J. Phys. Chem. 1995, 99, 798-804
798
Rotator Phases in Mixtures of n-Alkanes E. B. Siroh,* H. E. King, Jr., Henry H. Shao, and D. M. Singer Corporate Research Science Laboratories, Exxon Research and Engineering Company, Route 22 East, Clinton Township, Annandale, New Jersey 08801 Received: August 22, 1994; In Final Form: October 31, I994@ We present an X-ray scattering study of the effect of mixed chain lengths on the plastic-crystalline rotator phases of n-alkanes. When the width of the distribution is large, as is the case of commercial waxes and other alkane-like systems such as lipids, the range of stability of the rotator phases is increased, making the rotator phases occupy a more significant portion of the phase diagram than in pure model materials. As the distribution is widened several universal trends are found: the distortion in the orthorhombic RI phase is reduced, the hexagonal RJJ rotator phase is favored over the distorted RI phase, and the tilted Rv phase is suppressed. These effects can be understood in terms of a weakened coupling between layers caused by the spread in chain lengths.
Introduction Normal alkanes CH~-(CH&Z-CH~ (abbreviated Cn) have been shown to exhibit a great deal of novel behavior including five plastic-crystalline “rotator” phases which occur between the low-temperature crystalline phases and the melting temperature.’-’ The rotator phases have long-range translational order, however, they lack long-range order with respect to rotation about the molecule’s long axis. The rotator phases are characterized by very large thermal expansion, isothermal compressibility, and heat capacity. Transitions among the rotator phases involve such order parameters as tilt and distortion, and both first- and second-order transitions have been observed. Being one of the most basic organic homologous series and the building blocks for many other molecules including surfactants, lipids, and liquid crystals, the behavior of n-alkanes is of great interest in many fields. In most “real world” applications of alkanes and alkane-like molecules, mixtures of chain lengths are prevalent. Having already presented a detailed picture of the chain length, temperature and pressure dependence of the structures and transitions in the pure alkanes9-” we present here a study of the effect of chain length mixing on the rotator phases. It has been known for some time that chain mixing increases the range of stability of the rotator phases. In the present study we report on the effect of chain length mixing on the various rotator to rotator transitions and the rotator phases themselves. The various effects of the mixing can be explained by the effective reduction of the interlayer coupling. There has been a great deal of previous work on binary mixtures of alkane^.'^-'^ The main results from these involve phase diagrams showing the regions of single phase and multiphase coexistence and the crystal structures of mixtures. Recently, Snyder et al.20-22have performed detailed studies of phase separation and mixing in binary n-alkane crystal phases, finding slow kinetics of phase separation in crystalline mixtures previously thought to remain single phase. In mixtures, an orthorhombic crystal structure occurs, even if the pure components exhibit a triclinic structure. In some instances the chain mixing results in different orthorhombic structures than that of the single chain alkanes.23 Binary mixtures typically exhibit a single phase if the longer chain length carbon number is 4 1.22 times the number of carbons in the shorter chain.24 The rotator
’
* Corresponding author.
@Abstractpublished in Advance ACS Absrracrs, December 15, 1994.
