Scaling the dynamics of orientationally disordered ...

Scaling the dynamics of orientationally disordered mixed crystals M. Romanini, J. C. Martinez-Garcia, J. Ll. Tamarit, S. J. Rzoska, M. Barrio, L. C. Pardo, and A. Drozd-Rzoska Citation: The Journal of Chemical Physics 131, 184504 (2009); doi: 10.1063/1.3254207 View online: http://dx.doi.org/10.1063/1.3254207 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/131/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Low-temperature properties of monoalcohol glasses and crystals Low Temp. Phys. 39, 468 (2013); 10.1063/1.4807147 Scaling of the hysteresis in the glass transition of glycerol with the temperature scanning rate J. Chem. Phys. 134, 114510 (2011); 10.1063/1.3564919 α -relaxation dynamics of orientanionally disordered mixed crystals composed of Cl-adamantane and CNadamantane J. Chem. Phys. 132, 164516 (2010); 10.1063/1.3397997 Study of molecular dynamics of pharmaceutically important protic ionic liquid-verapamil hydrochloride. I. Test of thermodynamic scaling J. Chem. Phys. 131, 104505 (2009); 10.1063/1.3223540 Universal scaling, dynamic fragility, segmental relaxation, and vitrification in polymer melts J. Chem. Phys. 121, 2001 (2004); 10.1063/1.1756856

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THE JOURNAL OF CHEMICAL PHYSICS 131, 184504 共2009兲

Scaling the dynamics of orientationally disordered mixed crystals M. Romanini,1 J. C. Martinez-Garcia,1 J. Ll. Tamarit,1,a兲,b兲 S. J. Rzoska,2,a兲,c兲 M. Barrio,1 L. C. Pardo,1 and A. Drozd-Rzoska2 1

Department de Física I Enginyeria Nuclear, Grup de Caracterització de Materials, ETSEIB, Diagonal 647, Universitat Politècnica de Catalunya, Barcelona 08028, Catalonia, Spain 2 Institute of Physics, University of Silesia, ul. Uniwersytecka 4, Katowice 40-007, Poland

共Received 16 July 2009; accepted 17 September 2009; published online 11 November 2009兲 The evolution of the primary relaxation time of orientationally disordered 共OD兲 mixed crystals 关共CH3兲2C共CH2OH兲2兴1−X关共CH3兲C共CH2OH兲3兴X, with 0 ⬍ X ⱕ 0.5, on approaching the glass temperature 共Tg兲 is discussed. The application of the distortion-sensitive, derivative-based procedure revealed a limited adequacy of the Vogel–Fulcher–Tammann parametrization and a superiority of the critical-like description ␶ ⬀ 共T − TC兲−␾⬘, ␾⬘ = 9 – 11.5, and TC ⬃ Tg − 10 K. Basing on these results as well as that of Drozd-Rzoska et al. 关J. Chem. Phys. 129, 184509 共2008兲兴 the question arises whether such behavior may be suggested as the optimal universal pattern for dynamics in vitrifying OD crystals 共plastic crystals兲. The obtained behavior is in fair agreement with the dynamic scaling model 共DSM兲 关R. H. Colby, Phys. Rev. E 61, 1783 共2000兲兴, originally proposed for vitrifying molecular liquids and polymers. The application of DSM made it possible to estimate the size of the cooperatively rearranging regions 共“heterogeneities”兲 in OD phases near Tg. © 2009 American Institute of Physics. 关doi:10.1063/1.3254207兴 I. INTRODUCTION

