Raman Spectroscopic Studies of Liquid Phase Ordering and

Oct 21, 2010 - UniVersität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria. ReceiVed: July 13, 2010; ReVised Manuscript ReceiVed: September...
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Raman Spectroscopic Studies of Liquid Phase Ordering and Dynamics for Solutions of ME6N Liquid Crystal: The Approach to Simple Molecule Behavior at High Dilutions Maria Grazia Giorgini*,† and Maurizio Musso‡ Dipartimento di Chimica Fisica ed Inorganica, UniVersita` di Bologna, Viale del Risorgimento 4, I-40136 Bologna, Italy, and Fachbereich Materialforschung und Physik, Abteilung Physik und Biophysik, UniVersita¨t Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria ReceiVed: July 13, 2010; ReVised Manuscript ReceiVed: September 28, 2010

We have measured the Raman isotropic profiles of the ν(C≡N) band at 2235 cm-1 for five solutions of ME6N (4-cyanophenyl-4′-hexylbenzoate) liquid crystal dissolved in CCl4 in the range from x ) 0.12 to 0.007 (x, mole fraction of ME6N) and then obtained the corresponding vibrational correlation functions, Cv(t), by time Fourier transformation. The increase with dilution of the dephasing times τv complies with the behavior of the nonmonotonic concentration dependence predicted by the fluctuation concentration model for this concentration range (x < 0.5). The interpretation of Cv(t) within the Kubo stochastic theory which, being based on the assumption that the environmental modulation arises from a single relaxation process, e-t/τc, applies to simple liquids, has proved to be inadequate except for the most diluted solutions where the environmental correlation time τc amounted to 1.16 ps. On the other hand, we have found that the vibrational correlation functions for these ME6N/CCl4 solutions comply, in the whole concentration range, with the approach proposed by Rothschild, which, being based on the assumption that the environmental modulation R is described by a stretched exponential decay e-(t/τ0) , is more appropriate for the interpretation of the vibrational correlation function arising from a distribution of relaxation processes caused, as in the present case, by the persistence of pseudonematic domains. With dilution the dispersion parameter R and the average correlation time τ0 progressively increases and decreases, respectively, and tend to converge to the values appropriate for simple liquids, as given by the Kubo theory, i.e., R to unity and τ0 to approximately 1.16 ps. The relaxation time probability distribution h(τ) progressively shrinks and shifts down with dilution. The evolution of R and τ0 parameters and, contextually, of h(τ) with dilution offers a complete picture of the way a complex liquid attains the condition of a simple one. 1. Introduction Spectral band shape analysis in molecular liquids performed in the time correlation function approach allows access to the time domain of the molecular processes occurring in this condensed phase of matter1-4 and provides, by modellistic interpretation of the time correlation function, the dynamical parameters and regimes for the correspondent relaxation processes. Both vibrational and orientational relaxation processes contribute to the Raman band shape; the achievement of an effective experimental separation of the vibrational and orientational time correlation functions through the VV-VH Raman polarization technique relies upon the occurrence of statistical independence of the two relaxation processes4 which, however, can be assessed only a posteriory. It turns out that, in simple liquids, a substantial statistical independence can hardly be reached since vibrational and orientational relaxation processes occur approximately in the same time window (from fractions to a few picoseconds),5-7 a fact which has exposed fluctuation spectroscopy to some criticism.4 The isotropic Raman band shapes directly provide, by Fourier transformation to the time domain, the vibrational time autocorrelation functions.4 For high frequency vibrational modes, such as the ν(C≡N) stretching in nitriles (around 2235 cm-1), * Corresponding author. E-mail: [email protected]. Phone: ++39 051 209 3701. Fax: ++39 051 209 3690. † Universita` di Bologna. ‡ Universita¨t Salzburg.

the contribution of vibrational energy relaxation process to the vibrational autocorrelation function can be largely excluded since the energy of this mode does not match the bath thermal energy. A contribution of the resonant vibrational energy transfer to the isotropic band shape can also be excluded since the ν(C≡N) oscillators, due to their low transition dipole, do not couple with each other. Therefore, only pure dephasing contributes to the vibrational relaxation of the ν(C≡N) stretching vibration. For simple liquids, the determination of the dynamical regime and characteristic time for the intermolecular interactions responsible for these relaxations is obtained by modeling the vibrational time autocorrelation functions with the band shape stochastic theory,2,4 which is based on the assumption of the Markovian character of the perturbation process, a feature which makes the perturbation relaxation describable as a single exponential decay. In complex liquids, such as liquid crystals, the statistical separation may be achieved naturally since the orientational relaxation process, especially for the tumbling motion (reorientation of the long molecular axis), has very long characteristic times (from decades of picoseconds to nanoseconds) in these systems8,9 which are, in any case, longer than the dephasing times (typically in the picoseconds time scale). A manifestation of the statistical independence of the vibrational and reorientational processes in complex liquids is the observation of an