phases themselves have been studied in only a few selected binary mixtures by Ungar and Mask3 and Denicolo, Craievich and D o u ~ e t . ~ ~
Experimental Procedures The data presented in this paper were acquired with a variety of experimental techniques described in detail e l ~ e w h e r e . ~ - ” * ~ ~ High resolution X-ray scattering measurements were carried out at the National Synchrotron Light Source (NSLS) at Brookhaven on Exxon’s beamlines XlOA and XlOB. Low resolution data were taken on a Rig& 12 X-ray kW rotating-anode X-ray generator using a Huber 2-circle spectrometer. The samples from which the mixtures were made, were obtained from Sigma, typically labeled 99% pure and were used as obtained. Powder samples for X-ray measurements were held in a cell, 2-3” thick with kapton windows. Aligned samples were prepared on polished silicon wafer^.^ Differential Scanning Calorimetry (DSC) was performed on a modified Perkin Elmer DSC-2. Adiabatic scanning calorimetry was performed on a unit“ of a similar design to that of Thoen et aLZ7 Backround The Five Rotator Phases. First we will summarize what is known about the structures of the 5 rotator phases which are shown schematically in Figure 1 and were presented in detail in a previous paper.9 The 5 rotator phases are layered structures with the long axis of the molecule lying nearly along the layer normal. They exhibit 3-dimensional crystalline order, but there is no long-range order in the rotational degree of freedom of the molecules about their long axis. There are, however, shortrange correlations in this rotational degree of freedom which increase as temperature is r e d ~ c e d . It ~ is this lack of longrange order of the rotational degree-of-freedom that distinguishes the rotator phases from the low temperature crystal phases. The RJJphase is the rotator phase of highest symmetry. Each layer has an average hexagonal symmetry, and in pure materials the layers are stacked in an ABC trilayer stacking sequence. This phase is similar to the crystalline smectic-B phase found in liquid ~ r y s t a l s . ~ * - ~ ~ The RI phase has a rectangular or distorted-hexagonal lattice, where D is the distortion parameter. D is defined as the difference from unity of the ratio of the minor to major axis of an ellipse drawn through the 6 “nearest” neighbors (see Figure l).9 The hexagonal lattice distorts by compressing along the next-nearest neighbor bond direction and the RJJ to RI phase transition is first-order. The layers are stacked in an ABA
0022-3654/95/2099-0798$09.00/0 0 1995 American Chemical Society
Rotator Phases in Mixtures of n-Alkanes 0
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J. Phys. Chem., Vol. 99, No. 2, 1995 799
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Figure 2. Temperature width of the rotator phase plotted versus average chain length ii for An = 0 (solid circles), An = 0.5 (open squares), An = 1 (diamonds),and An = 2-3 (open circles). The lines are guides to the eye. To determine the width of the rotator phase, the
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melting temperature was taken to be the following form determined from a fit of pure material melting temperatures as discussed in the text. T,,, = -184.79 21.90n - 0.7820n2 0.01398n3- 9.884 x (Tin "C).
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Figure 1. Schematic showing the symmetries of the five rotator phases. The unfilled circles represent the chain-end positions in the second
layer of a bilayer structure. The gray circles for the Rn phase represent the third layer in a trilayer structure. The arrows represent the tilt direction in the tilted structures. (inset) Schematic showing distortion on the hexagonal lattice, where D is the difference from unity of the ratio of the minor to major axis. bilayer stacking sequence. It is this rotator structure that most closely resembles the prevalent low-temperature crystal phase (orthorhombic). This phase does not have long-range herringbone order; thus it is not equivalent to the crystalline smectic-E phase found in liquid crystals. The Rv phase has a similar distortion (D) to the RI and the same bilayer stacking sequence, but contains a finite molecular tilt 8 toward the next-nearest neighbors which is in the same direction as the distortion. The RI to Rv phase transition is essentially second-order. The Rm phase has monolayer end-to-end stacking with a molecular tilt (8) toward next-nearest neighbors. The distortion (D) is weak, in the same direction as the tilt and can be thought of as being induced by the tilt. This structure is isomorphous with the crystalline-G phase (of which the smectic-F is the hexatic analogue) in the liquid crystal nomenclature. In lyotropic systems such as hydrated phospholipids with ordered but uncorrelated bilayers, the phase with this tilt direction is the L p phase.31 The appearance of the tilted RWphase at higher temperatures than the Rn phase can be understood in terms of the tilt in the Rw phase being induced by a larger average area/ molecule near the chain ends associated with gauche bonds. The Rm phase derives from the Rw phase. It has monolayer stacking, a tilt 8, but the tilt direction rotates from the nextnearest neighbor direction by the azimuthal angle @. This phase is analogous to the L ~ phase L found in phospholipid bilayers.31 Mixtures. For the purpose of comparison, a useful way of presenting the various transition temperatures of mixtures are in terms of their proximity to the melting temperature of the pure alkane with the same average chain length (or an interpolation for non-integer average chain lengths). For chain