Puzzling artifacts associated with dynamics on approaching the glass temperature 共Tg兲 constitutes one of the major challenges for the modern condensed matter. The impressive changes in molecular dynamics concerning the extraordinary slowing down on cooling toward Tg have been described in terms of different models ranging from the thermodynamic fluctuations in a potential energy landscape,1,2 to soft-potential models,3,4 to theories based on the cooperativity of the motion,5,6 as well as mode-coupling theory,7 spinglass theory,8 and theories based on frustration,9 among others. Notwithstanding no ultimate theoretical model for the glassy dynamics has been proposed so far. The mentioned approaches are based on different physical pictures but most often include the concept of cooperative rearranging regions 共CRR兲, first hypothesized by Adam and Gibbs in 1965.5 These regions are defined as subsystems which can rearrange their configuration with increasing cooperativity when approaching the glass transition temperature and almost independently of their environment upon sufficient thermal energy.10 The appearance of such regions may be considered as a hallmark of a hidden thermodynamic phase transition. In the Adam–Gibbs approach it is related to the ideal glass temperature via the Vogel–Fulcher–Tamman 共VFT兲 equation, namely,10

a兲

Authors to whom correspondence should be addressed. Tel.: ⫹34 93 4016564. FAX: ⫹34 93 4011839. Electronic mail: [email protected]. c兲 Electronic mail: [email protected]. b兲

0021-9606/2009/131共18兲/184504/6/$25.00

冋 册

␶共T兲 = ␶VFT exp o

D TT o , T − To

共1兲

where T0 is the VFT estimate of the ideal glass temperature, DT is the fragility strength coefficient. A similar relation is expected for the structural relaxation time, viscosity, electric conductivity, etc. The VFT equation is the key tool for portraying “dynamic” experimental data on approaching the glass transition. Notwithstanding, its validity cannot be considered as a proof of the link between the glass transition and a hypothetical underlying phase transition since it can be derived also from phase-transition free models.10 Moreover, in the last years, severe objections have been raised against the general validity of such description. It has been shown that comparable quality of fit of primary relaxation times can be reached using Bässler–Avramov11 or Garrahan–Chandler12 equations for which no singularity below Tg exists. One may expect that showing a superior parametrization via an equation similar to the one used for critical phenomena might be fundamental for linking the glass transition to a critical-like singularity. Formally, such parametrization was introduced by the mode-coupling theory, namely,7,13

␶ ⬀ 共T − TMCT兲−␾ .

共2兲

Unfortunately, this equation is valid for the high temperature domain T ⬎ TMCT + 20 K and time scales ␶ ⬍ ␶共TMCT兲 ⬃ 10−7⫾1 s Ⰶ ␶共Tg兲 ⬇ 100 s. Moreover, the power exponent ␾ is a function of coefficients describing absorption curves in the high temperature domain whereas for critical phenomena exponents are universal and depend on the dimensionality of the order parameter, space dimensionality, and/or the range of interactions. Probably, the only equation for portraying dynamics on vitrification and directly coupled to critical phe-

131, 184504-1

© 2009 American Institute of Physics

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nomena was introduced within the dynamic scaling model 共DSM兲, namely,14,15

␶ ⬀ ␰z ⬀

冉 冊 T − Tc Tc

−␾⬘=−␯z=−9

,

TA ⬎ T ⬎ Tg

T0 ⬍ TC ⬍ Tg ,

and 共3兲

where z = 6 is the dynamic 共critical兲 exponent and ␯ = 3 / 2 is the exponent describing the divergence 共at Tc兲 of the correlation length ␰ of CRR—“precritical” fluctuations. TA denotes the caging temperature which stands for the temperature above which all entities are moving without cooperative motions. In terms of critical phenomena this is the temperature at which the order parameter, defined as the fraction of the material that has enough free volume for rearranging motions, saturates after a continuous rise from its zero value 共at TC and below兲. The DSM description assumed the same universal critical-type description for any polymer melt or low molecular weight supercooled liquid. However, for the latter the validity of using rather the activated DSM equation was postulated as the preferable one, namely,14,15

␶ ⬀ ␶0

冉 冊 冉 冊 T − Tc Tc

−␾⬘

T0 ⬍ TC ⬍ Tg .

