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Effect of Quenched Disorder on the RI-RV, RII-RI, and Liquid-RII Rotator Phase Transitions in Alkanes U. Zammit,* M. Marinelli, F. Mercuri, S. Paoloni, and F. Scudieri Dipartimento Ingegneria Meccanica, Universita di Roma “Tor Vergata”, Rome, Italy ABSTRACT: The ability of disorder to reduce the coupling between the distortion and tilt angle order parameters was tested over the RI-RV phase transition by measuring the specific heat in alkanes with different RI phase temperature range mixed with various concentrations of silica nanoparticles. It was found that the disorder significantly affects the character of the RI-RV transition, driving it toward a second-order character. The features about the RII-RI transition were progressively attenuated for increasing disorder in both alkanes, becoming very faint for the largest particle concentration, but the first-order character was maintained. Over the liquid-RII transition, the single peak observed in both the specific heat and the latent heat in the pure materials splits into two features, at different temperatures, as over the isotropic-nematic transition in liquid crystals.
’ INTRODUCTION Rotator phases in alkanes (CnH2nþ2) and the transitions among the phases have been the subject of extensive research work because of the interesting peculiarities they show in some physical properties and of the importance of simple alkanes as building blocks of more complex structures such as surfactants, lipids, polymers, and liquid crystals (LC). The rotator phases are encountered as intermediate phases between the fully ordered crystal and the isotropic liquid phases, the barrier for their nucleation from the liquid state being particularly low in alkanes. They possess three-dimensional crystalline order in the position of the molecules, but no long-range rotational order about the molecular long axis,1 and, because of this orientational degree of freedom, they are considered plastic crystalline phases. Associated with this peculiarity, they show particularly large heat capacity, large thermal expansion, and negative isothermal compressibility,2 and they also exhibit surface crystallization phenomena.3 Finally, they bear similarities to systems like Langmuir monolayers at liquid surfaces4,5 and liquid crystals.6 The different rotator phases have been characterized by X-ray diffraction experiments7 in terms of side packing, molecular tilt, layer stacking, and azimuthal ordering, and they have also been investigated, among others, by calorimetry.8 The phases investigated in this work are RII, RI, and RV, as ordered for decreasing temperature. The RII phase is rhombohedral, with molecules packed in an undistorted hexagonal lattice, untilted with respect to the layer normal, and with ABC layer stacking. The RI phase is orthorhombic: a rectangularly distorted hexagonal lattice with untilted molecules and AB layer stacking. The RV phase is similar to the RI phase except that the molecules are tilted toward the next-nearest neighbors. The order parameter for the RII-RI transition is a lattice distortion parameter, D, which characterizes the deviation from the hexagonal crystalline packing of the RII phase. D is defined as the difference from unity of the ratio of the minor to major axis of r 2011 American Chemical Society
the ellipse drawn through the nearest neighbors of a given molecule.5 The order parameter for the RI-RV transition is the molecular tilt angle θ with respect to the layer normal. As for the order character of the transitions, because for the RII-RI transition a change in the sign of the distortion would lead to a non equivalent state of the system, the mean field Landau free energy expansion must contain odd powers of D whose presence induces the transition to be of first order.9 This has been confirmed by X-ray measurements where a discontinuity in D was observed over the transition7 and also by the calorimetry studies.8 In the case of the RI-RV transition, a change in sign in θ leads to an equivalent state of the system, so only even powers of θ must appear in the free energy expansion, implying the RI-RV transition to be second ordered. In this case, X-ray diffraction experiments had shown a discontinuity of θ over the transition in alkanes,7 but it was argued that the limited temperature resolution of the experiment could not rule out a possible continuous behavior of θ,9 typical of second-order phase transitions. It was later shown, in studies carried out in alkanes with increasing ambient pressure,10 that the results are consistent with a change of the character of the transition from first to second with pressure increase.9 Moreover, it was shown that a strong correlation exists between the order parameters D and θ9,10 and that it is the presence in the free energy expansion of the coupling term between them that could justify, also from a theoretical point of view, a possible first-order-like behavior at the transition.9 Finally, on the basis of the Landau mean field theory, it was reported that the ambient pressure increase can indeed cause a first-ordered RI-RV transition to turn to secondorder passing through a tricritical point.11