10.1021/jp106487k  2010 American Chemical Society Published on Web 10/21/2010

Simple Molecule Behavior at High Dilutions anisotropic (VH) bandwidth approximately equivalent to the isotropic one. The vibrational correlation function in these complex systems can hardly be interpreted within the stochastic theory, since the persistence of short-lived fluctuating nematic domains with temperature dependent size,10 even in the isotropic phase and well above the nematic-isotropic transition, makes the character of the perturbation process no more Markovian, and its decay no longer describable by a single exponential function. The interpretation of the vibrational dephasing of these complex liquids requires, therefore, a model in which the structural relaxation of the aggregates is taken into account in the description of the perturbation decay process. The approach formulated by Rothschild and co-workers,11 successfully applied to a wide range of complex liquids,11-14 has provided a general framework for the interpretation of the vibrational correlation functions observed in liquids with local, short-lived order, by assuming for the perturbation decay a stretched exponential function: exp-(t/τ0)R. This model represents a generalization of that formulated earlier2,4 based on the assumption of a single exponential function for the perturbation decay. The latter, in fact, can be thought of as the limit to which the first tends in the absence of structuring processes, i.e., in simple molecular liquids, where the exponent R tends to unity and τ0 (the Williams-Watts lifetime) achieves the value of the collision time for the single process, τc. In a previous investigation15 we have been able to prove the general adequacy of this model to the interpretation of vibration dephasing of the ν(C≡N) oscillator in the molecules of neat ME6N liquid crystal at different temperatures. With the increase of temperature up to the highest reached in that study (135 °C) compatible with the molecular integrity of the neat liquid crystal, the dispersion parameter R progressively increased (up to 0.75) without reaching, however, the simple liquid condition, corresponding to the limit of unity for R and of τc for τ0. The main purpose of the present investigation is that of exploring, by dilution in an inert solvent, the approach of ME6N liquid crystal to the limit of simple liquid condition, in the range of R closer to unity not accessed in the previous investigation by increasing temperature.15 In analogy with the method reported there, the vibrational correlation function obtained from the Raman ν(C≡N) band of ME6N/CCl4 solutions will be used as a probe of the extent of persistence of pseudonematic domains in the liquid crystal solutions up to an ultimate dilution where the vibrational decay is expected to take up the predicted Kubo’s shape for a simple liquid. Confirmation of the attainment of the simple liquid condition will indeed be provided by the achievement of unity for the dispersion parameter R and, for the experimentally determined correlation time, τ0, by the achievement of the value of the purely statistical correlation time, τc. The paper will be organized as follows: In section 2 we illustrate the basic theoretical aspects, in section 3 we describe the experimental details for the determination of the Raman isotropic profiles and the treatments for thereby evaluating the vibration autocorrelation functions, and then in section 4 we illustrate the concentration dependence of the latter and their interpretation on the basis of both the Kubo and the Rothschild models and, additionally, discuss the progressive narrowing and down shifting with dilution of the relaxation time distribution. 2. Theoretical Background 2.1. Vibrational Correlation Functions: Simple versus Complex Liquids. The theoretical basis for the formulation of the vibrational correlation functions for simple and complex

J. Phys. Chem. B, Vol. 114, No. 44, 2010 14013 liquids, and their comparison, has been extensively analyzed in refs 15 and 16. Here, we report the most relevant aspects. The vibrational correlation function Cˆvk (t) is obtained by Fourier transformation of the isotropic Raman band associated with a given oscillator k of frequency ω and represents the time decay of the phase coherence of its normal coordinate, 〈Qk(t)Qk(0)〉/〈|Qk(0)|2〉, in the present case, that related to the ν(C≡N) oscillator of ME6N liquid crystal. In the presence of intermolecular interactions, the oscillator undergoes an instantaneous frequency shift which is modulated by the molecular motions, ω1(t). According to the Kubo theory,3,4 i.e., within the assumption that ω1(t) is a random Gaussian process (i.e., 〈ω1(t)〉 ) 0), the vibrational correlation function may be analytically related to the time-correlation function for the frequency shifts, ω1

〈Q(t)Q(0)〉 ) exp[-〈|ω1(0)| 2〉 Cˆv(t) ) 2 〈|Q(0)| 〉

∫0t dt′(t - t′)Fˆ(t′)] (1)

with

Fˆ(t′) ) 〈ω1(t′)ω1(0)〉 / 〈 |ω1(0)| 2〉 where 〈|ω1(0)|2〉 () ∆2) represents the frequency modulation variance and then the perturbation amplitude in the limit of a static environment (i.e., when the dynamics is switched off). It has been shown4 that ∆2 coincides with the frequency second moment M2 of the vibrational spectral distribution, an experimentally accessible quantity. Since the frequency modulation, depicted as a random process as proposed by Kubo, is both Gaussian and Markovian, its time correlation function Fˆ(t) takes, according to the Doob’s theorem,17 a purely exponential form, and the corresponding vibrational time correlation function results as 〈Q(t)Q(0)〉 Cˆv(t) ) ) exp[- 〈 |ω1(0)| 2〉(tτc - τ2c (1 〈 |Q(0)| 2〉 exp(-t/τc)))] (2)

which is referred to as the Kubo equation.3,4 Here the dynamical parameter τc is the correlation time of the modulation and then the average time between two subsequent perturbative events. The interpretation according to this equation provides for many simple liquids the dynamical parameter τc, and then the slow and fast dynamical regimes depending whether 〈|ω1(0)|2〉1/2τc . 1 or , 1. In complex liquids the perturbation relaxation F(t) is, to some extent, altered by the dynamical processes of formation/ disruption of aggregates. In the approach formulated by Rothschild and co-workers,11-14 these are taken into account by modeling the perturbation relaxation with a non-Markovian process, and explicitly in the form of a stretched exponential

