mixtures form continuous simple cubic (sc) OD mixed crystals (cC7-ol)1-X(cC8ol)X for the whole composition range.29 The OD phase for such mixed crystals does not transform into a crystalline phase at low temperatures, and thus OGs are easily obtained on cooling. Figure 1 displays the melting phase diagram together with the variation of the glass transition temperature as a function of the mole fraction.29 Recently, the dynamics of the OD mixed crystals was analyzed for a set of concentrations, nicely reinforcing the isomorphic relationship between the OD phase I of pure components.30 The properties of the dynamics

Martıńez-Garcıá et al.

Figure 1. Equilibrium melting phase diagram (L + OD(I)) and OG transition temperatures obtained from X-ray diffraction29 (b) and from dielectric spectroscopy (4).

concerning the R-relaxation process evolve continuously as a function of mole fraction, but surprisingly enough, the scenario of the secondary (β and γ) relaxations is strongly modified. More specificly, the fastest γ-process is observed whatever the mole fraction is, but the β-process seems to disappear even for mole fractions with a high content of cC8-ol. This experimental finding could cast doubts concerning the intramolecular character of such a β-relaxation which seemed to be well-stated from previous works.28,31,32,37 It is worth noting that the dynamics of mixtures opens new possibilities to disentangle the character of secondary processes because by mixing (i) the dipole-dipole interactions are modified (in a continuum way by changing the concentration) and (ii) the perturbation of the possible anisotropies of the host lattice is due to the change of the intermolecular constraints.13,45–49 The results presented in this work focus on the issue of the appearance of the secondary relaxations for the OD (cC7ol)1-X(cC8-ol)X mixed crystals and try to make clear if they are concomitant with those found for pure components or, on the contrary, if a change of the effects of multiple-molecule dynamics and intermolecular coupling or a change in the hydrogen bonding scheme can induce their disappearance, as claimed for the β-relaxation in a preceding work.30 2. Experimental Section Cyclooctanol and cycloheptanol were obtained from Acros Organics with purities higher than 99%. Details for the purification of pure compounds and preparation of mixed crystals were fully detailed in ref 29. Relaxation times were measured by means of broadband dielectric spectroscopy. The measurements were performed with a Novocontrol R analyzer spectrometer (10-2 Hz up to 107 Hz) and a Novocontrol BDS 80 (106 Hz up to 109 Hz), both equipped with a Quatro temperature controller using a nitrogen-gas cryostat and with a temperature stability at the sample around 0.1 K. Worth stressing is the large number of experimental points, with a density per decade of about 14. Dielectric relaxation times τ were determined as the reciprocal of 2πfp, where fp is the frequency maximum of the primary relaxation dielectric loss curves. The frequency range of the measurements was circumscribed to 10-2 Hz up to 107 Hz for the mixed crystals, while high-frequency (up to 109 Hz) measurements were performed for pure compounds. Samples were located into parallel-plate stainless steel capacitors with electrodes separated by 50 µm thick silica spacers. The primary dielectric loss curves of the R-relaxation process were fitted according to the Havriliak-Negami phenomenological equation:50

Secondary Relaxations in OD Mixed Crystals

ε*(ν) ) ε′(ω) - iε′′(ω) ) ε∞ +

{

εs - ε∞ (1 + (i2πντ)RHN)βHN

J. Phys. Chem. B, Vol. 114, No. 18, 2010 6101

}

(1)

The secondary relaxations at high-frequencies were fitted according to a Cole-Cole function (0 < RHN e 1, βHN ) 1 in eq 1),51 to keep the number of parameters to a reasonable level. To account for the quality of the fits, a key point for the goals of this work, the commonly accepted method is to minimize the squared distance between experimental values and those obtained by the proposed fitted model, that is, the function

χ2 )

n

(Yiexp - Yimod)2

i)1

σi2

∑

(2)

are the where n is the number of experimental points, Yexp i experimental values with a σi error, and Yimod are the values obtained by the fitted model. Nevertheless, such a function of merit is dependent on the number of independent parameters appearing in the selected model, making then hardly comparable fits between models with a different number of parameters. To solve such a model-selection problem, a reduced χ2 is defined as:

χr2 )

χ2 n-m

(3)

where m is the number of fitted parameters and, thus, n - m is the number of degrees of freedom. 3. Results and Data Analysis 3.1. Dynamics of OD Phases of Pure Compounds. Figure 2 shows examples of the dielectric loss spectra of cC8-ol (A) and cC7-ol (B) for a set of temperatures in the supercooled sc OD phases. In addition to the well-pronounced R-relaxation peaks with a continous temperature shift (characteristc of the freezing of the molecular dynamics), secondary relaxations show clearly up. The combination of the HN function for the R-relaxation process and CC functions for the secondary process (β and γ for cC8-ol and γ for cC7-ol) provided more than acceptable fits with a very good physical consistency for the obtained parameters. The fitting procedure was also tried by superimposing the Rand β-processes in the time domain (product ansatz by Williams)52 together with the addition of the γ-process in the frequency domain, but the results were virtually the same. Fits were performed by means of the Fabada software.53 Figure 3 shows the relaxation times for the different processes versus the reciprocal of the temperature (Arrhenius plot). As for the R-relaxation, with the exception of the liquid phases, it clearly exhibits distinct non-Arrhenius behavior, and thus the empirical Vogel-Fulcher-Tammann (VFT) function was used.50 This function can be written as

τ ) τo exp[DTo /(T - To)]

(4)

where τo is a prefactor of the order of the molecular vibrations, To is the temperature associated with the estimation of the ideal glass transition, and D (strength parameter) is a measure of the

Figure 2. Double logarithmic representations of dielectric loss spectra of cC8-ol (A) and cC7-ol (B) at several representative temperatures. Black solid lines are fits with the sum of a HN and one (cC7-ol) or two (cC8-ol) CC functions. The dotted lines show the CC parts of the fits for the β- and γ-relaxation processes. The black dotted line of the cC8-ol spectrum at T ) 174 K shows an example of the fits by using the product ansatz by Williams.52,53

fragility for the given temperature domain. Within the frame of the strong-fragile classification by Angell54 the high values of D classify the OGs obtained from phases I of cC8-ol and cC7-ol as strong glasses (see Table 1). It should be noted the relaxation times for phases I are not available for the whole temperature range, because of the irreversible transition to phases II for both cases, as previously stated in previous works.32,33,36,37 As far as the β-relaxation of cC8-ol is concerned, it is worth noting that the characteristic time difference from the R process increases upon decreasing temperature, enabling the β-relaxation times to be unambiguously determined in the former temperature range. On the contrary, the γ-relaxation times for both cC8-ol and cC7-ol glass formers are quite enough far away from the preceding (R and β) processes. For all of the secondary processes the relaxation times against temperature follow an Arrhenius law (τ ) τo exp(Ea/RT), R being the universal gas constant and Ea the activation energy) as evidenced in Figure 3. The fitted characteristic parameters are summarized in Table 1. 3.2. Dynamics of OD Phase I of Mixed Crystals. The number of dynamics studies on OD phases is relatively limited because of experimental problems in finding systems which give easily rise to glass formers (OGs) avoiding the irreversible transition to the low-temperature more ordered phase, as it has been shown for cC8-ol and cC7-ol OD phases I.55,56 Fortunately, this inconvenience does not appear for the OD mixed crystals phase I sharing cC8-ol and cC7-ol for the whole composition range, owing to the isomorphism relationship between that phase of the pure components and the appearance of the OG state.

6102



Figure 4. R-relaxation time as a function of the reciprocal of temperature for the pure compounds and mixed crystals. The inset displays the fragility index as a function of the mole fraction. Dotted lines correspond to the VFT fits according to eq 4.

Figure 3. Arrhenius plots of the dielectric relaxation times of pure components cC8-ol (A) and cC7-ol (B) for the R-(O), β-(0), and γ-()) relaxation processes. R-relaxation times for the different phases are denoted by colors: blue, liquid phase; green, phase I; and magenta, phase II of cC7-ol.