exp

Elow , RT

T ⬎ Tg

and 共4兲

Here the Arrhenius term is the same as the one appearing for the behavior in the glass state, i.e., for T ⬍ Tg. Despite its enormous attractiveness, the DSM description 关Eqs. 共2兲 and 共4兲兴 was not accepted by the glass-transition research community, mainly due to the fact that it did not describe experimental data as declared in the DSM paper.14,15 Worth recalling here is the critical state-of-the-art analysis by Richert,16 based on the same set of data as in Refs. 14 and 15. However recently, Drozd-Rzoska et al.17 showed that despite these results the DSM critical-like equations can have a general validity. The failures of the DSM model were due to the fact that the target system for such description was improperly identified, namely, it was suggested that Eq. 共3兲 should obey for polymers and Eq. 共4兲 for low molecular weight glass formers. It was indicated in Ref. 17 that Eq. 共2兲 can perfectly portray experimental “dynamic” data for supercooled glassforming systems where a single dominant element of symmetry exists. Consequently the basic DSM Eq. 共1兲 may be valid only for selected low molecular weight and polymeric glass formers, where the clear uniaxial symmetry of molecules exists. The validity of Eq. 共1兲 was shown also for vitrifying rodlike liquid crystals, colloidals, polymers, and the orientationally disordered 共OD兲 共plastic兲 phase of ethanol and spin-glass materials. Such symmetry constraint is not respected in the clear critical-like parametrization with an exponent of ␯ · z = 9.2⫾ 0.2 recently found for the OD phase of the 关共CH3兲2C共CH2OH兲2兴0.7关共CH3兲2C共CH2OH兲2兴0.3 mixed crystal 共for short NPA0.7NPG0.3兲.18 The OD phase for such a mixed crystal does not transform into a crystalline phase at a low temperatures and thus an orientational glass 共OG兲 is obtained on cooling.19,20 The OG state comes from the exclusive arrest of the orientational degrees of freedom, a sub-

stantial difference when compared to the structural glasses for which translational and orientational degrees of freedom are frozen. Nevertheless, it has been largely shown that dynamics of OD phases share many common features with liquid glass formers and that, in fact, the orientational degrees of freedom control almost completely the disorder of structural glasses.21 By a direct inspection of the chemical formulae of the NPA and NPG molecules, it is evident that both display a tetrahedral symmetry, thus far away from the required uniaxial symmetry. In addition, it is noteworthy that the data analysis carried out in these works was based on the same linearized derivative approach. This analysis evidenced for the first time the validity of the DSM model for a system displaying orientational disorder, for Tg ⬍ T ⱕ TB, where ␶共TB兲 ⬇ 10−7⫾1 s. The latter coincided with a hypothetical magic universal time-scale suggested for the dynamic crossover of molecular glass forming liquids.22 However, recently this idea has been strongly disregarded23,24 due to the fact that more careful analysis showed in fact the time scale spans from ␶共TB兲 ⬇ 0.2 ms in methanol25 to 50 ps in polymethacrylate.26 In spite of possible heterogeneities produced by the commonly found concentration fluctuations, the DSM described almost perfectly the relaxation time as a function of temperature for Tg ⬍ T ⬇ Tg + 100⬇ TB. Here we focus on the application of the DSM basic theoretical predictions in the homologous series of mixed crystals NPA1−XNPGX with 0 ⬍ X ⱕ 0.5 and investigate the possible existence of crossovers similar to those reported for the NPA0.7NPG0.3 mixed crystal on the basis of the linearized derivative analysis.27,28 We study in particular the dependence of such crossovers upon the chemical composition.

II. EXPERIMENTAL AND DATA ANALYSIS

NPA1−XNPGX mixed crystals were thermodynamically and structurally characterized in previous works.20 These mixed crystals are known to give rise to OGs in the composition range 0 ⬍ X ⱕ 0.5 when cooled at normal18 or high pressure.29 Samples were prepared by the same procedure described in Ref. 20. Figure 1 presents the glass transition temperatures for these materials obtained by means specific heat measurements.20 A well known artifact for liquid crystalline materials is the odd-even effect. For instance for probably the most classical liquid crystalline materials n-alkylcyanobipheneyls 共nCB兲 odd and even members of the homologous series follow different dependences of the evolution of the isotropic mesophase transition temperature, i.e., the clearing temperature TC共n兲. An issue worth further to test is some manifestation of such effect for the evolution of the glass temperature. Relaxation times were measured by means of broadband dielectric spectroscopy. The measurements were performed with a Novocontrol alpha analyzer spectrometer equipped with a Quattro temperature controller using a nitrogen-gas cryostat and with temperature stability at the sample around 0.1 K. Dielectric relaxation times ␶ were determined as the reciprocal of 2␲ f p, where f p is the frequency maximum of the primary relaxation dielectric loss curves. The frequency

