J. Phys. Chem. 1!393,97, 67374744
6737
Reversed Hexagonal Phase Structure in Lithium Phenylstearate Christopher Barron and Stephen J. Spells' Materials Research Institute, Sheffield Hallam University, Pond Street, Sheffreld SI I WB,United Kingdom Received: December IO, 1992; In Final Form: March 19, 1993
-
The structure of the reversed hexagonall phase and the reversed hexagonal (H2) (H2) reversed hexagonal (H2) phase transition in anhydrous lithium phenylstearate have been investigated using FTIR spectroscopy. CH2 wagging vibrations from {gtgl and (ggj conformers indicate consistently smaller number of thesc than would be expected from the rotational isomeric state model, although the number of (gtgj conformersapproaches the predicted value at the H2 phase transition. The I R results enabled the alkyl chain extension to be calculated, as a function of temperature. A new model of chain packing at the ionic core surface allowed the core radiua (re)to be estimated (5.6 A I r, I 7.1 A). In combination with the chain extension, an overall cylinder diameter was calculated. By the onset of the H2 transition, this dimension had decreased to a figure less than the X-ray lattice spacing. It is concluded that interdigitation of alkyl segments has then reduced sufficiently to allow translational and rotational freedom for the cylinders to become more closely packed. Changes in chain conformation are therefore seen as the driving force for the phase transition, allowing the X-ray lattice spacing to decrease.
Introduction In several respects, lithium phenylstearate (LiPS) has been shown to behave as a pure singlesubstancealthough, as produced from a Friedel-Crafts reaction between oleic acid and benzene, the phenylstearic acid is a mixture of 12 positional isomers. Substitution occurs at positions Cs41.1along the carboxylic acid chain, with 49.4% of the phenyl groups located between C9 and Cll. I Harrison et al. showed DSC phase transitions for anhydrous LiPS at -50,155,227, and 371 O C . Z On the basis of microscopy, X-ray diffraction, and 'Li NMR measurements, the respective phases were assigned. glass
HI
-
reversed hexagonal (H,) hexagonal (H,)
H3
H2
reversed
reversed hexagonal
-
melt
Here the two reversed hexagonal (H2) phases are believed to be partially crystalline. The transition labeled H2 by Harrison et al. was accompanied by an abrupt change in both the hexagonal lattice parameter (from X-ray measurements) and the 'Li line width, the latter being associated with the onset of hindered rotational and translational motion within the polar regions of the hexagonally packed cylinders. Alkali-metaland alkalineearth carboxylicacid soaps generally undergo a series of complex stepwise phase transitions on heating.s5 These apparently involve disordering of the hydrocarbon chains initially, followed by the polar groups. Lamellar, hexagonal, ribbon, and occasionally disklike phases have been observed. In the case of lithium stearate, it has been found that the incorporation of a single phenyl group results in a drastic modification of the phase behavior? LiPS forms stable reversed hexagonal phases, whereas lithium stearate shows only lamellar crystalline and ribbon phases before melting. Raman and infrared (IR) spectroscopies are widely used for the study of molecularconformations. For alkyl chains, IR bands have been assigned to localized CH2 wagging vibrations from specific bond conformations.6 These represent departures from the all-trans planar zigzag conformation: To whom correspondence should be addressed.
0022-3654/93 /2097-6737$04.O0 / O
1353 an-'
88
where g and g'represent the two gauche conformations and t the trans one. Maroncelli et al. have used this technique to measure the intensities of the bands and hence the disorder present in the premelt 9otator phase" in n-alkanes? Since then, the method has been widely applied to such fieldsas premelting in fatty acids? the fold surface in polyethylene! and the degree of order in phospholipid suspension^.^ In the last case, the La phase w a ~ found to be much more highly ordered than an isotropicn-alkane of equivalent chain length. The major changes in phase behavior observed on substitution of a phenyl ringon the alkyl chain of lithip stcarate arc intriguing, in that the changes appear to be induced 6y a modification to the hydrocarbon chain conformations, rather than by changts to the polar interactions. An infrared spectroscopic study of bond conformations is presented here, with the aim of understanding the correlation between phase structure and molecular conformations. Use of the simple rotational isomeric state model (RISM) allows a comparison between experimentally observed conformations and those predicted for an isotropic liquid. Further, we develop here a model to calculate the ionic core diameter,which ensures a realisticseparationbchvesncarboxylate chains leaving the core. By contrast, previous models have made use of either liquidlikeloor crystallinell densities for these chains or have made assumptions about the type of packing of chains in thebexagonal array.I2 A realistic model must take into account the degree of disorder in the carboxylate chains. Tho canformational statistics obtained from IR data allow the radius of the outer "sheath" of carboxylate chains to be estimated. Combthe ionic core and sheath dimensions then enables a comparison to be made with the measured X-ray lattice spacing.