TABLE 1: Characteristic Parameters of the r-Relaxation Process According to the VFT Fits X

T0/K

D

log[τo/s]

m

Tg/K

0 0.26 0.43 0.61 0.74 0.86 0.91 1

68 ( 2 65 ( 2 66 ( 1 57 ( 2 70 ( 2 73 ( 2 72 ( 1 58 ( 2

36 ( 1 47 ( 2 44 ( 2 68 ( 2 51 ( 1 50 ( 2 51 ( 2 77 ( 2

-(12.49 ( 0.76) -(13.80 ( 0.97) -(13.32 ( 0.87) -(15.04 ( 0.94) -(14.64 ( 0.73) -(14.95 ( 0.89) -(15.67 ( 0.82) -(16.14 ( 0.82)

28 ( 2 27 ( 1 28 ( 2 27 ( 1 29 ( 2 30 ( 1 31 ( 1 28 ( 1

140 ( 1 148 ( 2 149 ( 2 157 ( 2 162 ( 2 167 ( 1 166 ( 1 165 ( 2

Thermodynamic and structural properties of the mixed crystals were previously studied with detail.29 For (cC7-ol)1-X (cC8-ol)X OD mixed crystals the dielectric loss spectra were fitted by assuming the existence of the ubiquitous R-relaxation process (at T > Tg) and one or two secondary processes to disentangle their existence by means of the χr2 function of merit. Figure 4 depicts the R-relaxation times as a function of the reciprocal of temperature for the whole set of studied mixed crystals together with those of pure compounds for the sc OD phase I. It clearly evidences the continuous change of the relaxation time as a function of the mole fraction, supporting the conjecture that isomorphism between phases I of cC7-ol and cC8-ol involves also the dynamic behavior. The evidence of the secondary relaxations strongly depends on the mole fraction and on the temperature domain. For the γ-relaxation, it clearly appears for the whole temperature range (within the ubiquitous limit of the available frequency domain). Nevertheless, β-relaxation could be disentangled only for mole fractions with X g 0.74, while for smaller mole fractions the

Figure 5. Function of merit obtained from the fits of dielectric loss spectra for X ) 0.61 (A) and X ) 0.86 (B) by assuming the existence of one (Rγ) or two (Rβγ) secondary relaxations in addition to the primary R-relaxation. Insets display an example in the low-temperature domain for each composition.

applied fitting procedure gave better results for the whole temperature range when only two processes (R and γ) instead of three (R, β, and γ) were hypothesized. Figure 5 displays the results for X ) 0.61 (A) and X ) 0.86 (B). For the low-temperature range of the mixed crystal with X ) 0.61 (Figure 5A) the data analysis by means of χr2 reveals that the introduction of an additional third relaxation process is completely fictitious and thus that only R- and γ-relaxation processes are present. On the contrary, for mixed crystals with X g 0.74 (see Figure 5B for X ) 0.86) the presence of the


Figure 6. Dielectric strengths for the R-(0), β-(O), and γ-(4) relaxation processes as a function of temperature for the low-temperature domain of the (cC7-ol)0.14 (cC8-ol)0.86 OD mixed crystal.

Figure 7. Arrhenius plot of the β-(full symbols) and γ-(empty symbols) relaxation times as a function of the inverse of temperature for the set of analyzed mixed crystals (mole fraction is given as a subindex for each relaxation process, and symbols are as in Figure 4). The R-relaxation times are given only for pure components as a guide for the eyes (cC8-ol, blue continuous line, and cC7-ol, green continuous line).

three relaxation processes clearly improves the description of the experimental data. To elucidate if such a mathematical result provides a coherent physical meaning, Figure 6 shows the variation with temperature of the strengths for the different processes. Although in general the strength of secondary β-relaxation processes decreases when decreasing temperature, several OGs have been reported with this anomalous behavior.40,42 The relaxation times obtained for the different processes as a function of temperature and for the set of studied mixed crystals are plotted in Figure 7. It should be noted that the nonArrhenius behavior for the R-relaxation and the Arrhenius behavior for the β- and γ-relaxations exhibited by the pure compounds remain for the mixed crystals. 4. Discussion A large number of works have been undertaken on the OD state from the investigation of single compounds to correlate macroscopic and microscopic properties.20 In general, these studies are carried out by measuring the dependence of some physical measurable properties as a function of one intensive variable, either temperature or pressure, to change the intermolecular interactions by modifying the short-range order. A different way to modify the molecular surroundings consists of