+
lengths above C22 the melting temperature exhibits insignificant even-odd effect or hysteresis. For pure C20 and below, the sample goes from crystal to liquid on heating, while on cooling it goes from liquid to rotator, the latter occurring at a noticeably lower temperature. Since in the mixtures studied, the rotator phase occurs even at shorter chain lengths, it is the liquid to rotator transition temperature which we will use for comparison. When using this transition temperature, the even-odd effect is effectively negated. In mixtures, there is a finite range of temperatures over which melting occurs; i.e., there is liquidrotator coexistence. For similar chain lengths, the coexistence curve spans a region near the line connecting the pure material melting points. We will take the interpolation of the pure material melting point curve as our reference melting temperature (T,,,). To determine this curve, we used a combination of our own data and that tabulated by Small.32 The temperature was fit to a fourth-order polynomial over the range 15 < n < 40 (see Figure 2 caption). This resulted in a fit which is merely an empirical way to provide an interpolatable functional form for comparison of the data. To characterize the mixture itself, we need a measure of the chain length as well as the width of the chain length distribution. We define a mixture by its molar average chain length and its root-mean-square deviation from that value. Thus, if is the molar fraction of chain length n, where &#+, = 1, then ii C n h n and n
Although most of the data presented here are of binary mixtures, this scheme can parametrize a mixture of any number of components. Since the goal of this study is to understand of effect of mixing on the phase transitions and structures, and not on the multicomponent phase behavior (Le., multiphase regimes), we restricted our study to mixtures where the rotator phases are stable in single-phase regions such that phase separation does not occur. From the literature, it is known that for E between about 20 and 30, binary mixtures of An 2 3 will typically phase-separate. We have found that in temary and higher mixtures a single phase can be maintained with a slightly larger An; however, these higher mixtures were not studied systematically. Phase separation due to chain length segregation could easily be seen with X-rays, because the phase with longer
Sirota et al.
800 J. Phys. Chem., Vol. 99, No. 2, 1995
average chain length would have a larger layer spacing and multiple layer thicknesses would be observed.
Results and Discussion Rotator-Crystal Transition. We first discuss the overall range of stability of the rotator phases as a function of ii and An. We plot in Figure 2 the width ATR of the rotator phase with respect to the idealized melting temperature ATR = T,,,(ii) - Trot-xdversus ii for various An. At An = 0 there is a small increase in ATR as chain length decreases. This effect is significantly magnified as An increases. For An = 2 the rotator phase stability range reaches nearly ATR = 35 "C. In mixtures, the rotator phase present at the rotator to crystal transition is predominantly the RI. Both the crystal and RI phases are orthorhombic, and the transition is characterized by an abrupt drop in the aredmolecule AAm, an increase in the lattice distortion AD=, and a latent heat AHM. The symmetry change at the transition involves the development of long-range herringbone order resulting in a (121) X-ray reflection. Shown in Figure 3a is AAm plotted versus ATR for the An studied (0 5 n 5 3). We find that the decrease in AAM appears to be strongly coupled to an increase in ATR. As we shall mention again later, the thermal expansion in the RI phase is very large but does not depend on An. Therefore, the wider the temperature range of the rotator phase, the more nearly equal to the crystalline area per chain the rotator phase attains before undergoing the transition to the crystal phase. The area per chain for the crystal phase (in comparison to the rotator phases) is essentially temperature and chain length independent; thus, it can be thought of as a single reference state. It is not surprising then that AAM would only depend on ATR. In Figure 3b we plot the entropy of transition AS= = AHuITRx measured with DSC for all samples with 0 5 An 5 1, thus, the total range of ATR is smaller than for Figure 3a. The results have a large scatter due to experimental uncertainty, however, a trend similar to that for AAm is evident. Since the heat capacity in the RI phase decreases strongly with decreasing temperature when the temperature range is large," it