ExpcrimeetrlDet.ils
As previously described? phenylstearic acid was prepared by the Friedel-Crafts reaction of oleic acid (BDH Biochemicals, (6
1993 American Chemical Society
Barron and Spells
6738 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993
92% minimum assay) with an excess of benzene. Distillation allowed a fraction to be obtained at 212-217 OC (0.05-O.lO mmHg). Lithium phenylstearate was then prepared by titration of the acid with a molar 50%aqueous ethanol solution of lithium hydroxide monohydrate to a phenolphthalein end point. After solvent removal and drying, the soap was washed with water and ethanol at 60 OC, filtered, and washed with acetone. Final drying was accomplished over phosphorus pentoxide at 100 OC for 24 h. Elemental microanalysis of the product (Medec Ltd., Brunel University) provided percentages of carbon and hydrogen of 78.02% and 10.59%, respectively, compared with expected values of 78.64% and 10.72%. The H2 phase transition was found, by DSC, to peak at 153 OC, although the onset of the transition is in the region of 132 OC. These results agree well with previous data.* The saniple was stored in a desiccator. Infrared spectra were recorded using a Mattson Galaxy 6021 FTIRspectrometer. Aresolutionof 1 cm-*was used,and typically 100scans were recorded. Triangular apodisation and zero filling were used. The sample compartment was purged with dry air. The sample temperature was controlled to within fl OC using an RIIC heated cell and an RS CAL 9OOOtemperature controller. The L i B sample was cast from a toluene solution onto a KBr plate, using a PTFE spacer. This was then sealed with a second KBr plate, and the sides of the cell were sealed to minimize oxidation. Standard Mattson software used included the deconvolution program.
n
0.4
to..0
r
D n 0 0
0.-
experlmant
\
0.1-
I 0.
am
I..O
RadQ
lam
I..O
IYO
13.0
11.0
*.*.~.P.
Ftpn 1. IR spectrum of n-hexadecane at 25 OC, showing the rssulte
(a) Determinationof the Calibration Collstrntafor tbeNumber of Specific chrin Conformatio~~. The RISM has previously been applied to alkyl chains (e&, refs 13 and 14). We wish here to use IR data for a molecule in an isotropic liquid phase in order to make comparisons with LiPS conformational states. To minimize the pussible ambiguity in specifying an isotropic state, we have chosen a liquid n-alkane. The number of different local conformationsper mdeoule (Ni) can be calculated and compared with the integrated IR band absorbances observed (Ai). Calibration constants (ki) can then be calculated for each IR mode:
Ni = kiAi
(1)
Figure 1 shows the CH2 wagging region of the IR spectrum of n-hexadecane, after subtraction of a baseline from 1330 to 1395 cm-', Alsoshownarecurvesfittedtothe1376cm-*methylgroup mode and to the threg CH2 wagging modes. The integrated absorbances are normalized with respect to the methyl group vibration, since this is not expected to be conformationally sensitive. Sb$ grg and gig' conformations cannot be distinguished on the basis of their IR spectra, these conformationswill be grouped together and denoted (gtg]. This has certain implications: the gtg conformational band is expected to have a larger extinction coefficient than the gtg' band, on grounds of symmetry.1s However, in crystalline states, it has reasonably been assumed that the gtg' conformer is favored, with the gtg group unlikely to be accommodated within the crystal? It is possible that this argument has spme validity in the reversed hexagonal phase of Lips, withgtg conformers being preferentially excludednearer to theioniccase, Nevertheless, we group together grg and gtg'here for reasons of simplicity. Awg)/AM,= 0.553 Ab)/&
= 0.301
A w ) / A , = 0.180
(2)
These values are similar to those obtained by Senak et a1.,9 althougb A w ) L h eis somewhat larger. Note that gt refers to the "end-gauche" conformation.
Of Curve fitting.