J. Phys. Chem. B, Vol. 114, No. 18, 2010 6103 the addition of a guest molecule in the host system, that is, in the host lattice when mixed crystals are concerned. Assuming that steric restrictions permit the substitution and that the guest molecule does not possess the symmetry elements of the host lattice, a symmetry simulation emerges by the generation of as many orientations as required by the crystallographic site symmetry of the host molecule.57 When speaking about the OD phases, in which a large number of possible energetically equivalent feasible orientations exist, the orientational disorder is already present in the host lattice, and thus, mixed crystal formation does not require an additional symmetry simulation. In addition, for molecular systems with an extensively hydrogenbonded scheme, as for cC7-ol and cC8-ol, the competition of hydrogen-like and isotropic interactions (due to the OD character of the phase) should collapse or, at the very least, be compatible in a spatial and time averaging.58,59 Moreover, several studies have concluded that the characteristic relaxation time of the overall tumbling in the OD phase in which hydrogen bonds are present is considerably higher when compared to similar molecules lacking those types of molecular interactions.20 As established in Rute et al.,29 the lattice parameter varies linearly with the mole fraction, which physically means that the steric conditions do not play a relevant role on the mixed crystal formation in the cC7-ol + cC8-ol two-component system. More specificly, the shape of the molecules does not influence the miscibility, and the steric conditions will be totally controlled by the molecular size which will modify the packing of the system and/or the lattice parameter, as it has been found for the (cC7-ol)1-X (cC8-ol)X mixed crystals29 and the other OD two-component systems.57–59 As for the dynamics in hydrogen-bonded systems, molecular dipoles may reorient after the hydrogen-bond broke and formed again with a different neighbor (enabling then the orientational diffusion). Because the breaking and reforming hydrogen bonds is a slower process than orientational diffusion, the dielectric relaxation time will be dominated by the former process. Thus, the results of Figure 4 would imply that the dynamics of the R-relaxation (meanly dominated by the hydrogen-bonded scheme) continuously changes from X ) 0 (cC7-ol) to X ) 1 (cC8-ol) without a noticeable change of the fragility (see inset in Figure 4). It has been shown that many canonical glass formers display adistributionofrelaxationtimeprobingthedynamicheterogeneity.2,60–62 More specifically, for systems displaying a hydrogen-bond scheme, the dilution with nonpolar solvents induces a “softening” of the intermolecular interactions, giving rise to a decrease in the dipolar correlation and, accordingly, a slower relaxation time than the fully hydrogen-bonded system.26 Figure 8 shows the HN exponents for pure as well as mixed crystals. It clearly emerges that in spite of the broadening of the R-relaxation when mixing due to the inherent concentration fluctuations, mixed crystals display a behavior close to that of the pure compounds. On this basis, there is not a reason to think that, in the OD phase, the averaged molecular interactions could induce a reduction of the conformational degrees of freedom of the molecules shared in the mixed crystal. As a consequence, the secondary relaxations coming from the change of the dipole orientation due to the set of active conformations in pure components should also appear in mixed crystals. Figure 7 displays the relaxation time for the β and γ secondary relaxations. As for the β-relaxation times as a function of the mole fraction (for the range they could be determined, 0.74 e X e 1), it can be seen from the figure that whatever the mole fraction all are very close to that of pure cC8-ol. It is worth

6104



Figure 8. RHN (A) and βHN (B) Havriliak-Negami exponents (eq 1) as a function of temperature for the set of studied mixed crystals.

Figure 9. Activation energy of the β- and γ-relaxation processes as a function of mole fraction of the (cC7-ol)1-X(cC8-ol)X mixed crystals.

noting that β-relaxation was attributed to the ring conformations of cC8-ol, and according to the results obtained here (Figure 7), it clearly appears that the relaxation time is almost the same for the molecular mixed crystals (until X ≈ 0.74). Such a result reinforces the intramolecular character of this relaxation process.32,37 Moreover, the thermally activated character of the β process of cC8-ol is kept constant for the whole mole fraction domain in which it has been detected (0.74 e X e 1). Figure 9 includes the activation energy as a function of mole fraction, and according to the experimental error limits, it appears more or less constant (see Table 2).