is not surprising that the magnitude of the slope of AS=(ATR) decreases as ATR increases, because the excess heat capacity in the lower temperature range of the RI phase (which becomes accessible when the ATp, is large) is not as large as that at higher temperatures. We now discuss how the jump in the distortion at the transition depends on An. In Figure 3c we plot the jump in distortion, AD=, at the rotator-crystal transition versus ATR. Unlike the area change, ADw is noticeably dependent on An. That is, for the same ATR, ALlm is larger when An is larger. This means that the value of D at the transition is lower when An is larger. This is consistent with an interpretation that the distortion is strongly mediated by interlayer coupling, which is reduced by a dispersion in chain lengths. We plot versus
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parameter jump, decreases and even changes sign, the area jump is always finite for this transition. Rotator Phase Diagram. In Figure 4 we show the phase diagrams of the rotator phases for pure alkanes (An = 0), n:(n 1) 5050 mixtures (An = OS), and n:(n 2) 50:50 mixtures (An = 1). In addition to the increased range of the rotator phases as a whole with increasing An, we also observe the increase in RI as the predominant rotator phase, the squeezing out of the tilted Rv phase, and the increase in the temperature range of the Rw phase. We will now discuss some of the phases and transitions individually. The Rn Phase. We first point out that the areal thermal expansion (dAfdT) = 0.023 f 0.001 A2f"C in the Rn phases is
+
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Figure 3. (a) Aredmolecule jump at the rotator-crystal transition (AAm) plotted against the temperature range of the rotator phases (ATR) for the range of ii and An in the study. (b) Molar entropy of transition for the rotator-crystal transition (AS,) plotted against ATR. The solid (open) circles are cooling (heating). These are for various ii with 0 d An 5 1 . The bifurcation at low ATR results from the even-odd effect in pure materials. (c) Jump in the distortion & at the rotator-tocrystal transition plotted versus the temperature width of the rotator phase ATR for varying A and An = 0 (solid circles), An = 0.5 (open squares), An = 1 (diamonds), and An = 2-3 (open circles). Curves are guides to the eye. (d) The jump in the distortion &at the rotatorto-crystal transition plotted versus AA, for varying ii and An = 0 (solid circles), An = 0.5 (open squares), An = 1 (diamonds), and An = 2-3 (open circles). Lines are guides to the eye.
Rotator Phases in Mixtures of n-Alkanes
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. I Phys. . Chem., Vol. 99, No. 2, 1995 801
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without any observable trends in Ti or An. We can characterize the Rn phase by its width in temperature (AT) as well as the jump in the distortion AD at the Rn to RI transition. In Figure 5a we plot AT of the R11 phase versus An as a composite of our data at various Ti. It is clear from this plot that there is an overall increase in the range of stability of the Rn phase with mixed chain lengths. For example, in pure materials, the RU phase does not appear below C22. In a binary mixture of C20 and C21 (E = 20.5, An = 0.5) it still does not appear. However, in a mixture of C20 and C22 (Ti = 20.9, An = 0.9) the RII phase has a 3 "C range. In a multicomponent mixture (E = 19.9, An = 2.1) the RII phase has a 13 "C range. In Figures 5b,c we have extracted points in the range of 22 5 ii 5 23 and 24 5 E 5 25, respectively, and plotted them versus (An)z. The data appear to follow a line which implies that AT = AT0 a (An)2,where AT0 = 2.8 "C and a = 2.7 for 22 Ifi 5 23 and AT0 = 4.5 "C and a = 2.2 for 24 5 E I 25. We can understand this dependence on (An)2as follows: The Rn phase does not have significant interlayer correlations with respect to the rotational degree of freedom of the molecules,
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while the RI phase does. The energetic favorability and entropic opposition to such correlations are responsible for the stability of the RI phase at lower temperatures. A mixture of chain lengths tends to "roughen" or smear out the interlayer surface, causing a decrease in the interaction energy of correlated rotations. In the case where there is a single chain length, the layer spacing is set by the position of a potential minimum. At such a position the first derivative of the energy with respect to position should vanish, and the energy should vary as the square of the deviation from that distance. Since An represents the root-mean-variation of chain lengths and a shorterllonger chain would have a larger/smaller distance to the next average layer, we expect the energy cost in the RI phase to vary as (An)2. We then ask how the jump in distortion, D,at the RII to RI transition is affected by the extended range of the Rn phase. We plot in Figure 5d, AD versus AT. The AD data is a composite from different measurements, and since the reported
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Sirota et al.