Received: November 19, 2010 Revised: January 17, 2011 Published: February 18, 2011 2331
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The Journal of Physical Chemistry B In a recent work, the authors reported on the character of the RII-RI and the RI-RV phase transitions by analyzing the hysteretic behavior of the specific heat, typical of first-order transitions, in various samples of alkanes with varying RI range.12 It was found that hysteresis is systematically present over the RII-RI and RI-RV transitions in all the investigated samples, but in the latter case the extent of the hysteresis is found to decrease as the RI range is reduced, suggesting a consequent shifting of the transitions toward a second-order character. This has been ascribed to a possible decrease of the D-θ coupling, associated with a reduction of the interlayer molecular interaction, in samples with smaller RI range. In this context, it would be interesting to probe how the order character of the RI-RV transition would be affected when the degree of the D-θ coupling was externally controlled. One possible way of doing so is suggested by the results obtained in LC where the tuning of the coupling between the smectic A (A) and nematic (N) order parameters, over the NA transition, is obtained by introducing varying quantities of quenched random disorder (QRD) in the sample. This has been achieved by confining the LC in pores of different kind of systems such as Vycor glass,13 aerogel14 and aerosil15 networks, Anopore,16 and Millipore membranes.17 The NA phase transitions had originally been predicted to be of second order, belonging to the 3D XY universality class.6 Increasing coupling strength between the smectic and nematic order parameters could drive the transitions toward a first-order character,6 passing through a tricritical point (TCP). This was verified in samples with varying nematic range18 where the effective values of the critical exponent R of the specific heat, for example, varied between the values predicted by the XY model and that at the TCP. The introduction of QRD, in the case of the aerosil network, for example, decreased the coupling strength between the two-order parameters, thus driving the value of R toward the XY-like one.19 The aerosil network is obtained by mixing the sample with different concentrations of silica nanoparticles. The advantage over the other disordering systems is that the amount of disorder can easily be tuned by selecting the concentration of the introduced particles. It so happened, however, that the aerosil-induced disorder also dramatically changed the characteristics of the specific heat over the isotropicnematic (IN) phase transition, where the largest temperature ordered phase nucleates from the melt, and where the disorder and strain in the material caused a splitting in two features of the single peak normally found for the specific heat in pure material.19,20 Several effects have been observed in alkanes confined in different kind of systems. For example, vanishing of the lamellar ordering was observed in nanoporous Vycor glass,21 reduction of the hysteresis at the melting-freezing transition and novel phase sequence in mesoporous Vycor glass,22 and lowering of the crystallization temperature in systems with silica nanospheres.23 In this Article, we seek to find out whether in alkanes the introduction of disorder produces also effects related to the decoupling between the distortion and tilt angle order parameters over the RI-RV phase transitions. Moreover, changes induced over the nucleation from the liquid of the largest temperature ordered phase, caused by disorder, are also investigated. To this aim, we report results concerning the behavior of the specific heat and also of the detected latent heat observed over the RI-RV, RII-RI, and liquid-RII phase transitions in alkane samples, with different RI phase temperature ranges,
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mixed with various concentrations of silica nanospheres and therefore with different extents of introduced disorder. It was found that, over the RI-RV phase transition in C24 phase the disorder reduces the extent of the hysteretic region of the specific heat, thus driving the transition toward a secondorder character. In C25, the profile of the specific heat also gets modified but in a more dramatic way than in C24 at the largest particle concentration. These results are discussed in terms of the weakening of the interlayer interactions induced by the disorder, ultimately responsible also for the reduction of the D-θ coupling. Over the liquid-RII transition, the first-ordered single peak observed in both the specific heat and the latent heat in the pure material,does split into two features, at different temperatures, as over the IN transition in LC. The hysteresis over the RII-RI transition is maintained, although the features over the transition get attenuated for increasing disorder in both alkanes.