Fˆ(t) )

〈ω1(t)ω1(0)〉

〈|ω1(0)|2〉

) exp(-t/τ0)R

(3)

Here R, called the dispersion parameter, is a fractional exponent 0 < R < 1, and τ0 is related to the average perturbation correlation time of the complex liquid 〈τ〉 ) τ0Γ[1 + 1/R] (Γ is

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the complete gamma function). From a statistical point of view the modulation correlation function for the observed nonMarkovian process F(t) is described as the average of the many independent Poisson relaxation pathways, exp(-t/τ), with individual relaxation times τ, weighted by the probability density function FR(τ): R

e-(t/τ0) )

∫0∞ dτFR(τ)e-t/τ

(4)

With the assumption described in eq 3, the vibrational correlation function reported in eq 1 takes the form

Cˆv(t) ) exp[- 〈 |ω1(0)| 2〉(τ20 /R){(t/τ0)γ[1/R, (t/τ0)R] -

γ[2/R, (t/τ0)R]}] (5)

where γ is the incomplete gamma function. For a close comparison between the two above-mentioned models, we refer to Table 1 reported in ref 16. It may be expected that complex systems reach the condition of simple liquids (where the Gauss-Markov regime is recovered and then the Kubo model is again valid) when aggregates are destroyed as a consequence of thermodynamic changes such as the increase of temperature or dilution. Therefore, in this limit R tends to 1, τ0 to τc, and the distribution FR(τ) to some sort of delta function (see Table 2 in ref 16). As, in fact, the complex liquid tends to the simple one and Rf1, the argument of Γ tends to 2 and the value of Γ tends to 1. Progressively, FR(τ) becomes narrower and peaked at a specific value of τ progressively closer to the average 〈τ〉 coincident with τc; this means that τ0 tends to τc being Γ[1 + 1/R] ) 1 in this limit condition (see Table 2 in ref 16). The above considerations generally apply to complex liquids and are here adopted for liquid crystals in which pseudonematic domains persist even in the isotropic phase up to temperatures well above the nematic-isotropic transition10,15 and are expected to persist up to high dilution. The determination of dynamical parameters from the vibrational correlation functions of complex liquids must consequently be based on the latter theory, which implicitly takes into account the formation/disruption processes of domains of aggregated structures. 3. Experimental Details, Data Treatments, and Computations 3.1. ME6N Material. This material

is a liquid crystal that exhibits, on heating, the following phase sequence: K-N (46 °C), N-I (47.9 °C). It is stable in the presence of the ambient oxygen up to approximately 100 °C and above this temperature only under inert atmosphere. ME6N liquid crystal shows a rather high solubility in CCl4 at ambient temperature. Five dilute solutions in CCl4 were prepared with mole fractions x ) 0.12, 0.06, 0.03, 0.015, and 0.007. 3.2. Raman Experiments. The ν(C≡N) Raman spectra of ME6N liquid crystal in the ME6N/CCl4 solutions were obtained with the experimental apparatus we describe shortly. The exciting laser light at 514.5 nm from an Ar+ laser, with a power of 300 mW on the sample, at first passed a Glan polarizer, and then it was rotated to V or H polarization by a Halle polarization