802 J. Phys. Chem., Vol. 99, No. 2, 1995
TABLE 1: Latent Heat AH of the Rn-R1 Transition, the Temperature Width of the Rn Phase, and the Jump in D at the RH-RI Transition for Various ii and An; Also Shown Is AT - ATEnum and AHIAHBnum AH
H
An
(kJ/mol)
22 23 24 25 26 23.49 22.49 20.55 24.93
0 0 0 0 0 0.50 0.50 1.oo 2.43
1.o 0.61 0.44 0.25 0.10 0.24 0.135 0.16 0.80
AT ("C) 1.82 2.90 3.97 4.81 3.39 4.27 3.37 3.10 16.8
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0 0 0 0 0 0.87 0.96 5.90 12.01
1 1 1 1 1 0.41 0.17 0.16 2.87
value of hD is the smallest observed value in the RI phase, it is sensitive to the temperature step size. Despite the gap in our data near the AT range where AD increases, the data clearly imply that AD is rather flat, or even slightly negatively sloped until AT increases above -10 "C, where hD increases significantly. The latent heat AH, of the RII-RI transition has been measured in a few of the binary mixtures. The results are shown in Table 1. Since in the pure materials there is a strong chain length dependence to AH and AT, we also include in the table the ratio AH/AHEpure, (the ratio of the latent heat of the mixture to that of a pure material with that average chain length) and AT - AT,,,, (the difference in the RII range between the mixture and a pure material). Looking at the ratio as a function of temperature range difference; there appears to be at fiist a decrease in the latent heat and then a stronger increase. We have only measured one value of AH where AT =- 10 "C, but it is likely that the latent heat effect reflects the increase in AD as shown in Figure 5d. We have noted another change in behavior associated with AT > 10 "C which relates to the layer stacking sequence in the Rn phases. When An < 1.8 (corresponding approximately to the range where AT < lo), the stacking of the hexagonal layers is the ABC trilayer sequence characteristic of the pure alkanes. When An > 1.9 the stacking becomes ABAB bilayer. Thus, the increased AD appears to occur in the same mixtures which contain the bilayer Rn phase. We have not yet found a mixture which shows a temperature driven bilayer. to trilayer RII transition. The bilayer ABAB is the more disordered structure, and in the crystalline smectic B phase of thermotropic liquid crystalline materials an ABAB to ABC transition typically occurs upon decreasing t e m ~ e r a t u r e . ~ ~ In mixtures which result in a large hD, apparently associated with the bilayer modification, a rather unique phenomenon occurs as the temperature is reduced through the Rn phase.26 On reducing temperature, when the temperature is about 10 "C below Tm,the Bragg component of the in-plane peaks decrease continuously. The diffuse scattering under the Bragg peak does not appear to change in intensity, and if the range of the RII phase is wide enough, the Bragg component disappears completely. The lack of an in-plane Bragg peak implies .that this phase has the symmetry of a smectic liquid crystal. As the temperature is further reduced, the system undergoes a transition to the RI phase, where the Bragg peaks are restored. It is for this case that AH/AI&,,, becomes large (in Table 1). A detailed X-ray study of this phenomena was carried out on aligned samples of C23K28 mixturesz6 which allowed a clear determination of the origin of the scattering. A series of high resolution powder scans for the C23/C28 50% mixture (E = 25.26, An = 2.49) is shown in Figure 6(a-e) elucidating this effect. With a low-resolution X-ray spectrometer setup, this effect appears as a broadening of the peak. The Bragg intensity
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Figure 6. A series of high resolution powder scans for a C23IC28 50% mixture (ii = 25.26, An = 2.49) at (a) T = 48.5 "C , (b) 43.7 "C, (c) 40.0 "C, and (d) 37.5 "C, in the Rn and at (e) T = 36.1 "C in the Rl phase. (f)Bragg peak intensity versus temperature for the C23lC28 50% mixture (ii = 25.26, An = 2.49) in the RE phase showing the disappearance of long-range order. The solid line is a fit to the form e c f i .