’ EXPERIMENTAL SECTION The study was performed using photopyroelctric calorimetry (PPE),24 as in our previous work, where its high temperature resolution capabilities are pointed out and where the difference, with respect to other dc and ac calorimetric techniques, of the effective values of the specific heat obtained in the coexistence region of first-order phase transitions is discussed.12 Over second-order phase transitions, on the other hand, PPE has been widely used for the high temperature resolution measurements necessary for the study of the behavior of the thermal parameters.25-28 Its advantage over other ac and dc calorimetry techniques is that it allows the simultaneous measurements of the specific heat, thermal conductivity, and thermal diffusivity over the phase transitions. This has enabled one to rule out any critical behavior of the thermal conductivity in all the investigated transitions in LC,25-27 as well as in some solids.28 Moreover, an improved data analysis procedure has been recently introduced29 by which it is possible to indirectly evaluate the latent heat exchanged over first-order phase transitions, a detection normally denied to ac techniques. Finally, an implementation with a visual inspection system and an optical transmission set up now allows, if necessary, polarization microscopy observations and light scattering measurements31 to be carried out together with the thermal parameters investigation. In this work, each analyzed sample was sandwiched between a 0.5 mm-thick LiTaO3 pyroelectric transducer and a glass cell with calibrated spacers of thickness of 0.1 mm. The side of the glass plate in contact with the sample was coated with a 300 nm thick metallic layer. Light from a modulated laser diode was absorbed by the metallic coating in contact with one side of the sample, and the induced temperature oscillations were detected on the opposite side of the sample by the transducer. The modulation frequency was 1 Hz. The amplitude and phase of the PPE signal were measured by a two phase lock-in amplifier and then processed to determine the specific heat, the thermal conductivity, and the involved latent heat.29 To achieve the high temperature resolution conditions during the measurements, the laser light intensity was limited to a value (99.8%), and then the silica nanoparticles32 were added. To achieve homogeneity in the dispersion, the solution was then sonicated at 70 °C until complete evaporation of the solvent was obtained. Finally, the mixture was placed in a vacuum in the molten state (60 °C) to achieve removal of residual solvent and/or humidity. The investigation was carried out in samples of tetracosane (C24) and of pentacosane (C25) containing concentrations (mass ratio) of silica particles of 5% and 10%.
’ RESULTS AND DISCUSSION The aerosil particles grow as agglomerates of three to four lightly fused nanospheres, each of mean diameter of about 7 nm. The hydrophilic particles used in this work possess hydroxyl groups on their surface, and, when dispersed in an organic liquid, they tend to form a network, linked by hydrogen bonds, via a diffusion-limited aggregation process. When the network is subject to strain, the relatively weak hydrogen bonds easily break and re-form within a moderate time scale, partly relieving the strain itself.33 In octylcyanobephenil (8CB) LC, the network is reported to form for particle concentration exceeding approximately 1%.19 The host liquid is then confined in the interconnected voids of the network and therefore subject to finite size effects. In self-ordering systems, also random field effects that oppose the mean molecular ordering field play a role, being associated with the random pinning of the molecules on the particle surface. When strong bonding of the molecules with the solid surface occurs, strain may build up in the ordered system and affect the system properties because, like random fields, strain also disturbs long-range order. As shown in the following, the effects of the disorder associated with the presence of the silica particles is particularly important over the phase transitions of the alkanes, but also within the phases themselves. Liquid-RII Transition. Figure 1 shows the results for the specific heat at constant pressure, c, for measurements carried out during heating and cooling runs, over the liquid-RII transition of C24 for the pure sample and when containing concentrations of aerosil of 5% and 10%. Figure 2 reports the corresponding values obtained for the so-called “latent heat coefficient” IL, described in ref 29, where it is shown that it is proportional to the latent heat exchanged over first-ordered transitions and to other kind of enthalpy exchanges associated, for example, with relaxing strain and/or defect annealing as observed over the hexatic-Bsmectic-A transition in pure n-hexyl-40 -n-pentyloxybiphenyl-4-
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Figure 2. Latent heat coefficient IL (see text) during heating (black symbols) and cooling (gray symbols) measurements over the liquid-RII transition for C24 alkane: (a) pure sample; (b) sample with 5% aerosil particles; and (c) sample with 10% aerosil particles.