As far as the γ-relaxation is concerned, assigned to the -OH axial and equatorial conformations (thus intrinsically related to the hydrogen-bond scheme), it clearly shifts to higher frequencies with decreasing mole fraction at a given temperature. This γ process shows up for all of the mole fractions (see Figure 5) rather clearly, shifting to higher frequencies with increasing temperature as a thermally activated process (Figure 7). Moreover, the associated activation energy continuously changes between values of pure compounds (see Figure 9 and Table 2). This result confirms the intramolecular character of the γ-relaxation associated with the transitions between the two possible conformations of the -OH side group. On this basis, the introduction of a guest molecule (cC8-ol) in the host lattice (cC7-ol) when increasing the mole fraction will slightly perturb the strong and isotropic (due to the OD character of the phase) intermolecular interactions (via hydrogen bonds) in such a way that the dynamics of the γ process smoothly and continuously changes through the change of composition. Nevertheless, it should be noticed that, although the γ-relaxation for cC7-ol is faster than for cC8-ol (see Figure 7), for high mole fractions of cC8-ol (X ) 0.91, 0.86) the dynamics of the γ process is slightly slower than that for pure compound cC8-ol, while for mole fractions lower than X ) 0.86 γ-relaxation times fall into those corresponding to the pure components at a given temperature. We have not, at present, a clear explanation for such a detail, but it is obvious that such an effect should come from a special molecular short-range order in the hydrogen-bond map for this composition range and not from a possible confusion with the β-relaxation process, which for such a composition domain is clearly seen as an intermediate dynamical process between the mean R-relaxation and the fastest γ-relaxation. In spite of the evidence concerning the intramolecular character of the secondary relaxations for the pure components as well as for the mixed crystals, one may ask if one of these processes is a JG relaxation, that is, the secondary relaxation inherent to glass-forming materials.8 In spite of the still controversial discussion for such process, the coupling model (CM)9–12,14,15 proposes a correlation between the (secondary) β-relaxation time (τβ) and the Kohlrausch exponent (βKWW) of KWW the KWW stretched relaxation function (φ(t) ∝ exp(-t/τ)β ) with the primary relaxation time (τR) by means of the equation.

τβ ) tC1-β

KWW

KWW

τβR

(5)

with tC ) 2ps. Here 1 - βKWW(Tg) ) n is usually considered as the intermolecular coupling parameter: the greater the value of n, the greater the effect of intermolecular constraints leading to the many-molecule dynamics. Thus, according to CM, for a given value of τR the separation of the inherent JG peak (τβ)

TABLE 2: Experimental Parameters of the Thermally Activated (τ ) τoe-(Ea)/(RT)) β- and γ-Relaxation Processes and Comparison with the Activation Energy Obtained from Equation 6 for the β-Relaxation (EaJG)a β-relaxation βKWW(Tg)

X 0 0.26 0.43 0.61 0.74 0.86 0.91 1 a

0.62 ( 0.04 0.67 ( 0.04 0.64 ( 0.03 0.55 ( 0.03

Eexp a /eV

0.55 ( 0.08 0.50 ( 0.07 0.48 ( 0.08 0.47 ( 0.07 (0.51)b

γ-relaxation log[τo/s]

-(19.74 ( 0.73) -(16.49 ( 0.69) -(16.09 ( 0.48) -(15.84 ( 0.22) (-16.74)b

EJG a /eV

Eexp a /eV

log(τ∞)

0.49 ( 0.02 0.42 ( 0.04 0.39 ( 0.03 0.32 ( 0.02

0.32 ( 0.06 0.28 ( 0.05 0.26 ( 0.09 0.36 ( 0.07 0.37 ( 0.08 0.45 ( 0.04 0.46 ( 0.05 0.47 ( 0.02 (0.47)b

-(17.07 ( 0.24) -(15.72 ( 0.17) -(14.96 ( 0.21) -(17.24 ( 0.34) -(16.26 ( 0.39) -(15.54 ( 0.33) -(16.79 ( 0.26) -(18.09 ( 0.616) (-18.5)b

Values of the stretched exponent βKWW used for the application of eq 6 are given. b Values from ref 37.