To obtain a simple comparison between the chain statistics in LiPS and in a liquid at the same temperature, RIS calculations were carried out for the n-alkanes, including one with equivalent chain length (Le., n-heptadeeane). Following Jernigan and F10ry,13 energies for the various bond pairs ( i - 1 and i ) were taken as E,, = 0 ( p = 2, g, and g ') Et, = 500 cal mol-'( p = gand g') Egg = E8" = Et, Ed = Edg = 3000 cal mol-'
With the assumption that the conformational energies are independent of bond position along the chain, a simple statistical model was used to simulate 1OOOO alkane molecules. The numbers of various conformers were calculated as a function of chain length at constant temperature. As exptcted, the conformers {&, (gig), and k& were found to increase in number in proportion to chain length (carbon number). The SiBnificance of the sequences (gtg) and (gg) is that both conformers give rise to IR bands which may be used to determine their concentrations. The number of (ss) and &g) conformers present in n-heptadecane over the temperature range -270 to 500 OC, as calculated using the RISM, are plotted in Figure 2. The assumption of a liquid state over the whole temperature range is clearly invalid but provides a useful comparison for LiPS. In both cases, the dependence on temperature is nonlinear, with (the number of (gs) conformers) becoming larger than nhd around 190 OC. This behavior is expected, as the number of available trans sites decreases with increasing temperature. Nevertheless, the maximum +r, is not reached within the chosen temperature range. It should be noted that the changua in the predicted numbers of (gts) and conformers are relatively small: over the temperature range of our spectroscopic studies (0-200 OC), %.is expected to increase by about 50% for an isotropic liquidhke chain. The relationships between PIM and both n~ and b d were also determined from this model, as IR data provide values
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6139
Reversed Hexagonal Phase Structure in Lips
,Fit
0.4
o.a A 0
EO -2iQ.O
a c
n,o
I%E T r r r a t m /e
-U.O
X80
H.0
b
n
Ftpre 2 Variation of the number of (ird and IopI conformer0 per molecule of n-hcptadecaec with temperature. as cakulatcd from the RISM.
a
0.1
0.1
0.0
0
Figure 4. Curve fitting for th;t Lips IR spectrum at 25 OC. The fit involyts five peaks, plus a coptribution from the 1406-cm-1 peak. These correspond to the 1378-cm-l methyl group vibration, two && CH2 wagging modes, a (& CH2 wagging peak, and an end-gauche CH2 wagging peak.
s
e m
m
1870
-"-e
eIQ
1-
e-
e-
Figure 3. CH2 wagging region in the IR spcctrum of LiPS as a function of temperature.
of %fit whaeaa afull analy8is of thechain wnformation rcquira the consideration of all gauche units. Values obtained in this way for n M and nf@gJwere nu& = 1.356 conformations per molecule n,&
= 1.210 conformations per molecule
(3)
From eq 1, the respective calibration constants are
,k
= 2.452 per molecule
k,& = 4.020 per molwule
(4)
(b) Teapar- J h p d e ~ % nl t kC H 2 W e MO&Sia UFS. Figure 3showsthe C& wegging region ofthe IR spectrum of LiPS as a function of temperature. Apart from the CHI wagging vibrations, we must COnriBcr the pmsibility of phenyl
group vibrations in this region. Weak bands at 1328 and 1310 cm-I in the IR spectrumof atactic polystyrenehave been assigned to ring vibrations.16 Their intensities should be extremely small in LiPS, and they lie outside the range of immediateinterest. The preaenceof an additionalshoulder at about 1363cm-l, not observed in n-hexadecane, is notable: its origins have been investigated elsewhere,17and an assignment has been made to a distorted grg or gtg'conformer. In this work, the area under the 1363-cm-I peak has been included with the 1369-cm-I peak for this reason. Figures 4 and 5 show the results of curve fitting for Lips spectra at 25 and 156 OC using Mattson "curve fit" software. The fitsinvolve the use of five peaks, plus a contributionfor the intense peakat 1406cm-'. Thepeaksrepresentthemethylgroupvibration at 1378 cm-I, two peaks within the (gtg)CH2 wagging region, a (gdpeak, and the end-gauchepeak A xz value of 1 V or lower was taken to indicate an aceaptable fit, although this figure could be improved by using additional peaks. Only the number of pttks has been fixed for the fitting, with peaks allowed to includevariable proportions of Gaussian and Lorentzian character and variable frequency, width, and abprknce. With the exception of the methyl group vibration, for which a predominlantly Lorentzian line shape was used, the fits indicated at least Sa% Gaussian contribution to all peaks. %me confidence in the quality of fit is provided by the observation that the peak area of the endgauche vibretion, normalized with respect to the methyl group vibration, correspondsclosely to that observed for n-hexadecane. Figures 6 and 7 show the variation of absorbance of 1369- and 1352-cm-1 bands with temperature. Over the temperature range from 25 to 156 OC,both absorbances have more than doubled. Both plots show a steady increase in absorbance up to a temperature of about 130 W, which corresponds to the onset of the H2 phase transition in LipS. The variation in absorbance with temperature above 130 OC is then small, indicatingthat the hydrocarbon chain confarmations are influencod by the phase involved.