rotator before impinging on the sample. The Stokes scattered light, collected in the V polarization and in a 90° geometry configuration, was spectrally analyzed by the use of a JY-Horiba U1000 spectrometer, with an entrance slit width of 100 µm corresponding to a Gaussian instrumental function fwhm ) 0.67 cm-1, and it was revealed by a multichannel detector (Spex LN2cooled CCD camera with 1024 × 256 pixels) held at 140 K. In the spectroscopic region of the ν(C≡N) mode around 2235 cm-1, the spectral separation of the CCD pixels amounts to 0.16 cm-1. The collected spectra cover a frequency range of 144 cm-1, with the CCD active area being limited to 906 pixels due to technical reasons for the setup of the U1000 spectrometer. To achieve comparable signal/noise values for all solutions, integration times increasing with the decrease of the solution concentration, from 20 s up to 80 s, were used with correspondingly increasing accumulation numbers. The measurement reproducibility was evaluated by comparing, for each solution concentration, two subsequent VV and HV alternating runs. The effective polarization conditions were checked with CCl4 by measuring the depolarization ratio of the 314 cm-1 depolarized (F ) 0.75) and of the 459 cm-1 totally polarized (F ) 0.002) bands. Since the Raman spectrum of CCl4 is completely free from bands in the region around 2235 cm-1, subtraction of the solvent spectrum from the ME6N/CCl4 solution spectrum was unnecessary. To correct the spectra for instrumental frequency drifts, each VV and HV spectral collection was followed by a frequency calibration using a Ne pen light (atomic line at 17 228.16 cm-1). The same atomic line was used for the determination of the instrumental slit function which, at the nominal slit width of 100 µm, was well fitted by a Gaussian profile with a full width at half-maximum (fwhm) value of 0.67 cm-1. This spectral resolution determines the time range in which the time correlation function of the ν(C≡N) profiles are reliable.18 To correct the spectra for the CCD response, the fluorescence spectrum of a fluorescein aqueous solution was used as reference. Experimental temperatures have been kept constant at 20.0 °C by a flow of thermostatted water with a nominal accuracy of 0.1 °C (Lauda thermostat). 3.3. ν(C≡N) Band-Shape Treatment and Evaluation of the Vibrational Correlation Function. The VV and HV profiles in the ν(C≡N) spectral region are characterized by, in addition to the ν(12C≡N) fundamental vibrational band at 2234 cm-1, a satellite band at 2200 cm-1 (depolarized, due to some combination band) and one at 2180 cm-1 (polarized) clearly deriving from the 13C≡N isotopic impurity. After intensity correction for the spectral response of the spectrometer and the CCD, the VV and HV profiles for each ME6N/CCl4 solution were combined to give the corresponding isotropic profile (Iiso ) IVV - 4/3IHV) which contained, in addition to the main ν(C≡N) oscillator band, only the 2180 cm-1 satellite. By fitting the isotropic spectrum with the superposition of two Voight functions peaking at 2180 and 2234 cm-1, the latter could be extracted by subtracting, from the whole isotropic profile, the fitted component obtained at the 2180 cm-1 peak frequency. After normalization, the isotropic profiles were Fourier transformed in the time domain to give the experimental, normalized vibrational time correlation functions, Cˆv(t), through a homemade software routine which, in addition to the correction for the instrumental slit distortion, evaluates the frequency second moment, M2, the vibrational relaxation time τv (as the integral ˆ v(t) over its time range of reliability), and the correspondent of C uncertainties. The spectral resolution, given by the instrumental

Simple Molecule Behavior at High Dilutions

Figure 1. Isotropic and anisotropic Raman spectra of the region around the cyano-group stretching mode ν(12C≡N) of ME6N in the ME6N/ CCl4 solution at mole fraction x ) 0.12. The peak around 2180 cm-1 is due to the ν(13C≡N) mode of the natural impurity C6H13C6H4-(12CO)OC6H413CN. Note the approximately equal values of the isotropic (8.0 cm-1) and the anisotropic (8.4 cm-1) band halfwidths (FWHM) indicating that the orientational relaxation occurs at a time scale much larger than that of the vibrational dephasing.

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Figure 2. Normalized experimental (b) and Kubo model (---) vibrational relaxation functions Cˆv(t) for ν(12C≡N) of ME6N in the ME6N/CCl4 solution at mole fraction x ) 0.12. The value of τc ) 0.8 ps for the correlation time has been obtained by fitting the Kubo Cˆv(t) to the experimental Cˆv(t) by using the experimental spectral second moment M2 ) 0.9 ps-2. Notice the failure of the Kubo model for t > 3 ps. The same decay is reported in the inset as a semilog plot.

slit function (0.67 cm-1), and the spectral range covered (144 cm-1) by the experimental isotropic profiles, dictated the time ˆ v(t) was reliable (12.4 ps) and its time resolution range in which C (0.24 ps), respectively.18 For the interpretation of the experimental Cˆv(t) in terms of the Rothschild theory, we have applied a nonlinear fitting of eq 5 and obtained the structural (R) and dynamical (τ0) parameters. For comparison purposes, a parallel nonlinear fitting of the Kubo stochastic equation, eq 2, to the experimental Cˆv(t) was carried out which provided the dynamical parameter (τc). 4. Results and Discussion The isotropic and anisotropic spectra in the region around the ν(C≡N) stretching mode of ME6N in the ME6N/CCl4 solution at x ) 0.12 and at 20.0 °C are displayed in Figure 1. It can be noticed that the half-widths σ (fwhm) of the two profiles are approximately the same (σani ) 8.4 cm-1, σiso ) 8.0 cm-1), indicating that the contribution σor ∼ 0.4 cm-1 from the reorientational motion (being σor ) σani - σiso strictly valid for a Lorentzian profile) is rather small, and then that the reorientational time, τor () π/Γor, being Γor ) 2πcσor), is much longer (41 ps) than the vibrational relaxation time τv ∼ 2.0 ps () π/Γvib, with Γvib ) 2πcσiso). The two processes can then be considered statistically independent. The peak frequencies of the isotropic and anisotropic profiles are close to coincidence (NCE ∼ 0.2 cm-1), confirming the absence of the intermolecular transition dipole coupling and then of the process of the resonant vibrational energy transfer. Since, additionally, the energy relaxation process from this high-lying energy level (2234 cm-1) is believed to be very unlikely as stated from ultrafast antiStokes Raman scattering of the ν(C≡N) stretch of acetonitrile,19 we can assert that only the vibrational dephasing process contributes to the vibrational time correlation function Cv(t) for the ν(C≡N) band. In Figure 2 we report the vibrational time correlation function Cv(t) for the ν(12C≡N) band of ME6N in the ME6N/CCl4 solutions at x ) 0.12. It clearly indicates the inadequacy of the Kubo model for the interpretation of the experimental Cv(t) in