carboxylate (65OBC).34 So IL does not provide absolute values of the involved latent heat but only relative values such as the ones shown in the relative profile of IL observed over the coexistence region of a sample and/or those obtained as a function of the different sample preparation conditions as shown in Figure 2. In the case of the pure sample, only a single peak structure is observed for both c and IL, showing a hysteresis between the heating and cooling runs, typical of first-order phase transitions. The range where IL is nonzero determines the twophase coexistence region, as also previously shown.29 In such a range, the obtained values of c correspond only to effective values, and thus also the absolute values of such a quantity are of no significance, with only their change as a function of the sample conditions being relevant. For samples with aerosil, a double peaked feature appears in both c and IL. Qualitatively similar results are obtained also for the C25 samples shown in Figures 3 and 4. The onset of a double peaked structure in both the specific heat19,20 and the latent heat20 results was obtained in 8CB and other LC, mixed with aerosil, over the NI phase transition, and that is at the melting point of the largest temperature ordered phase, as in the present case. The higher temperature peak (HTP) was associated with bulk-like material undergoing the transition sufficiently distant from the particle surfaces so as not to substantially feel their disordering effect. The lower temperature peak (LTP) was, on the other hand, ascribed to the layers of LC lying closer to the particles, where it is subject to the effect associated with the strong anchoring of the LC molecules to the particle surface. The LC molecules are known to bind with an orientation locally perpendicular to the solid surface they are in contact with, and thus can give rise to strain, which propagates in the neighboring layers of the nucleating ordered phase as the molecular director stiffens with decreasing temperature. The strain in the material causes a lowering of the transition temperature with respect to the bulk. In this respect, it should be mentioned that the nonzero values of IL over the LTP may not necessarily correspond to latent heat but also to enthalpy exchange associated with strain relieve as discussed in ref 20. The double peaked feature we report at the melting transition of alkanes can thus be associated with a situation similar to the one occurring in LC, which is caused by strain. In this respect, it should be reminded that it was shown by ellipsometric35 and X-ray36 measurements that alkane molecules (C32), in contact 2333
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Figure 3. Specific heat data during heating (black symbols) and cooling (gray symbols) measurements over the liquid-RII transition for C25 alkane: (a) pure sample; (b) sample with 5% aerosil particles; and (c) sample with 10% aerosil particles.
with an SiO2 surface, tend to form a monomolecular or bimolecular layers aligned parallel to the surface on top of which the subsequent molecular layers assume an orientation perpendicular to the surface. Moreover, it was also shown that the bulk layers growing on top of the perpendicular layers form ordered structures whose orientation bears a strong correlation with the perpendicular orientation. In fact, they give rise to orthorhombic structure with the molecules with the same orientation of the perpendicular layers or forming small angle with them in a monoclinic structure.36 The above-mentioned tendency to form layers parallel followed by layers perpendicular to the solid surface resulted also in a molecular dynamics simulation study, with the alkane molecules in contact with a gold surface,37 and where the perpendicular layer consisted of molecules with gauche defects. So, like in LC, it is the molecules with orientation perpendicular to the particle surface that govern the bulk growth, and the strain originating at the SiO2/alkane interface can propagate into the bulk. As was already observed in LC, the results for alkanes in Figures 1-4 show that the HTP peak values progressively decrease with particle concentration while the opposite occurs at the LTP. This reflects the progressive decrease of the fraction of material nucleating as bulk-like material, a process associated with the decrease of the mean void size in the aerosil network. At concentrations of 5% and 10%, the mean void size, in 8CB LC, was determined to be 130 and 70 nm, respectively.19 The results in alkanes show, however, several substantial differences with respect to what was observed in LC. First, the separation between the two peaks in alkanes is of the order of °C, while it was at most only a few tenths of a degree in LC. Moreover, the height of the LTP relative to that of the HTP is substantially smaller than in LC with the corresponding concentration of aerosil.20 This should be ascribed to the softer nature of the N phase in LC with respect to the RII phase in alkanes. In fact, in softer material, the molecules are able to conform to the distortion induced by the particle surface over a larger distance, giving rise to a larger volume of affected material but with a smaller local strain. The hysteresis observed between cooling and heating runs in the temperature range of the LTP is also considerably larger than in LC and also much larger than that of the HTP in alkanes. In this respect, it should be pointed out that, while the hysteresis at the HTP is only related to the supercooling associated with the firstorder character of the transition, at the LTP, where the hysteresis
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Figure 4. Latent heat coefficient IL (see text) during heating (black symbols) and cooling (gray symbols) measurements over the liquid-RII transition for C25 alkane: (a) pure sample; (b) sample with 5% aerosil particles; and (c) sample with 10% aerosil particles.