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Scaling dynamics of disordered crystals

冋 册 冋 册 d ln ␶ d共1/T兲 =

−1/2

Ha R

−1/2

= 关Ha⬘兴−1/2

= 关共DTTo兲−1/2兴 − =A−

FIG. 1. Characteristic temperatures for the NPA1−XNPGX mixed crystals. Squares: Glass transition calorimetric 共C p兲 temperatures. For circle, red triangle, and green diamond symbols see text. For NPA the glass transition temperature was obtained from x-ray powder diffraction. Lines are guides for eyes.

range of the measurements was circumscribed to 10−2 Hz up to 10 MHz. Samples were located into a special parallel-plate stainless steel capacitor with electrodes separated by 50 ␮m thick silica spacers. It was shown in Ref. 27 that assuming the critical-like description 关Eq. 共2兲兴 the following equation can be obtained:

Ha⬘共T兲 =

冉 冊

d ln ␶ ␾ ⬘T 2 Ha共T兲 =R = , R d共1/T兲 T − TC

共5a兲

from which

T2/Ha⬘ = 共1/␾⬘兲T − 共TC/␾⬘兲 = BT − A.

共5b兲

The same occurs for the MCT model 关Eq. 共4兲兴, with ␾⬘ → ␾ and TC → TMCT. By displaying the experimental data in the form of Eq. 共5b兲, the range of validity of the critical-like Eq. 共2兲 can be obtained, together with optimal values for the phenomenological parameters. The same approach was used for testing validity of the VFT description, namely,27

关T0共DTT0兲−1/2兴 T

B . T

共6兲

The latter equation resembles the analysis proposed by Stickel and co-workers30,31 关d log10 ␶ / d共1 / T兲兴−1/2 versus 1 / T, although it was used solely for estimating the loci of the dynamic crossover between domains described by VFT equations with different sets of parameters. As shown in Refs. 27 and 28, the analysis employing Eqs. 共5b兲 and 共6兲 made it possible to avoid the arbitrariness which has to appear for direct fit with the VFT Eq. 共1兲 or DSM Eq. 共2兲 共Table I兲. Dielectric loss curves were fitted according to the Havriliak–Negami 共HN兲 phenomenological equation32 ␧ⴱ共␯兲 = ␧⬘共␻兲 − i␧⬙共␻兲 = ␧⬁ +

再

冎

␧s − ␧⬁ ␴ , ␣HN ␤HN − i ␧o2␲␯ 共1 + 共i2␲␯␶HN兲 兲

共7兲

the conductivity term being fitted from the imaginary part at low frequencies. III. RESULTS AND DISCUSSION

Figure 2 shows dielectric loss spectra of the NPA0.60NPG0.40 OD mixed crystal acquired at different temperatures upon cooling from room temperature. The inset displays the relaxation time as a function of the reciprocal of the temperature. In previous works concerning exclusively the NPA0.70NPG0.30 mixed crystal, the temperature dependence of the relaxation times was fitted according to the Cohen and Grest 共CG兲 four-parameter equation due to the extremely large frequency and temperature ranges of the measurements.33,34 Nevertheless, it was found that neither a CG model nor the VFT three-parameter equation are able to reproduce the results.18 Even though the frequencies reached in the present measurements are two decades smaller 共up to 107 instead of 109 Hz兲, we found that at least two regimes

TABLE I. Characteristic temperatures as a function of molar composition 共X兲 for the VFT and DSM fits. VFT 共Tg ⬍ T ⬍ TB兲