The Journal of Physical Chemistry, Val. 97, No.25, 1993
Barron and Spsllr &I 0 0
0.0.
t
;i
0
0
0.04
u !
L
0 L.1
O
0
P
LP 1
a a r a n
:O.OL
0.0,
0.00
,
aam
r m
ram
w-e
L
Y
L
Y
r-
L W
Figwe 5. Curve fitting for the Lips IR ipsctrum at 156 OC. The fit involver five p e h , p l u a contribution from the 1406-m-1 peak. These corrupond to the 1378-cm-1 methyl group vibration, two &g) CHZ wageing moder, a kg)CH2 w a e g peak, and an end-gauche CH2 wagging peak.
&a XI
r
f
%.I
#.I mi 7meuaturm f c
1
MI
u
Elgum 6. Variation in atmorbancc of the 136pCm-1IR band in Lips, after nonnalizotionwithrespectto the 1 377-cm-1 band,with temperature.
The number of specific conformers p r a m t can bs calculated from cqs 1 and 4, bearing in mind that LiPS has one methyl group per molecule, as oppoeadto two for n-hexadccane. Figures 8 and 9 provide a comparieon between the numbers and those predicted for isotropic alkyl chains of the same length, asauming that the RISM is obeyed in the latter case. At room temperature, the values of ~8 and w obtained for LIPS are approximately half the values calculatedfor the RISM. The Lips system rhows considerably more order in the chain conformation than a liquidlike chain, a point which is discwed in more detail elsewhere.17~18 It is noteworthy that at the beginningof the H2phase transition (about 130 "C),the number of (gtsl conformers per molccule approximates that expocted for an alkyl chain in the isotropic state (RISM), whereas the number of {gg) conformers per molecule is only about 75% of the isotropic liquid value. This suggests that the gg conformation is particularly difficult to
#A m,i T w J t V . /C
Y.1
mi
ml
Plgm 8. Variation in the experimentally determind number of &g) confor"perm1eculeinLipswithtcmpmature.Solidline: predicted behavior from the REM.
1 4 1
0
:I 1s
bl " P Io
"h
0
I
0
0
0
-
I4
ILI 1111 T a w m " fc
MU
I u
pbrr 9. variation in the expl3rinmtally dctmnhd number of conf~~permoleculeinL~withtcmpsntPre. Solidline: predicted behavior from the RISM.
incorporate within the r w d hexagonal phase and that the number of such conformsn is rertricted for some reason. Nwcrthelsrr, it can be concluded that the chains approach a liquidlike overall dormatiw in the vicinity of the olwt of the H2 transition. Thie is supported by the evidence that the rate of change of both q td , and w with temperature is rigdicantly reduced in the m n d r w d hexagonal phase (Figures 8 and 9). (e) Temperature Deped" of tb Average cbri.Extedoa in LIPS dthe Rotatiod I " d c State Modal. The experimental determination of the numbersof &gj and conformsrs
per~l~eofliPSuatunctionoftempcrahuc(Fi~8~d 9 )a h &Uhh60IlOf thOrOdial OXtQUiOB Of the hydrocarbon chain from the i d c core of tbc hexagonally packed cylinders. ~in~lves(i)the~ofth6RISMtocalcuk~thetotalnum~r
R e v d Hexagonal Phase Structure in LiPS
The Journal of Physical Chcmisrry. Vol. 97, No. 23, 1993 6141
n
l4I I
LU
1LI 1
"0"
LI LY
nrpC 10. VPriati~inthsawraeeChainextsarion.Rv,forn-hsptadecaae with the number of gauche units pcr molecule.