Figure 3. Experimental vibrational correlation functions Cˆv(t) in semilog plots for the ν(12C≡N) of ME6N in the ME6N/CCl4 solutions at progressively lower mole fractions of ME6N in CCl4 reported as full circles: black, x ) 0.12; light blue, x ) 0.06; magenta, x ) 0.03; blue, x ) 0.015; and red, x ) 0.007. The ν(C≡N) vibrational dephasing progressively gets slower with dilution and approximately coincides at the two lowest concentrations as indicated by the reported experimental vibrational relaxation times, τv.

the whole time range. In fact, for times above approximately 3 ps the experimental vibrational dephasing notably disagrees with the prediction of this model. This is even more evident in the inset to Figure 2, where we report this correlation function in a semilog plot. A collective view of the experimental vibrational time correlation functions Cv(t) of ME6N for the ν(12C≡N) band for ME6N/CCl4 solutions at x ) 0.12, 0.06, 0.03, 0.015, and 0.007 is reported in the semilog plot in Figure 3. The vibrational correlation decays get slower, and consequently, the vibrational relaxation times τv get longer, as dilution increases (see the inset in Figure 3), and tend to reach limiting behavior at x ) 0.007, which only slightly differs from that obtained for x ) 0.015. To this increase of the dephasing time of the ν(12C≡N) mode

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Figure 4. Vibrational correlation functions Cˆv(t) in semilog plots for the ν(12C≡N) of ME6N in the ME6N/CCl4 solution at mole fraction x ) 0.12: experimental (b), Kubo model (---), Rothschild model (s). At t > 3 ps, the Kubo model fails in describing the decay of the experimental vibrational relaxation function.

corresponds an analogous decrease of the isotropic spectral bandwidth σv with dilution. As first experimentally noticed by Bondarev and Mardaeva,20 Raman band profiles of molecular liquids get broader with dilution reaching the highest bandwidth at x ) 0.5 and then get narrower for concentrations below this value. According to the analysis carried out in ref 20 in the limit of slow modulation, then extended by Knapp and Fischer to all modulation speeds,21 this nonmonotonic behavior of the bandwidth concentration dependence, symmetric around x ) 0.5, must be traced back to concentration fluctuations, i.e., variations of chemical composition of the environment surrounding the active oscillator, for vibrational modes having peak frequencies (or better first moment) linearly dependent on concentration. The ν(C≡N) vibrational mode belongs to this category as resulting from a band shape analysis of the ν(C≡N) stretch performed on acetonitrile/CCl4 mixtures,22 where the concentration dependence of the ν(C≡N) isotropic bandwidth and of the dephasing time, respectively, exhibits this nonmonotonic behavior with the maximum and minimum, respectively, around x ) 0.5 (see Table 2 of ref 22). Along this line of reasoning, the increase with dilution of the dephasing time of the ν(12C≡N) mode observed in the present investigation of ME6N/CCl4 mixtures at concentrations below x ) 0.5 can then be qualitatively explained as the manifestation of a progressive narrowing with dilution of environmental distribution around the active oscillator. In Figures 4 and 5 we report the experimental Cv(t)’s for the ν(12C≡N) band of ME6N at the highest (x ) 0.12) and the lowest (x ) 0.007) concentrations of the ME6N/CCl4 solutions, respectively, and the parameters obtained by fitting them to the Kubo (τc) and the Rothschild (τ0, R) models. From the comparison it emerges that in the most concentrated solution (x ) 0.12) only the latter model is able to reproduce the Cv(t) with the parameters τ0 ) 1.99 ps and R ) 0.78 (see Figure 4), whereas in the lowest concentration solution (x ) 0.007) the time decay is reproduced by both models (see Figure 5). In this limit of lowest concentration the Rothschild model gives a dispersion parameter R reaching unity and a dynamical parameter τ0 value of 1.18 ps, closely coincident with the correlation time τc (1.16 ps) obtained from fitting the experimental Cˆv(t) to the Kubo model. In this limit, the product of the square root of the frequency modulation 〈|ω1(0)|2〉 (M2 ) 0.76 ps-2 in Figure

Giorgini and Musso

Figure 5. Vibrational correlation functions Cˆv(t) in semilog plots for the ν(12C≡N) of ME6N in the less concentrated ME6N/CCl4 solution at mole fraction x ) 0.007: experimental (b), Kubo model (---), Rothschild model (s). Dashed and continuous lines almost overlap. In the limit of high dilution Cˆv(t) values obtained from the Kubo and the Rothschild theories converge in predicting the decay of the experimental vibrational relaxation function. The characteristic times of the two models (τc and τ0) converge to approximately the same value, and the dispersion parameter (R) reaches unity.

Figure 6. Experimental (b) vibrational correlation functions for the ME6N/CCl4 solutions at different concentrations fitted to the Rothschild model (s) by the use of the parameters R and τ0 reported as inset.