DSM

X

Tg共CG兲 共K兲

T0 共K兲

DT

␶o 共10−9 s兲

TC 共K兲

␹2

␾⬘

0.1 0.2 0.3 0.4 0.48 0.50

143.7 143.5 160 155.5 154.8 158.6

106⫾ 6 87⫾ 1 134⫾ 6 107⫾ 2 89⫾ 9 111⫾ 2

8⫾2 22⫾ 1 5 ⫾ 0.5 14⫾ 1 26⫾ 7 14⫾ 1

0.33 0.53 1.64 5.97 5.32 2.02

130 128 150 139.2 139.5 146.8

0.017 0.01 0.01 0.014 0.013 0.017

9.3 11.2 9.2 11.4 11.75 10.8

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Romanini et al.

FIG. 2. Relaxation dielectric loss curves for the NPA0.60NPG0.40 mixed crystal in the OD fcc phase from 249 to 173 K every 4 K and from 171 to 165 K every 2 K after subtraction of the electrical conductivity. Inset: Relaxation time as a function of the reciprocal of temperature for the mixed crystal as well as the fits for the CG and the two VFT functions 共see text兲. Dashed line at 186 K indicates the crossover temperature used for the fits with the VFT functions while dashed lines at low temperature point out the different glass transition temperatures according to the different fits.

exist each described by a distinct VFT equation. The evidence for this is shown in Fig. 3 for the NPA0.60NPG0.40 and NPA0.50NPG0.50 OD mixed crystals. By applying a derivative-based analysis using Eq. 共6兲, two temperature domains are identified, which implies the existence of two VFT

FIG. 3. Derivative-based analysis of the temperature variation of the dielectric relaxation according to Eq. 共6兲, displaying the crossover between two distinct ranges of validity of the VFT model 关Eq. 共1兲兴. The parameter DT and To obtained for NPA0.50NPG0.50 共top panel兲 and NPA0.60NPG0.40 共bottom panel兲 OD mixed crystals are also shown. Insets: ␣ and ␣␤ exponents for the low- and high-frequency wings characterizing the distribution of relaxation times according to the HN equation 关Eq. 共7兲兴.

J. Chem. Phys. 131, 184504 共2009兲

FIG. 4. Derivative-based analysis of the temperature variation of the dielectric relaxation according to the critical-like behavior 关Eq. 共5b兲兴 for the various molar fraction of NPA1−XNPGX mixed crystals.

regimes separated by a crossover temperature 共TB兲. This crossover temperature puts apart the two temperature domains for the two required VFT equations 共see inset in Fig. 2 for the case of the NPA0.60NPG0.40 mixed crystal兲. It is noteworthy that on cooling in subsequent dynamical domains the fragility strength coefficient DT decreases while the value of To increases. This behavior is opposite to the one usually occurring in supercooled liquids and polymers.27,35 However, a similar behavior was observed in the isotropic phase of rodlike liquid-crystalline compounds when approaching the continuous isotropic-nematic phase transition.27 In order to check the validity of the critical-like behavior predicted by the DSM theory 关Eq. 共1兲兴, we applied a derivative-based analysis using Eq. 共5b兲. Figure 4 displays the quantity T2 / Ha⬘ as a function of T. The distortion sensitive analysis reveals a clear preference for the critical-like description 关Eq. 共1兲兴 over the VFT parametrization. A single critical like dependence is able to portray the critical-like behavior expressed by Eq. 共1兲, as it clearly emerges from the observed linear dependence, in agreement with Eq. 共5b兲, thus corroborating the validity of the DSM in the temperature range Tg ⱕ T ⬇ Tg + 80 for these OD mixed crystals. The critical-like behavior is described by an exponent g = ␯ · z ⬇ 10⫾ 1, close to the universal value 共␾⬘ = ␯ · z = 9兲 proposed by Colby. The DSM seems thus to describe quite well the dynamics of OD phases for temperatures lower that those for the dynamical domain close to the glass temperature. The half width of the ␣-relaxation peak clearly exceeds the width of a simple Debye relaxation process and, as it is inferred from a simple inspection of Fig. 2, the width as well as the asymmetry of the peak increase with decreasing temperature. To account for both experimental features, dielectric losses were fitted according to the empirical Havriliak– Negami Eq. 共7兲. The insets of Fig. 3 display the variation with temperature of the HN coefficients for the low-共␣兲 and high-共␣␤兲 frequency wings for two mole fractions as speaking examples. Two striking features show up from these parameters. On one hand, around 186 and 200 K for NPA0.60NPG0.40 and NPA0.50NPG0.50 mixed crystals, respectively, there are dynamic crossovers in the distribution of the relaxation time which, for each composition, are virtually