versus temperature for a C23/C28 50% mixture is shown in Figure 6f along with a fit to a simple square-root form which suggests that there might be a phase transition associated with the disappearance of the in-plane Bragg peak. We have verified that this effect is reversible and is an equilibrium and not a kinetic effect. A small-angle neutron scattering study 33 on perdeuterated C23 in protonated C28 resulted in no evidence of local chain length segregation in this disordered phase. We explain the origin of this effect as follows: In the RU phase which has an average hexagonal symmetry, the molecules form small orthorhombically distorted domains (Le., RIfluctuations). Associated with these fluctuations are correlation lengths both within the layers and normal to the layers. (In principle, a measurement of the width of a diffuse peak at the (121) position would give us these lengths, however, such a peak is too weak to measure.) In pure materials, the correlation lengths (Le., size of the "cybotactic groups") are very small at the transition to the RI phase.3 Due to the weakened interlayer coupling in the mixtures, the RI phase is suppressed and the RII phase continues to be stable to lower temperature. This allows the RI fluctuations in the RII phase to grow larger, but they are still not preferentially oriented in one direction, thus maintaining the overall hexagonal symmetry (Figure 7a). When the transition occurs to the RI phase, the orthorhombic domains spontaneously choose a preferential direction, breaking the overall 6-fold symmetry. To understand the decrease in intensity of the Rn peaks, we note that one of the distinguishing features of the rotator phases is that the symmetry of local packing is lower than that of the overall structure. Thus, in the hexagonal Rn phase, the molecular positions are not exhibiting harmonic vibrations about
J. Phys. Chem., Vol. 99,No. 2, 1995 803
Rotator Phases in Mixtures of n-Alkanes
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27 a well defined hexagonal lattice, but rather there is a structurally 3-fold disordered orthorhombic l a t t i ~ e . ~This * ~ *results ~ ~ in an extremely anharmonic crystal where this anharmonicity has been demonstrated by thermal expansion, isothermal compressibility, and calorimetric measurements.loq1 It is clear that 3-fold rotationally disordered orthorhombic domains will result in an overall hexagonal structure. A parameter which effects the intensity of the Bragg peaks is the mean square displacement (u2) of the average molecule from an average hexagonal lattice. (u2)clearly increases with the magnitude of the local distortion and with the size of the orthorhombic domains. (This is shown schematically for a rectangular distortion of a square lattice in Figure 7b.) The Bragg peak intensities will fall off as exp( -q2(u2)) becoming weaker as (u2) increases. The RV Phase. We now discuss the behavior of the tilted RVphase in mixtures. This phase appears to be the least stable of the rotator phases, occurring only in an intermediate chain length range of pure alkanes (C23-C27). High pressure studies1° on C23 have shown that the tilt angle 8 appears to be strongly related to the distortion for a particular chain length with a tilt onset at a particular distortion 0,. This threshhold distortion D, increases with decreasing chain length, such that for chains shorter than C23 the distortion necessary for finite tilt is never attained. On the high chain length side, the RV phase is replaced by the tilted Rm and Rw phases stabilized by disordering at the chain ends. Another observation in the high pressure study is that the presence of an intercalating gas strongly suppresses the RVphase, not only by decreasing D but also by increasing D,. Adiabatic scanning calorimetry studies have shown that the transition from RI to RV is second-order." In Figure 8 we plot the maximum D observed before crystallization, the minimum D observed before the transition to Rn, and D,,the distortion at the onset of the Rv phase. D,
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-