5) with the correlation time τc (1.16 ps, Figure 5), the so-called Kubo product, is appropriate for providing the motional regime. Since this Kubo product amounts to ∼1 it is possible to infer that the system at the highest dilution experiences an intermediate dynamical regime. In Figure 6 we report a collective view of the experimental Cv(t)’s and of those predicted within the Rothschild model with the use of the parameters reported in the inset. In Figure 7 we report the concentration dependencies of the dispersion parameter R from x ) 0.12 to x ) 0.007. The progressive increase of the dispersion parameter up to unity and the progressive decrease of τ0 down to 1.18 ps (close to the value of τc obtained for the single process, 1.16 ps) are a clear indication that at the lowest concentration the condition of simple liquid can be considered attained. If we compare these results with those reported in ref

Simple Molecule Behavior at High Dilutions

Figure 7. Concentration dependence of the dispersion parameter R. At the two highest dilutions this parameter reaches approximately the same value (R ∼ 1).

15 where the achievement of the simple liquid condition was promoted by thermal energy, we can conclude that dilution is a more efficient route for the destructuration of the pseudonematic domains surviving in this liquid crystal even in the isotropic phase. Very limited results are reported in the literature on the effect of dilution on the dispersion parameter and then on the rate of achievement, by dilution, of the simple liquid condition. Rothschild determined values of R falling in the range 0.5-0.7 for CCl4 solutions at x ) 0.02 of n-CB (i.e., 4-n-alkyl4′-cyanobiphenyl) liquid crystals with n (the carbon number of the alkyl chain) equal to 8, 9, and 12.13 Incidentally, the n-independence of R for this family13 suggests the extension of the above result to n ) 6. The values of R found for n-CB (R ) 0.5-0.7) are remarkably lower than that (R ) 0.93) we have obtained for ME6N (n ) 6) in the CCl4 solution at approximately the same concentration (x ) 0.03). According to the physical meaning attributed to R, its higher value found in ME6N indicates that in this liquid crystal system the presence of pseudonematic domains is less remarkable than in n-CB or, alternatively, that this system has a more relevant simple liquid character than n-CB. Since for the two liquid crystal systems the thermodynamic conditions (temperature and dilution) in which the dispersion parameter has been determined are approximately the same, we argue that the difference in the dispersion parameters of the two liquid crystal systems is necessarily ascribable to the difference in their molecular structure. Note that in the structure of the members of the n-CB family the two phenyl groups (Ph) are directly linked (CnH2n+1sPhsPhsCN), whereas in that of ME6N they are linked through the -COO- grouping (C6H13sPhsCOOPhsCN, see section 3.1). Since the remaining groups are either equal in the two liquid crystals, as CN, or not responsible for variations of the R values, such as the alkyl chain, CnH2n+1 (as noticed above), we are left with the (core) linkage between the two phenyl groups as the possible source of the difference of the dispersion parameter. We have good reasons for thinking that the higher dispersion parameter found for the ME6N/CCl4 solution could be attributable to the core linkage of this liquid crystal. It has been found,23 in fact, that in strongly polar liquid crystals the absence of interphenyl groupings (as it occurs in n-CB) and the consequent high molecular stiffness represent the condition favoring the observation of pretransitional effects and of their magnitude, such as the convex-shaped anomaly in the temperature dependence of dielectric constant in the vicinity

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Figure 8. Concentration dependence of the normalized time-length biased probability density function hˆ(τ): black line, x ) 0.12; light blue line, x ) 0.06; magenta line, x ) 0.03; blue line, x ) 0.015; red line, x ) 0.007. With dilution the probability density function gets narrower, its peak shifts to lower values, and the average perturbation correlation time 〈τ 〉 (calculated as τ0Γ[1 + 1/R]) decreases from 2.29 ps, to 1.79, 1.53, 1.23, and 1.19 ps, not reported in the Figure.

of the I-N transition.23 On the contrary, the presence of interphenyl groupings in the ME6N molecule is expected to confer to it a lower molecular stiffness with respect to n-CB and then a lower propensity to the formation of pseudonematic domains with respect to n-CB, thus justifying the higher dispersion parameter obtained in this work for ME6N with respect to that obtained for n-CB.13 As suggested in ref 13 the structural and dynamical changes of the complex liquid can be discussed by using the time-length biased probability distribution function h(τ) () τFR(τ)/〈τ〉), where FR(τ) describes the probability of finding in the liquid the Poisson relaxation process with characteristic time τ. The probability distribution function FR(τ), introduced at the end of section 2, can be obtained by inversion of eq 4. We have evaluated it from the first term of the expansion reported in eq 1.4 in the treatment developed by Helfand24 by using the values of R and τ0 parameters obtained in the fitting of eq 5 to the experimental vibrational correlation function. The time-length biased probability distribution function, reported in Figure 8 in normalized form hˆ(τ) for all ME6N/ CCl4 solutions, shows two peculiarities: (i) a reduction with dilution of the probability distribution half-width (fwhm) (from 2.86 ps at x ) 0.12 to 0.03 ps at x ) 0.007 with the intermediate values of 1.28 ps at x ) 0.06, 0.40 ps at x ) 0.03, and 0.06 ps at x ) 0.015), indicating a narrowing of the aggregate distribution with dilution, and (ii) a progressive shift of the peak, i.e., of the characteristic time of the most probable decay channel, to lower values to eventually reach that of the single process relaxation at the highest dilution. The distribution obtained for the highest dilution is sharply peaked at τ ) 1.2 ps, which, being closely coincident with the value of τc (1.16 ps) obtained from the Kubo approach to the vibrational correlation function analysis for this dilution, strongly suggests the achievement of the single relaxation process regime and then of the simple liquid condition. A comparison of the probability distribution function hˆ(τ) obtained at different dilutions reported in Figure 8 and that at different temperatures for the same probe oscillator of the same liquid crystal15 reveals a remarkable difference in the approach to the condition of