is considerably larger, it arises also because the transitions are defect “assisted”, and therefore it can depend on the different kinetics of formation and elimination of the defects during the heating and cooling runs. Finally, the temperature positions of both the LTP and the HTP in alkanes do not change substantially with increasing particle concentration, while the progressive shift to lower temperatures for both peaks and the broadening of the LTP had been observed in LC . Recently, DSC studies on C19 alkane mixed with 40 nm silica particles have been reported23 where the changes induced by the increasing particle concentration on the first-ordered peaks over the crystal-RI and liquid-RII transitions were shown. Over the liquid-RII transition, only a single peak was observed for the entire range of concentration. The authors do not provide details on the possible presence of hydroxyl groups on the particle surface and explain that the particles aggregate, with increasing concentration, adopting a nearly close packed structure, differently from the random networks formed in the present work. This, combined with the much larger size of the adopted silica particles with respect to the present case, leads to a considerably smaller surface to volume ratio at equal particle concentration, and therefore smaller total silica-alkane interface, in the vicinity of which the distorted material can form. This, combined with the smaller resolution associated with the considerably larger scan rate (2 K/min) adopted for the DSC temperature scans, with respect to the high resolution conditions adopted with PPE, possibly makes the detection of the eventual, substantially lower peaked, LTP features rather difficult. The width of the detected single peaks at the liquid-RII transition is in fact considerably larger (couple of degrees) than the ones observed in the present work. In any case, also the DSC results show that only a moderate shift of the temperature position of the peak is observed with increasing particle concentration as observed in the present case. RII-RI and RI-RV Transitions. Pure Samples. Figure 5a-c shows the specific heat results obtained in the RII, RI, and RV temperature regions for the C24 samples, while Figure 6a-c shows the corresponding ones relative to C25. Over the RII-RI transition in the pure samples (Figures 5a and 6a), the hysteresis in the transition temperatures between the heating and cooling measurements is present in both C24 and C25, confirming the first-order nature of the transition in both, as previously pointed out.12 The specific heat shows a more pronounced feature over the transition for C25 than for C24. In particular, peaked features appear for both cooling and heating runs in the former case, while 2334
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Figure 5. Specific heat data during heating (black symbols) and cooling (gray symbols) measurements over the RII-RI and RI-RV phase transitions for C24 alkane: (a) pure sample; (b) sample with 5% aerosil particles; and (c) sample with 10% aerosil particles (enlarged in inset).
only more moderate step-like features appear in C24. Moreover, the peak feature is more pronounced for the cooling run in C25, resulting in a very faint peaked feature being detected also in IL for such a run (inset of Figure 6a), where the involved values are much smaller than those observed over the liquid-RII transition. Nonzero values of IL could be not be detected for C24 over the RII-RI and also over the RI-RV transitions presumably because they would correspond to values below the resolution limit of such a kind of latent heat detection. In these cases, only the detection of the hysteresis proves to be useful to probe the firstorder character of the transitions. In this respect, it must be pointed out that, with the present high temperature resolution set up and at the employed rates of temperature change, the transition temperature hysteresis associated with temperature lag between sample and thermistor is at most a few millikelvin as obtained over second-order phase transitions such as, for example, the AN transition in LC.25 In C24, which has a larger RI temperature range than C25 (Figures 5a and 6a), the RI-RV and RII-RI transitions are well
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Figure 6. Specific heat data during heating (black symbols) and cooling (gray symbols) measurements over the RII-RI and RI-RV phase transitions for C25 alkane: (a) pure sample (for arrow see text; IL in inset); (b) sample with 5% aerosil particles; and (c) sample with 10% aerosil particles (enlarged in inset).