J. Phys. Chem. B, Vol. 114, No. 18, 2010 6105

should be larger for greater values on the coupling parameter (n), that is, for smaller values of βKWW. The βKWW values as a function of composition were determined from the relation of Alegria et al.,63 βKWW ) (RHNβHN)(1)/(1.23), and are gathered in Table 2. It can be seen that βKWW slightly increases with decreasing the mole fraction and thus, according to the CM theory the β-relaxation time should increase with the mole fraction, while it can clearly seen in Figure 7 that it remains almost constant with the decrease of the mole fraction. Thus, within the premise of the validity of the CM and that the concentration fluctuations are neglected, it comes clear that the β process for cC8-ol and mixed crystals for which it appears is far from a description as a JG relaxation process. Moreover, if the β processes were to be described by the CM, the activation energy would be described by the relation64

Ea ) 2.303(2 - 17.7n - log τ∞) RTg

(6)

Table 2 gathers the activation energy values obtained for such a relation and clearly shows that they are far off of the values obtained experimentally in this work, confirming once again the intramolecular character of the β-relaxation. 5. Conclusions Dielectric loss spectra of cycloheptanol (cC7-ol) and cyclooctanol (cC8-ol) and their mixed crystals [(cC7-ol)1-X (cC7ol)X] in the OD simple cubic phase are presented. We have performed a detailed analysis of the dielectric loss spectra, showing clear evidence of the relaxation processes for the OGformer pure compounds. Results confirm those reported in earlier reports for the primary R- and intramolecular in nature secondary β- and γ-relaxations for cC8-ol and R- and γ-relaxations for cC7-ol.28,30,31,37,38 For mixed crystals, in addition to the inherent primary R-relaxation due to the freezing in the orientational disorder, it has been possible to disentangle the secondary relaxations. As for the β-relaxation process, it has been shown that it appears for a reduced mole fraction range (0.74 e X e 1) and that relaxation times are very close to those of pure cC8-ol, which demonstrates that it comes from the ring conformations of cC8-ol, as previously hypothesized, reinforcing then the intramolecular nature. The process, which is determined to be thermally activated, shows activation energy which slightly changes with the mole fraction. As for the γ-relaxation, assigned to the -OH axial and equatorial conformations, it shows up for all of the mole fractions and clearly shifts to higher frequencies with increasing temperature as a thermally activated process, the associated activation energy continuously changing between values of pure compounds. This result confirms the intramolecular character of the γ-relaxation associated with the transitions between the two possible conformations of the -OH side group, and its continuous variation (relaxation time and activation energy) evidences its intrinsic relation to the hydrogen-bond scheme. Acknowledgment. This work was supported by the Spanish Ministry of Science and Innovation (Grant FIS2008-00837) and the Catalan Government (Grant 2009SGR-1251). S.J.R. and A.D.-R. gratefully acknowledge the financial support from the Grant Ministry of Science and Higher Education for years 2009-2012 (Poland, Ref No. N202 231737). References and Notes (1) Capaccioli, S.; Shahin Thayyil, M.; Ngai, K. L. J. Phys. Chem. B 2008, 112, 16035.