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simple liquid depending if temperature or dilution is used to achieve it. In fact, while the probability distribution function gets progressively narrower both by either increasing dilution or temperature, its peak value drifts to progressively lower values with increasing dilution while remaining approximately constant with increasing temperature. This suggests that the different behaviors of the distribution peak might be a peculiarity connected with the two thermodynamic parameters, temperature and dilution. The liquid structure of ME6N in CCl4 solution consists of “isolated” inhomogeneous pseudonematic domains whose characteristic time gets shorter with their decreasing size. With dilution the solvent penetrates the clusters, which progressively get smaller and less inhomogeneous, so that the peak of the h(t) distribution shrinks and shifts to lower values as the system converges to simple liquid behavior. With increasing temperature the pseudonematic domains of the neat liquid crystals, like ME6N and n-CB, become less inhomogeneous too, making the h(t) distribution progressively narrower without, however, appreciably reducing the average dimension of the clusters, since the strong intermolecular interactions between the polar CN groups still persist. Only at very high temperature (usually not reached in these experiments to avoid chemical degradation of the liquid crystal) would the thermal energy overcome these intermolecular interactions and allow the complete achievement of the single process limit. Rothschild13 proposed a procedure to evaluate the “local relaxation domain” in the medium as the range of distances R (measured from the position of the active oscillator, here the CN oscillator) from which the perturbations causing the oscillator dephasing arise. In his approach, this quantity has been formulated as the product, R ) Vsound · τ, of an appropriate relaxation time τ and a representative value of the sound velocity, Vsound. This latter assumption is based on the considerations that the most probable relaxation frequency, defined as (1/τpeak), occurs, typically,13 in the far IR and that to this spectral region acoustic phonon motions give the prevalent contribution. For the lowest and highest concentrated ME6N/ CCl4 solutions, in fact, τpeak amounts to 1.2 and 3.6 ps, respectively, as displayed in Figure 8, and their inverses occur both in the far IR (1/cτpeak ) 27.8 and 9.3 cm-1). Along these lines of reasoning we have evaluated R for the highest (x ) 0.12) and lowest (x ) 0.007) concentrated ME6N/CCl4 solutions. For the highest concentrated solution the hypersonic velocity amounts to 1 × 105 cm s-1 (see Figure 4 of ref 25) and the most representative relaxation time (see Figure 8) to 3.6 ps so that R turns out to be 36 Å, a relaxation range rather large if compared with that occurring in simple liquids.13 The hypersonic velocity in the lowest concentrated solution amounts to 0.9 × 105 cm s-1, and R decreases to 10 Å. Since the long axis molecular dimension of ME6N is 13.3 Å (obtained from ab initio quantum chemical calculations of ME6N geometric structure reported in ref 15 and displayed in Figure 9 of ref 24) we are led to conclude that at the highest concentration the intermolecular correlation involves more than two shells around the active oscillator whereas no correlation is present in the less concentrated mixture. This result reinforces our idea of aggregate species of ME6N liquid crystal surviving in solution, with the simple liquid behavior being approached only at very high dilution. 5. Concluding Remarks In the present work we have measured the Raman isotropic profiles of the ν(C≡N) band of ME6N liquid crystal in ME6N/ CCl4 solutions in the concentration range from 0.12 to 0.007