of g units per molecule corresponding to the values of %d and Q observed experimentally,(ii) the assumption that each {@g) and each (gg) conformer has an equal probability of appearing at any position along the chain, and (i) the insertion of the required numberof gunits into a modcl of the molecule (simplifkd here to that of an n-alkyl chain) to enable the overall molecular conformation to be determined. The model allows a set of 'molecules" tobegen~~andforeachvalueofn,comrpondine to a different temperature, the average chain extension can be calculated. ( d ) U t h i n m P b e n y b t e 8 r 8 t e ~(i)chrbaExbmh ~ It has been shown that the numbers of and conformers present in Lips is, at least in the temperature range below the H2 phase transition,significantlylower than the values predicted from the RISM at equivalent temperatures, indicating a more extended chaii conformation in LiPS. We now make the assumption that the relationship between Q and both u and %d is the same in Lips as predicted from the RISM. It is evident from Figures8 and 9 that thisapproximation is not strictly valid in the entire temperature region shown, as u and %d show different behavior with respect to the RISM. Indeed, it will be shown elsewhere that the phenyl group in Lips is expected to influence the backbone conformations in its immediate vicinity.17 Conformational restrictions may not result from the reversed hexagonal phase structure itself, as such a phase in cadmium stearate has been shown to be characterized by and %d values only marginally smaller than predicted from the RISM.I9 Nevertheless, in the prsaent case,we have no feasible alternative but to use and %d in the way propod. The consequence is likely to be an underestimate of As will be shown later, the chain extension is not unduly sensitive to 80 that the error introduced may not be excessive. Representative conformationsof thestearatechainin Lipscanthus begenerated, using values for nu obtained from the relationships with %d and tqd in the previous section. A model n-heptadecane chain was again used for this calculation, with between 1 and 15 guuchc units per chain and a total of 10 OOO molecules simulated. The quantity of interest here is the extension of the alkyl chain from the ionic core surface. If the fmt carbon atom of a particular chain has coordinates (xo, YO,ZO) and the ith carbon atom is at ( X I , yt, 2,) (where the z axis is the cylinder axis), then the chain extension is taken 81 the value of R,where R = [ ( X , - X ~ ) ~ +Cyf-yo)2]"2
.
such that R is "izdd It therefore repredents the maximum radial extension of the chaii from the surface of the ionic core. An idtalized geometry was chosen, with the C-C bond length of 1.54 & the C-C-C bond angle as tetrahedral, and the p u c k dihedral angle as f120°. Figure 10 shows the variation of the
in,
,.--'i
LU
?
LD U. 1.1
11
1.6
n.4
11.1
U
Flgm 11. Distribution of chaii C X ~ C M(R) ~ for n-heptadeane for a different number of puche unitr per chain.
i- udI
u
I
SJ
1.1
m.1
T r m a t u m /c
IUI
mi
pbw 12. Variation in the average chain extension, &, beyoad the ionic core for Lips with temperature. The solid linea arc intoadd only aa guides.
average value of R obtained for all simulationsM w. Clearly, the chain extension decreases with increasing Q as the chain becomes more compact. Using values predictedfor w for model n-heptadccane at different temperatures (from the RISM),we f i d that 4,decreasesfrom 11.3 A at 20 O C to 9.8 A at 500 O C . In both cases, the molecule is assumed to be isotropic, and this explains the small change in kV. F m e 11shows how the distributions of chaii extension8vary with the number ofgauche units. For one puche bond per chain, the distribution is very narrow. It rapidly broadens on incresting w,as the number of permutations of positions of gauche bonds sienificantly afftcts the chain extension. Finally, M the chain becomes crowded with p u c h e bonds, the distribution narrow again. After converting and %d values for Lips into c a m sponding values of the chaii extension for Lips can be calculated as a function of temperature. The result ( F m 12) shows R ." decreasingin an almost linear fashion up to the pham transition (H2) at around 130 OC, where the rate of dccreaw is much reduced. (U) I d c CoraR a d b Conventional methods of dctcrminhg the ionic core radius of soaps (e.g., ref 10) rely on estimater of
6742 The Journal of Physlcul Chemistry, Vol. 97, No. 25, 1993
Barron and Spells
the volumes of the polar headgroup and the alkyl chain. For a hexagonal array of cylinders,the number of polar groups per unit length of cylinder (n) is given by
where u is the cylinder separation, 3lI2a2/2is the cross-sectional area of the unit cell, 6 is the density of the soap, m is its molar mass, and Nis Avogadro’s number. The radius of the ionic core (r,) may then be expressed as