(2) Roland, C. M.; Hensel-Bielowka, S.; Paluch, M.; Casalini, R. Rep. Prog. Phys. 2005, 68, 1405. (3) Ngai, K. L. J. Non-Cryst. Solids 2007, 353, 709. (4) Lukenheimer, P.; Schneider, U.; Brand, R.; Loidl, A. Contemp. Phys. 2000, 41, 15. (5) Ruocco, G. Nat. Mater. 2008, 7, 842. (6) Shintani, H.; Tanaka, H. Nat. Mater. 2008, 7, 870. (7) Go¨tze, W.; Sjo¨gren, L. Rep. Prog. Phys. 1992, 55, 241. (8) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (9) Ngai, K. L. Comments Solid State Phys. 1979, 9, 127. (10) Ngai, K. L. In Disorder Effects on Relaxational Properties; Richert, R., Blumen, A., Eds.; Springer: Berlin, 1994; p89. (11) Ngai, K. L. J. Phys.: Condens. Matter 2003, 15, S1107. (12) Ngai, K. L.; Paluch, M. J. Chem. Phys. 2004, 120, 857. (13) Capaccioli, S.; Ngai, K. L. J. Phys. Chem. B 2005, 109, 9727. (14) Lunkenheimer, P.; Pardo, L. C.; Ko¨hler, M.; Loidl, A. Phys. ReV. E 2008, 77, 031506. (15) Ngai, K. L. Phys. ReV. E 1998, 57, 7346. (16) Ngai, K. L. J. Phys.: Condens. Matter 2003, 15, 1107. (17) Schneider, U.; Brand, R.; Lunkenheimer, P.; Loidl, A. Phys. ReV. Lett. 2000, 84, 5560. (18) Ngai, K. L.; Lunkenheimer, P.; Leoń, C.; Schneider, U.; Brand, R.; Loidl, A. J. Chem. Phys. 2001, 115, 1405. (19) Kudlik, A.; Benkhof, S.; Blochowicz, T.; Tschirwitz, C.; Ro¨ssler, E. J. Mol. Struct. 1999, 479, 201. (20) Brand, R.; Lunkenheimer, P.; Loidl, A. J. Chem. Phys. 2002, 116, 10386. (21) Pathmanathan, K.; Johari, G. P. J. Phys. C 1985, 18, 6535. (22) Capaccioli, S.; Ngai, K. L. J. Phys. Chem. B 2005, 108, 1118. (23) Zuriaga, M.; Pardo, L. C.; Lunkenheimer, P.; Tamarit, J. Ll.; Veglio, N.; Barrio, M.; Bermejo, F. J.; Loidl, A. Phys. ReV. Lett. 2009, 103, 075701. (24) Parsonage, N. G.; Stavely, L. A. K. Disorder in Crystals; Clarendon: Oxford, 1978. (25) Jimenez-Ruiz, M.; Gonzalez, M. A.; Bermejo, F. J.; Miller, M. A.; Birge, N. O.; Cendoya, I.; Alegria, A. Phys. ReV. B 1999, 59, 9155. (26) Drozd-Rzoska, A.; Rzoska, S. J.; Pawlus, S.; Tamarit, J. Ll. Phys. ReV. B 2006, 74, 064201. (27) Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. (28) Lunkenheimer, P.; Brand, R.; Schneider, U.; Loidl, A. Philos. Mag. B 1999, 79, 1945. (29) Rute, M. A.; Salud, J.; Negrier, P.; Lo´pez, D. O.; Tamarit, J. Ll.; Puertas, R.; Barrio, M.; Mondieig, D. J. Phys. Chem. B 2003, 107, 5914. (30) Singh, L. P.; Murthy, S. S. N. J. Phys. Chem. B 2008, 112, 2606. (31) Puertas, R.; Salud, J.; Lo´pez, D. O.; Rute, M. A.; Diez, S.; Tamarit, J. Ll.; Barrio, M.; Pe´rez-Jubindo, M. A.; de la Fuente, M. R.; Pardo, L. C. Chem. Phys. Lett. 2005, 401, 368. (32) Puertas, R.; Rute, M. A.; Salud, J.; Lo´pez, D. O.; Diez, S.; van Miltenburg, J. C.; Pardo, L. C.; Tamarit, J. Ll.; Barrio, M.; Pe´rez-Jubindo, M. A.; de la Fuente, M. R. Phys. ReV. B 2004, 69, 224202. (33) Leslie-Pelecky, D. L.; Birge, N. O. Phys. ReV. Lett. 1994, 72, 1232. (34) Leslie-Pelecky, D. L.; Birge, N. O. Phys. ReV. B 1994, 50, 13250. (35) Dixon, P. K.; Wu, L.; Nagel, S.; Williams, B. D.; Carini, J. P. Phys. ReV. Lett. 1990, 65, 1108. (36) Shablakh, M.; Dissado, L. A.; Hill, R. M. J. Chem. Soc., Faraday Trans. 1983, 79, 383. (37) Brand, R.; Lunkeheimer, P.; Loidl, A. Phys. ReV. B 1997, 56, R5713. (38) Tyagi, M.; Murthy, S. S. N. J. Chem. Phys. 2001, 114, 3640. (39) Ngai, K. L. J. Phys.: Condens. Matter 1999, 11, A119. (40) Benkhof, S.; Kudlik, A.; Blochowicz, T.; Rossler, E. J. Phys.: Condens. Matter 1998, 10, 8155. (41) Kishimoto, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1978, 51, 1691. (42) Pardo, L. C.; Lunkenheimer, P.; Loidl, A. J. Chem. Phys. 2006, 124, 124911. (43) Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1972, 45, 1960. (44) Poser, U.; Schulte, L.; Wu¨rflinger, A. Ber. Bunsen-Ges. 1985, 89, 1278. (45) Prevosto, D.; Kessairi, K.; Capaccioli, S.; Lucchesi, M.; Rolla, P. A. Philos. Mag. 2007, 87, 643. (46) Power, G.; Vij, J. K.; Johari, G. P. J. Chem. Phys. 2007, 126, 034512. (47) Huang, W.; Richert, R. J. Chem. Phys. 2006, 124, 164510. (48) Kalinovskaya, O. E.; Vij, J. K. J. Chem. Phys. 2001, 114, 2718. (49) Grzybowska, K.; Grzybowski, A.; Zioło, J.; Paluch, M.; Capaccioli, S. J. Chem. Phys. 2006, 125, 044904. (50) Kremer, F.; Schoenhals, A. Broad Band Dielectric Spectroscopy; Springer: Berlin, 2003. (51) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341. (52) Bo¨hmer, R.; Diezemann, G.; Geil, B.; Hinze, G.; Nowaczyk, A.; Winterlich, M. Phys. ReV. Lett. 2006, 97, 135701.