Giorgini and Musso mole fraction and derived, by time Fourier transformation, the corresponding vibrational time correlation functions Cv(t). The purpose was that of extracting, from the latter, information on the molecular dynamics featuring this complex liquid. The experimental Cv(t) values have shown the following features: (i) There is a general reluctance at all concentrations, except the most diluted solution, to the modelling proposed by the Kubo stochastic theory which typically applies to simple liquids, since formulated with the assumption that a single modulation process, exp(-t/τc), contributes to the dynamics of the liquid system. (ii) There is a general agreement, in the whole concentration range, with the modeling proposed by the Rothschild approach which applies to complex liquids being formulated with the assumption that a distribution of modulation processes exp(-t/τ0)R contributes to the dynamics of the liquid system (with 0 < R < 1 the distribution parameter and τ0 an average correlation time). (iii) The experimental vibrational correlation function decays progressively slower with dilution, and that obtained at the highest dilution (x ) 0.007) becomes adequately reproduced by both theories. (iv) With dilution, the parameters R and τ0 deduced from the application of the Rothschild theory increases up to unity and reduces down to the single process correlation time τc, respectively, indicating that, at the most highly diluted solution, the single modulation process regime, typical of the dynamics of simple liquid systems, has been achieved. (v) The probability distribution function of the correlation times, h(τ), which is a measure of the probability that aggregate species (the pseudonematic domains) with correlation time τ survive in each solution, progressively gets narrower and downshifts with dilution reaching a sort of delta function peaking at approximately the same value taken up by τc in the most highly diluted solution. These results confirm the idea that the structural organization present in the nematic phase persists as domains in solutions of liquid crystals up to very high dilution, and give a strong indication that the parameters R and τ0 of the Rothschild model represent a reliable tool to monitor the approach of these complex liquids to the regime of simple liquids. The merit of this investigation, aimed to shed light on the molecular organization of an isotropic liquid crystal, is (i) that of having accessed by dilution the window not previously reached by temperature and (ii) that of having monitored it through the evolution of reliable structural and dynamical parameters (R and τ0) obtained by a systematic liquid crystal dilution rather then through only one concentration as reported by other authors (ref 13). Acknowledgment. M.G.G. gratefully appreciates the financial support to this study given by the Italian Ministry of Education and Research (MIUR) within the project PRIN 2007 N. 2007NZLYE5: Transfer of energy, charge and molecules in complex systems. References and Notes (1) Gordon, R. G. AdV. Magn. Reson. 1968, 3, 1. (2) Kubo, R. In Fluctuation, Relaxation and Resonance in Magnetic Systems; Haar, D. T., Ed.; Oliver and Boyd: London, 1962. (3) (a) Kubo, R. AdV. Chem. Phys. 1969, 15, 101. (b) Kubo, R.; Toda, M.; Hashitume, N. Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd ed; Springer-Verlag: Berlin, 1998. (4) Rothschild, W. G. Dynamics of Molecular Liquids; Wiley: New York, 1984. (5) Cataliotti, R. S.; Foggi, P.; Giorgini, M. G.; Mariani, L.; Morresi, A.; Paliani, G. J. Chem. Phys. 1993, 98, 4372. (6) Marri, E.; Morresi, A.; Paliani, G.; Cataliotti, R. S.; Giorgini, M. G. Chem. Phys. 1999, 243, 323.

Simple Molecule Behavior at High Dilutions (7) Giorgini, M. G.; Morresi, A.; Mariani, L.; Cataliotti, R. S. J. Raman Spectrosc. 1995, 26, 601. (8) Fontana, M. P. In Molecular Dynamics of Liquid Crystals; Luckhurst, G. R., Veracini, C. A., Eds.; Kluwer: Dordrecht, 1994. (9) Torre, R.; Ricci, M.; Saielli, G.; Bartolini, P.; Righini, R. Mol. Cryst. Liq. Cryst. 1995, 262, 1679. (10) Sengupta, A.; Fayer, M. D. J. Chem. Phys. 1995, 102 (10), 4193. (11) Rothschild, W. G.; Perrot, M.; Guillaume, F. J. Chem. Phys. 1987, 87, 7293. (12) Rothschild, W. G.; Perrot, M. J. Chem. Phys. 1988, 89 (10), 6454. (13) Rothschild, W. G.; Perrot, M.; De Zen, J.-M. J. Chem. Phys. 1991, 95 (3), 2072. (14) Perrot, M.; Rothschild, W. G.; Cavagnat, R. M. J. Chem. Phys. 1999, 110 (18), 9230. (15) Giorgini, M. G.; Arcioni, A.; Polizzi, C.; Musso, M.; Ottaviani, P. J. Chem. Phys. 2004, 120, 4969. (16) Giorgini, M. G.; Arcioni, A.; Venditti, G.; Asenbaum, A.; Musso, M. J. Mol. Liq. 2006, 125, 123.

J. Phys. Chem. B, Vol. 114, No. 44, 2010 14019 (17) (a) Doob, J. L. In Selected Papers on Noise and Stochastic Processes; Wax, N., Ed.; Dover: New York, 1954; pp 319-337. (b) Doob, J. L. Ann. Math. 1942, 43, 351. (18) Keller, B.; Kneubu¨hl, F. HelV. Phys. Acta 1972, 45, 1927. (19) Deak, G. C.; Iwaki, L. K.; Dlott, D. D. J. Phys. Chem. A 1998, 102, 8193. (20) Bondarev, A. F.; Mardaeva, A. I. Opt. Spectrosc. 1973, 35 (2), 161. (21) Knapp, E. W.; Fischer, S. F. J. Chem. Phys. 1981, 76, 4730. (22) Morresi, A.; Sassi, P.; Paolantoni, M.; Santini, S.; Cataliotti, R. S. Chem. Phys. 2000, 254 (2-3), 337–347. (23) Sridevi, S.; Prasad, S. K.; Rao, D. S. S.; Yelamaggad, C. V. J. Phys.: Condens. Matter 2008, 20, 465106. (24) Helfand, E. J. Chem. Phys. 1983, 78, 1931. (25) Aliotta, F.; Giorgini, M. G.; Ponterio, M. C.; Saja, F. J. Mol. Liq. 2010, 153, 67.

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