is plotted for both An = 0 and An 0.5. In single chain materials, below n = 23 the D,curve goes above the Dmaxcurve, and therefore crystallization occurs before the RV phase is encountered. At about n = 26 the D, curve drops below the D,,,j,, curve, and a direct Rn - RV transition occurs. In mixtures with An = 0.5, the 0,curve is displaced upward, requiring a larger distortion before the onset of the RV phase. We have found the RVphase to be absent in 5050 mixtures of n and n -I-2 alkanes. In a series of C23/C25 mixtures the RV phase was absent between 5% and 85% C23. This data is consistent with a picture of the interlayer coupling being important for the stability of the Rv phase and weakened interlayer coupling due to either mixed chain lengths or intercalated gases suppressing that phase. The Rm and R ~ Phases. v The range of stability of the Rw phase with respect to the Rm phase for mixed chains is of interest. On this point our data are rather limited; however, one trend is clear from Figure 9. As An increases, the range of the Rw phase becomes enhanced. This effect is weak for An = 0.5, but for An = 1 (corresponding to a 5050 C28/C30 mixture) the RIVphase width has increased from -3 to -6 "C. From adiabatic scanning calorimetry we observed this transition to be second order, with a jump in the heat capacity at the transition of AC, = 0.07 kJ/mol, which is slightly less than that for pure C29." From the phase diagram in Figure 4, we can also see that in mixtures the tilted Rw and Rm phases have been slightly squeezed out by the Rn phase. The RIPhase. Since, with increasing An, the RV phase is eliminated and the transition temperature to the crystal phase
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Acknowledgment. We acknowledge discussions with X. Z. Wu and the technical assistance of Kim Mohanty and Steve Bennett. The N.S.L.S. at Brookhaven is supported by the U.S. Department of Energy.
0.05
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References and Notes
0.10
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n
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phases are likely to play an important role in real systems which consist of mixtures. Regarding the transitions among the various individual rotator phases, we find that the hexagonal Rn rotator phase is favored over the orthorhombic Rr phase, and the tilted Rv phase is suppressed. We have argued that the main effects of chain length mixing come from the weakened interlayer interactions.
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A rA2i Figure 10. D(A) in the RI phase of various compositional binary mixtures of C21/C23. Note the reduction of D with increasing A n . The data have been split into two plots to better illustrate the point.
is lowered, it is the RI phase which shows the most noticeable increase in range of stability. This phase exhibits nonmonotonically varying heat capacity and a dramatic change in thermal expansion and isothermal compressibility over the temperature range of that phase. These effects will be discussed in detail in another paper. Two of the parameters which we find useful to compare are the aredmolecule (A) and the distortion (0).In a study of the n-alkanes under pressure,lO we found that increased pressure (with a nonintercalating gas) decreased A much more than it increased D , relative to the case where the change was induced by temperature. Another effect observed in that study was that when the pressure was applied with an intercalating gas, the increase in distortion with pressure was noticeably reduced. This was attributed to the decreased coupling between layers caused by the intercalated gas. To see the effect on the relationship between D and A of mixing chain lengths, we measured a series of C21/C23 mixtures as a function of temperature in the RI phase. We present the data in Figure 10 as D vs A for the different mixtures. In the pure materials, D for a given A is high. As An increases, D(A) decreases. This is the same effect as observed for intercalating gases and is consistent with the picture of the distortion being mediated by interlayer interactions and the mixing of chains reducing those interactions. In the complete absence of interlayer interactions as in surface crystallized monolayers of the alkanes floating on their own bulk liquid, even in chain lengths as low as C15 where the melting transition is far from a transition to the hexagonal RE phase, only the hexagonal phase is observed at the surface.35
Conclusions We have presented a study of the effect of chain length mixing on the rotator phases of n-alkanes. The range of stability of the rotator phases, in general, is greatly enhanced by increasing the width of the distribution. This shows that rotator
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