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found at the same temperature as the crossovers obtained from the derivative-based analysis 关Eq. 共5b兲兴. On the second hand, exponents for the HN equation seem to approach the value 1/2 claimed to be universal to temperatures close to Tg.36These results extend for the whole studied concentration range 共see crossover temperatures in Fig. 1 as a function of composition兲. In addition, the crossover for each mixed crystal is found to be for a relaxation time close to 10−3⫾1 s regardless the composition of the mixed crystal. As it has been pointed out by Rössler and co-workers,37 the crossover for OGs can be found much closer to Tg as compared to most structural glass formers for which it commonly occurs at around 10−8 – 10−9 s, whereas for OD phases it may appear at quite different time scales. It is noteworthy that for chloroadamantane-cyanoadamantane mixtures they reported a crossover at around 10−3 s from the data provided by Decressain et al.,38 virtually the same that the crossover relaxation time found in this work for the mixed crystals. The broadness of the ␣-relaxation process clearly evidenced by ␣ and ␤ parameters of the HN equation 共see insets in Fig. 3兲 vary with temperature and are compositiondependent. It indicates then that the William–Watts polarization function ␸共t兲 corresponds to a stretched exponential function. The nonexponential character of the relaxation distribution times could be caused by the heterogeneities produced by the concentration fluctuations which are the consequence of a statistic 共chemical兲 disorder and not induced by dynamic correlations. Nevertheless, results show that regardless of the possible existence of heterogeneities due to concentration fluctuations, the crossover temperatures obtained from the derivative-based analysis and from the fits of the phenomenological HN function are in fair agreement for the whole concentration range studied. This paper and Refs. 18 and 29 indicate that the criticallike description with the power exponent close to DSM predictions can yield fairly well parametrization for orientationally vitrified systems. We would like to stress that we do not discuss issues related to the general validity of the DSM theory, originally proposed for supercooled molecular liquids and polymers. Notwithstanding we would like to recall that the underlying hypothesis of DSM is the existence of cooperative dynamics through the CRRs. Accordingly, the length scale ␰ of cooperative motion of all glass formers appears to have universal temperature dependence 关Eq. 共2兲兴, which, assuming ␯ · z ⬇ 9, can be written as15

␰共T兲 = ro

冉 冊 T − Tc Tc

−3/2

,

共8兲

where ro 共⬇1.1 Å兲39,40 is the value that the cooperative length scale would have if cooperative motion was still necessary, assumed at T = 2TC. On the basis of the experimental correlation found between the steepness index based fragility measure and 共Tg − Tc兲 / Tc, 共m ⬀ 关关Tg − TC兲 / TC兴−2/3兲 共Ref. 15兲 for a set of glass formers 共low molecular weight organics, polymers, inorganics, etc.兲 and with the definition of the fragility coefficient m = 关⳵ log10 ␶共T兲 / ⳵共Tg / T兲兴T=Tg, Eq. 共8兲 at T = Tg yields

FIG. 5. Fragility index calculated by Eq. 共9兲 from the CG fitting 共triangles兲 and from the relation 共Ref. 41兲 m ⬇ 16+ 590/ DT 共circles兲 as a function of the normalized difference between glass and critical temperatures. Dotted line corresponds to the slope of the correlation found in Ref. 15 for a set of glass formers, i.e., m ⬀ 共Tg − TC / TC兲−2/3. Errors are within the size of the symbols.

␰共Tg兲 ⬵ ro

冉 冊 m 14

9/4

共Å兲.