(7) where V,I is the polar headgroup volume. Harrison et a1.2used the density of lithium stearate to estimate VWp, the volume of the LiPS molecule, and the density of stearic acid in the /3 crystallineform to estimate VCH~, thevolume of the stearatechain. End effects were incorporated by estimating the volume of the methyl group, VCH,. from differences in the densities of crystalline n-alkanes with different chain lengths. This led to a value of 1.8 A-1 for n and 4.8 A for r,. Previouswork on the reversed hexagonal phase of cadmium stearate made use of the density of n-heptadecane at a similar temperature,1° thus avoiding the use of crystallinedata, although the core was assumed to show crystalline 11 made use12 of the data of Spegt and Skoulioslo g a graph of the spacing between the centers of polar cylindersin the reversed hexagonal phase (a)vs the number of carbon atoms (N,), with data from cadmium laureate to cadmium arachidate. The extrapolation back to Nc = 1 was taken to represent the core radius so that any possible interleaving of the carboxylate chains from neighboring cylinders was neglected. The values of u obtained from cadmium stearate were 4.11° and 8.5 A.12 (iii) A New Structural Model for Lithium Phenylstearate. Wide-angle X-ray diffraction allows the determination of two separate parameters of particular relevance to hexagonal phases, namely, the hexagonal lattice parameter, u, and the separation ( D ) which characterizes the ‘liquidlike” diffuse peak. In the case of LiPS, the latter peak has an equivalent spacing of 4.6 A,’ similar to values reported for n-alkanes or carboxylic acids in the liquid phase.20 D represents a characteristic separation between chains leaving the ionic core. An arrangement that is any more closely packed is clearlyunreasonable. We describe here a model dependent on these two quantities, u and D, to derive r,. The result can then be combined with chain extension calculationsin section (a) above to give the overall cylinder dimensions. We assume, for simplicity, a dgular array of points on the ionic core surface, corresponding to the points from which chains leave the core. For a two-dimensional crystal lattice of points (corresponding to the ionic core surface), with lattice parameter 0, it is possible to determine a value for r, which will accommodate the lattice, but this cannot be madecompatible with the calculated number of ions per unit cylinder length (n,from eq 6). Conversely, a choice of r, to fit the calculated value of n will not allow the twedimensional lattice to fit onto the core surface. A helical arrangement of lattice points, & the other hand, allows the core radius to be adjusted to fit the calculated value of n. Although a single helix does not provide effdent packing on the surface, the situation is greatly improved f6r a double helix, with lattice points equally spaced along the helical strands. It should be stressed here that we do not imply that there is perfectly regular packing of ions in the core: we are using the device of a helical arrangement of lattice points, with a realistic value for the separations,in order to obtain a reasonable estimate for the core radius. Figure 13 shows a two-dimensionalrepresentation of the double helical arrangement of lattice pointson the cy&drical core surface of circumference C. Taking the value of D from the wide-angle
Figure 13. Two-dimensional representation of thedouble helical packing of carboxylate chains on the ionic core for Lips molecules: the model docs not represent in detail the true packing of the chain but rather ia a device enabling the ionic core radius to be determined, as compatible with the number of polar groups per unit length of cylinder. The spots reprcstnt the p i t i o n s of carboxylate chains on the ionic core surface. D is the closest separation between chains, P the helical pitch, and 2h’ the number of chains leaving the ionic core (of circumference C)within the pitch of the helix.
X-ray peak position as the minimum separation between lattice points, the dependence of r, on the pitch, P, of the double helix can be calculated. If the number of chains leaving,@eionic core within the pitch of the helix is 2N, then for the fwst and 2Nth chains to be verticallyaligned (thereby increasing the efficiency of packing) requires that
p = -2N n where n is calculated from eq 6. From the geometry of Figure 13,
2rrC
L=and
N
(9)
$r
(P - + t 2= 4D2 Combining eqs 9 and 10 gives
+
+(N2 - 2N 1) + 47r2r2 = 4N2& Substituting for N from eq 6 , we obtain
(1 1)
The variation of r, with P can then be calculated using a value of 1.8 A-l for n3and 4.6 A for D, and the result is shown in Figure 14. There are, however, further restrictions: the pitch cannot be less than D so that the minimum value of P is 4.6 A. The double helical structure (Figure 13) also limits the pitch to a maximum value of 20. The condition DIPS20 (13) then implies a minimum value of r,. The maximum value is not determined by eq 13 but is limited by the maximum predicted in r, as a function of P (Figure 14). Figure 15 shows how these maximum and minimum values of r, (rcmox and r, -) vary with the number of chains per unit cylinder length (n). The values obtained for LiPS are shown in Table I. To provide a comparison
The Journal of Physical Chcmlstty, Vol. 97, No. 25, 1993 6743
Reversed Hexagonal Phase Structure in LiPS
TABLEII: DimeosiomoftheRenreedHexigdWuoin Lips
I
0
0
temp/QC
0
25.1 123.0 135.2
I 1.1
1-0
4.6
Pltch
fII
i*4
B.8
1.1
Flpm 14. Calculatedvariation in the radius of the ionic core (r,) with pitch of the helix (P)for the model shown in Figure 13. ?,lo I
1
X X X
X
I
1,e
181
184 186 llurkr o f i o m #r
LO
1,:
A Fig"15. Maximum (top) and mini" (bottom) valuesof r,calculated as a function of the number of ions per unit cylinder length (n).