separated by a stretch where the values of the specific heat of the cooling and heating runs overlap. Over the RI-RV transition, the profile of c shows a moderate peaked feature over the transition region, showing a hysteresis in the peak temperature position and in the profile about the peak. The transition in C24 is therefore definitely first ordered. In C25, the two transitions are closer, and only a rounded shoulder, where c shows its maximum, appears about the RI-RV transition region. In ref 8, through the comparison of the specific heat data against the results of the X-ray diffraction study,7 the RI-RV transition temperature was placed some 0.5 °C above the inversion point of the shoulder region, corresponding, in our results, to the temperature indicated by the arrow in Figure 6a. If that were the case, no hysteresis would be involved over the RI-RV transition, implying its second-order nature. The indetermination in the actual positioning of the RI-RV transition temperature may, on the other hand, allow for a larger value of such temeparture. The hysteresis in the data of c on the lower temperature side of the RII-RI transition could then actually be associated with the RI-RV transition region merging with the hysteretic region of the RII-RI one. 2335
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The Journal of Physical Chemistry B Even with this latter possibility, the reduced first-order character of the RI-RV transition in C25 with respect to C24 would still be certified by the smaller hysteretic range in C25 as pointed out in our previous work.12 There, the attenuation of the first-order character of the RI-RV transition in the samples with smaller RI range was associated with the reduced strength, in the free energy, of the coupling term between the distortion and tilt angle order parameters, ultimately due to the reduction of the effectiveness of the interlayer molecular interaction with respect to the intralayer one. Finally, it should be pointed out that in the RI phase of both C24 and C25, the specific heat shows a rapid increase with decreasing temperature, which was ascribed to the temperature dependence of the translational and rotational degrees of freedom and their correlations.8 Samples with the Silica Particles. The effect of the disorder associated with the introduction of the silica particles is the attenuation of the features observed over both the RII-RI and RI-RV phase transitions and also the change of the temperature profile of the specific heat in the phases themselves. Because the induced changes are probed, among others, also by the detection of variations in the hysteretic behaviors over the phase transitions, the possibility that the introduced particles could act as nucleation centers for the low temperature phases, thus reducing the possible hysteresis, must be considered. This possibility should be ruled out on the basis of the following arguments. First, the hysteresis in the transition temperatures over the liquid-RII transition is very similar in the pure material and at the HTP in the sample with particles, this being true also over the RII-RI transition shown later on. Moreover, as was also previously observed in LC, the strain associated with the interaction of the alkane molecules with the particle surface is shown to lead to larger hysteresis over the LTP than that in the pure material. In the sample of C24 with 5% aerosil (Figure 5b), over the RII-RI transition the hysteresis between the heating and cooling runs remains. The step-like feature over the transition is still detectable but with a substantial reduction in the difference between the values of c in the two phases. Moreover, such values are larger than in the pure sample because of the presence of the LTP associated with the liquid-RII transition. In fact, the tail of the anomalous increase over such a peak affects the temperature region of the RII phase and part of that of RI. On the other hand, the increase of the values of c with decreasing temperature in the RI phase is now more moderate than in the pure material because of the quenched disorder introduced by the particles interfering with the temperature evolution of the previously mentioned translational and rotational degrees of freedom. Over the RI-RV transition, the peaked feature is no longer detectable, being replaced by a shoulder-like profile, similarly to the case of pure C25. Moreover, the effect of the disorder is also to shrink the temperature range of the hysteresis, which now only extends on the high temperature side of the shoulder. The first-order character of the RI-RV transition in C24 thus seems to be attenuated by disorder. The above-mentioned scenario is even more emphasized when the concentration of aerosil is brought up to 10% (Figure 5c). The RII-RI transition can now barely be detected (inset of Figure 5c), but it is still present. The tails of the LTP of the liquid-RII transition cause a vertical relative offset in the values of c of the two data sets in the RII and RI phases. The hysteresis in the RII-RI transition temperatures in the two runs is