共9兲

Figure 5 displays the fragility coefficient as a function of the ratio between the glass transition temperature and the critical temperature TC for the OD crystal fcc NPA1−XNPGX mixed crystals. It can be seen that the relationship predicted between fragility and the scaled Tg − TC difference is fulfilled for these OD phases. By inserting the obtained fragility values into Eq. 共9兲, the correlation length at Tg共␰共Tg兲兲 is found to lie between 7–12 Å. Because the fcc lattice parameter of the mixed crystals is approximately 8.9 Å,20 this would imply that the cooperative rearranging dynamics in plastic crystals should be thought as short-range fluctuations with a spatial extent of roughly one unit cell. To the best of our knowledge, no experimental results have been published concerning cooperativity at the nanometer scale at the molecular glass transition, nor on the correlation length in plastic crystals.42 Nevertheless, molecular dynamics simulations for adamantane derivatives43 pointed out the existence of fluctuations on the same length scale as found here. This picture of CRR regions is strongly different from that emerging from other theories such as the random first-order transition,6 which predicts dynamically reconfiguring regions with larger size 共100–200 molecules兲, or the so-called “stringlike” motion coming from molecular dynamics simulations in structural glasses.44,45 As for the size of the CRRs in glass, a wide range of values can be found in the literature, but they commonly lie clearly above 1 nm.46–48 Nevertheless, most of the published work, as well as the one presented here, is model dependent and thus submitted to the validity of the initial hypothesis. Thus, the model-dependent predictions performed in this work concerning the size of CRR are waiting for nondependent model data analysis to be compared. IV. CONCLUSIONS

We have shown that the dynamical scaling model can perfectly account for the scaling exponent of the relaxation

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time as a function of temperature for all the OD mixed crystals studied by using the linearized derivative analysis, in spite of the lack of a molecular axial symmetry. The VFT focused derivative based analysis revealed two dynamical domains in tested OD mixed crystals. It is noteworthy that upon cooling the value of the fragility strength coefficient decreases in subsequent dynamical domains. In “classical” glass formers, namely, supercooled liquids and polymers, the opposite behavior occurs, i.e., the value of DT was smaller in the immediate vicinity of Tg. Such unusual sequence was already noted in the isotropic phase on LC materials27 and in earlier tests on OD crystals.18 For both cases this was associated with approaching the point of nearcontinuous phase transition at which the dynamics are influenced by pretransitional fluctuations. The same can be postulated for the materials tested in this paper. Although the hypothetical line of phase transitions is “hidden” for temperature tests under atmospheric pressure, it should emerge in pressure-temperature measurements. This paper shows that possible heterogeneities generated by concentration fluctuations are not responsible of the validity of DSM for OD phases. The exponent equal or close to 9 seems to be a general property for phases with only one kind of disorder, translational for liquid crystals, and orientational for OD phases. The perfect agreement with the DSM predictions allows us to apply the model to the determination of the correlation length of the CRRs. It clearly emerges that the present understanding of structural glass formers should be revisited for OD phases. In particular, the correlation length is comparable with the lattice parameter of the highsymmetry unit cell 共less than 1 nm兲 so that the correlated dynamics should be thought as short-range fluctuations. Based on the results presented here as well as on the results of Refs. 18, 27, and 49, the question arises if the simple quasiuniversal critical-like description offers an optimal description for ODICS, superior to the VFT parametrization used so far. Values of obtained power 共“critical”兲 exponent are close to the DSM universal exponent ␾⬘ = ␯z = 3 / 2 ⫻ 6 = 9 but a small and permanent increase on shifting within the homologous series occurs. Consequently, one may expect that studies in homologous series may appear to be important for understanding the molecular basis of the critical like parametrization, lacking so far. ACKNOWLEDGMENTS

This work was partly supported by the Ministry of Science and Innovation under Contract No. FIS2008-00837. S.J.R. and A.D-R gratefully acknowledges the financial support from the grant Ministry of Science and Higher Education for years 2009-2012 共Poland, Ref. No. N N202 231737兲. 1

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