TABLE I: Ionic Core Radius Cdculrted by Different
Methods
material
ionic core radius no. of metal ions r ?,/Ac unitlength ( n ) / f i rc/Aa r,/Ab min max
lithium phenylstearate
1.802
4.62
cadmium
0.781°
4.11°
0.53521
3.621
stearate Calcium
5.6
7.1
8.5
4.9
6.3
7.0
3.5
4.6
stearate a Data calculated from the method of Spegt and Skoulioa.lo* Values calculated by Small,I2using data from refs 10 and 21. This work. with other calculation methods, data are also shown for the reversed hexagonal phases of cadmium stearate and calcium stearate. For these divalent metal soaps, we assume that each n-carboxylate group behaves as a single monocarboxylate ion. There are then 2n carboxylate ions per unit length of cylinder. There is a similarity in the r, values obtained using the method of Spegt and Skouliosand the r, ,,,i,, valuescalculatedhere, whereas the values obtained by Small are significantlyhigher than those from both of the other methods. Small neglected possible interleaving of the chains in his extrapolation method, and this may account for the higher r, values obtained. The choice of hexadecane by Spegt and Skouliosmay result in an overestimate of the aliphatic chain volume in these materials, because of the extended nature of the carboxylate chains as compared with the R E M . Hence, the ionic core radius, as calculated from their method, may be expected to be slightly smaller. r,, as calculated above, can now be combined with the average chain extension, determined above from IR data, to obtain the overall dimensions of the hexagonally packed cylinders. This is
X-ray lattice spacing a/A2 35.9 36.1 3 1.4,36.1
min cyliidw diam &/A
*
37.3 0.4 34.0 33.1 k 0.8
max cylinder
diam &/A 40.3 0.4 37.0 36.1 f 0.8
*
now carried out, with the assumption that r, is independent of temperature. (e) Dhmsifms within the Revereed Hexagod pbrra. The ionic core diameter of the Cylinderswithin the reversed hexagoal phasea of Lips has now been d e t d e d to lie between 11.2 and 14.2 A. This dimension can be combined with the average hydrocarbon chain extonfion (section c above) to obtain an overall cylinder diameter. Table I1 shows a comparison between limits of the cylinder diameter, D, determined in this way and the lattice parameter, a, determined by Harrison et aL2 The errors quoted are calculated on the basis of the experimental e m in determining the number of (gts) and (gs) conformers (Figures 7 and 8). We have thus neglected possible errors due, for example, to a gtg' conformation being favored with respect to a gtg conformer and errors in determining r,. There is good agreement between the values of D and u at each temperature, but the two quantities show quite different behavior as a function of temperature. The lattice spacingincreasesby a very smallamount on raising the temperature from 25 to 123 "C, whereas the D values show a progressive decrease. At 135.2 "C, there are two spacings present, with the higher one absent at higher temperatures. Thisdiscontinuousbehavior contrastswith the continuous decreasebeyondthetransition. Itshouldbenotedthattheaverage chain extension defines a cylindricalsurface which is not a hard impenetrable boundary but sjmply represents the average molecular extension from the ionic core. Thus, at 25 "C,the average chainextensionhasavalueof 13.1A, butthereisa0.49probability of the chain extending beyond that distance and a higher probability (0.59) of the chain extending into a neighboring cylinder. At 135 "C,the probabilities become 0.51 and 0.61, respectively. An "interdigitation" of chains from neighboring cylinders must, therefore, be considered.