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still present, indicating that the transition maintains its first-order character. The rise of the values of c for decreasing temperature in the RI phase is now even more attenuated. The shoulder feature over the position of the RI-RV transition is also still present, with the inversion point at the maximum occurring at the same temperature as in the less disordered samples. The hysteresis, although now very small, still shows (inset of Figure 5c), indicating that the RI-RV transition, even in such a highly disordered scenario, does take place in C24 and maintains a small first-ordered character. In this respect, it can be thought that the increasing disorder progressively weakens the coupling between the distortion and tilt angle order parameters, which, as we have previously suggested,12 should be related to the weakening of the interlayer molecular interaction. The decoupling causes the RI-RV transition to attenuate its first-order character, shifting toward a second-order one, similarly to the effect induced by the disorder over the NA transition in LC.19 It should be pointed out that in the C24 samples where the disorder induces, in the specific heat, a shoulder-like profile over the RI-RV transition, similar to the one observed in pure C25, the midpoint of the residual hysteretic region, where we can reasonably place the transition temperature, lies approximately 0.5 °C above the inversion point of the shoulder region. This makes realistic the positioning of the RI-RV transition temperature in pure C25 (arrow in Figure 6a) discussed earlier and based on previous X-ray scattering results.8 Figure 6b and c shows the results obtained in C25 with aerosil. Over the RII-RI transition, the peak features progressively get attenuated until they disappear for the highest aerosil concentration where the transition is once more barely detectable (inset of Figure 6c) but still shows the hysteresis. This confirms that, despite the disorder, whenever present the RII-RI transition remains first ordered. Moreover, because in C24 the hysteretic behavior over the RI-RV transition is substantially affected even when the lower concentration of aerosil is introduced, the fact that in C25 the hysteretic behavior of c on the lower temperature side of the RII-RI peak feature is practically unaffected by disorder (Figure 6b) should indicate that such hysteresis region should be associated with the RII-RI transition rather than with the RI-RV one as possibly suggested earlier on. The disorder lowers the values of c throughout the RI and RV phases also in C25, but the shoulder profile typical of the RI-RV transition region is still observable in the sample with the smaller particle concentration (Figure 6b). The higher degree of disorder introduced in the sample with 10% aerosil induces a substantial change of the profile of c, with a shift of its maximum to considerably lower temperature. So the transition is heavily disrupted if not completely eliminated in this case. As stated earlier on, it is known that the average distortion, characteristic of the RI phase, and the tilt angle in the RV phase are correlated9,10 and that the onset of the tilt angle requires a large enough value of the distortion.38 Moreover, as previously indicated,38 the formation of a nonzero average distortion in the sample requires the presence of an interlayer molecular interaction so that the distortions within the various layers become correlated and do not average out. The introduction of a substantial amount of disorder can weaken the interlayer molecular interaction, relative to the intralayer one, in turn reducing also the average distortion in the sample and thus hindering the onset of the tilt angle of the RV phase. Now, the greater RII range in pure C25 and the corresponding smaller RI range can be associated with a smaller interlayer interaction with respect to pure C24.10,38 2336
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The Journal of Physical Chemistry B So the fact that the disruption of the RI-RV transition by an equivalent amount of disorder is more severe in C25 than in C24 is likely to be ascribed to the less effective initial interlayer interaction.
’ CONCLUSIONS We have studied the effect of disorder, induced by the presence of silica nanoparticles, on the RI-RV, RII-RI, and liquid-RII phase transitions in C24 and C25 alkanes by analyzing, among other, the hysteretic behavior, between heating and cooling runs, of the specific heat and the latent heat, both measured by photopyroelctric calorimetry. We have found that, over the RI-RV phase transition in C24, where in the pure sample it has a first-order character, the disorder changes the profile of the specific heat and reduces the hysteresis. This is interpreted in terms of the reduction of the coupling between the distortion and tilt order parameters induced by the disorder, a mechanism that drives the transition toward a second-order character and that has also been observed over the nematic-smectic A transition in LC. In C25, where the RI-RV phase transition is second ordered or weakly first ordered in the pure sample, the profile of the specific heat also gets modified but in a more dramatic fashion at the largest particle concentration, with respect to C24. This has been ascribed to the disrupting of the interlayer molecular interaction by the disorder, causing more severe consequences in C25 whose pure sample is characterized by a lower degree of interlayer interaction than C24. The features about the RII-RI transition progressively get attenuated for increasing disorder in both alkanes until they become very small for the largest particle concentration. Nevertheless, the hysteretic behavior is observed in all cases, confirming the first-order character of the transition whenever present. Over the liquid-RII transition, the single peak observed in both the specific heat and the latent heat in the pure material splits into two features at different temperatures, similarly to what occurs over the isotropic-nematic transition in LC. A considerably larger hysteresis was observed for the peak at lower temperature, associated with strained material situated in the vicinity of the particle surface, than for that at larger temperature ascribed to bulk-like material. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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