6106


(53) Pardo, L. C.; Rovira-Esteva, M.; Busch, S.; Ruiz-Martıń, M. D.; Tamarit, J. Ll.; Unruh, T. arXiv:{0907.3711v3}[{physics.data-an}]; Fabada software (Fit Algorithm for Bayesian Analysis of Data), http://gcm.upc.edu/ members/luis-carlos/bayesiano (accessed 2009). (54) Angell, C. A. In Relaxations in Complex Systems; Ngai, K. L., Wright, G. B., Eds.; NRL: Washington, DC, 1985. (55) Salud, J.; Lo´pez, D. O.; Barrio, M.; Tamarit, J. Ll. J. Mater. Chem. 1999, 9, 909. (56) Tamarit, J. Ll.; Pe´rez-Jubindo, M. A.; de la Fuente, M. R. J. Phys.: Condens. Matter 1997, 9, 5469. (57) Barrio, M.; Lo´pez, D. O.; Tamarit, J. Ll.; Negrier, P.; Haget, Y. J. Mater. Chem. 1995, 5, 431.

Martıńez-Garcıá et al. (58) Lo´pez, D. O.; Salud, J.; Tamarit, J. Ll.; Barrio, M.; Oonk, H. A. J. Chem. Mater. 2000, 12, 1108. (59) Barrio, M.; Lo´pez, D. O.; Tamarit, J. Ll.; Negrier, P.; Haget, Y. J. Solid State Chem. 1996, 124, 29. (60) Richert, R.; Weinstein, S. Phys. ReV. Lett. 2006, 97, 095703. (61) Donth, E. Acta Polym. 1999, 50, 240. (62) Liu, W. J.; Bedrov, D.; Kumar, S. K.; Veytsman, B.; Colby, R. H. Phys. ReV. Lett. 2009, 103, 037801. (63) Alvarez, F.; Alegria, A.; Colmenero, J. Phys. ReV. B 1991, 44, 7306. Phys. ReV. B 1993, 47, 125. (64) Ngai, K. L.; Capaccioli, S. Phys. ReV. E 2004, 69, 031501.

JP100270Z

Disentangling the Secondary Relaxations in the Orientationally

Recommend Documents