Discuwion It has been shown that the number of &dand (gs)conformers present in Lips in the fmt reversed hexagonalphase is consistently lower than the values predicted for an isotropicliquid using the RISM. On approachingthe H2phase transition,nbd approaches values expected for liquidlike behavior, although is about 0.75 of the predicted value. The reason for this is believed to be related to the phenyl group restricting the allowed conformations of neighboring bonds." The hydrocarbon chain can therefore be regarded as becoming liquidlike around the onset of the phase transition. At room temperature, the X-ray lattice spacing is slightly smaller than the cylinder diameter, but the temperature dependence of the two quantities is quite different, with the lattice parameter changing discontinuously at the H2 phase transition, at about the temperature where the hydrocarbon chain conformation has become liquidlike. At 123 "C, the minimum cylinder diameter has become smaller than the lattice spacing, suggesting that the hydrocarbon chain conformation plays a vital role in determining the phase transition: interdigitation of chains from neighboring cylinders is a major effect at 25 OC (probability of 0.59 of a chain extending into a neighboring cyliider) but has become less important at 123 "C(probability0.37). We suggest that this reduction in interdigitation is sufficient to allow some rotational and translational freedom among the hexagonally packed cylinders and that they are then able to form a more closely packed reversed hexagonal lattice. The X-ray evidence
6744 The Journul of Physical Chemistry, Vol. 97, No. 25, 1993 shows that the two structures can co-exist over a limited temperaturerange. It is noteworthythat the X-ray lattice spacing is around 1.5 Asmauer than Ddnat both 25 and 135.2 O C , if the "new' l a t h spacing is considered in the latter case. This demonstrates the close relationship between these parameters, with D apparently determining the minimum lattice spacing at aparticulartemperatu. Itshouldbenotedthat 'LiNMRstudies have shown that the ionic core also becomes more mobile after the phase transition.2
A c k a ~ w l e d ~ Support t. for C.B.from SERC is acknowledged. We would like to thank Dr. M. P.McPonald for bringing to our attention the properties of LiPS and for useful and stimulating discussions. We are grateful to Dr. S. Johnson, Dr. J. Tipping, and Dr. A. Allen (Unilaver R w r c h , Part Sunlight) for helpful discussionsand use, in the initial stages, of their FTIR equipment. Refere" rad Notea (1) Harrison, W.J.; Mcbnald, M.P.; Tiddy, G. J. T. J . Phys. Chem. 1991, 95, 4136. (2) Harrison, W .J.; McDonald, M. P.; Tiddy, G. J. T. Liq. Cryst. 1990, 7,509.
Barron and Spells (3) Skoulim, A. E.; Luzzati, V. Acra Crysrallogr. 1961, 14, 278. (4) Gallot, B.; Skoulim, A. E. Kolloid 2.Polym. 1966, 213, 143. ( 5 ) Luuati, V.;Tardieu, A.; Gulik-Krzywichi, T. Nature 1968, 217, 1028. (6) Maroncelli, M.; Qi,S.P.;Strauss, H. L.; Snyder,R. G. J. Am. Chem. Soc. 1982,104, 6237. (7) Zerbi,G.;Conti,G.;Minoni,G.;Pison,S.;Bigotto,A. J.Phys.Chem. 1987, 91, 2386. (8) Spells, S.J.; Organ, S.J.; Keller, A.; Zerbi, G. Polymer 1987, 28, 697. (9) Senak, L.; Davies, M. A.; Mendelsohn, R. J. Phys. Chem. 1991,95, 2565. (IO) Spegt,P.; Skoulios, A. Acta Crysrallogr. 1963, 16, 301. (11) Harrison, W.J. PhD. Thesis, Sheffield City Polytechnic, 1987. (12) Small, D. M. Handbook of Lipids Research. 4. The Physical Chemisrry of Lipids; Plenum Press: New York, 1986. (13) Jernigan, R. J.; Flory, P. J. J. Chem. Phys. 1%9,50,4165. (14) Flory, P. J. Statistical Mechanics of Chain Molecules; Wiley-Interscience: New York. 1969. Snyder, R. G. J. Chem. Phys. 1%7,47, 1316. Lipng, C.Y.; Krimm, S . J. Polym. Sci. 1958, 27, 241. Barron, C.; Spells, S.J. To be published. Spells,S.J.; Barron, C. J. To be published. Barron, C. Ph.D. Thesis, Sheffield City Polytechnic, 1991. Muller, A. Proc. R. Soc. London, Ser. A 1932,138,514. Spegt, P.; Skoulios, A. Acra Crysrallogr. 1964, 17, 198.
