Molecular Orientational Correlations and Local Order in n-Alkane Liquids BY E. w. FISCHER," G. R. STROBL, M. DETTENMAIER,? M. STAMM$ AND N. STEIDLE~ Institut fur Physikalische Chemie, Universitat Mainz, and Sonderforschungsbereich 41, Federal Republic of Germany Received 12th September, 1979 The molecular orientation correlation, the short-range order and the chain conformation in liquid n-alkanes have been studied by various experimental methods supposing that the nature of " order " in these simple systems will reflect the typical features of the organization of polymer molecules. The orientational correlation has been investigated by means of the dependence of depolarized light scattering and magnetic birefringence on concentration of diluents, on chain lengths and on temperature.There exists a very weak orientational correlation, which is far from a nematic-like state and which can be characterized by a correlation length -=c 1OA. The orientational correlation shows a temperature dependence as predicted by de Gennes' theory of pretransitional ordering in the isotropic phase of a liquid. Alternatively the temperature dependence of order in the n-alkanes can be described in terms of a heterophase fluctuation (Frenkel), but again the number of CH2 units in an " ordered phase " is extremely small (z 8 to 9 units). The conformation of the chains has been studied by small-angle neutron scattering and Raman spectroscopy. In spite of the local segmental orientation correlation it was found that the conforma- tion of the single chains behaves as expected from Flory's theory: no conformation changes occur in the melt. The problem of local order and " structure '' within the amorphous state of poly- mers has attracted much attention in recent years.Two kinds of models have been proposed: (i) In the " coil model " it is assumed that the material is homogeneous in structure and that the configuration statistics of a single molecule in the melt or glassy state are the same as those of an unperturbed molecule in so1ution.1'2 (ii) The various " bundle models " are based on the assumption of domains with nematic liquid- crystal like arrangements of the macromo1ecules.3-5 The structure of polymeric glasses and melts has been studied by means of various methods [for recent reviews see, e.g., ref. (6)-(9)].The evaluation of the experimental data has often been impeded, however, by difficulties characteristic of polymer samples, e.g., incomplete information about chemical structure and molecular weight distribution, artificial heterogeneities being present in the sample and other sources of possible errors. Therefore it may be advisable to attack the problem of the organiza- tion of macromolecules in the condensed state by studying the simplest systems of chain molecules, namely the n-alkanes. We suppose that the nature of " order " in these systems will reflect the typical features of organization of polymer molecules. 7 Ecole Polytechnique FtdCrale de Lausanne, Dtpartment des MatCriaux, Laboratoire des $ Institut fiir Festkorperforschung der Kernforschungsanlage Jiilich, Postfach 19 13, 5 170 Jiilich, 0 Universitat Ulm, Abt.Exp. Phys. 1, Oberer Eselsweg 9,7900 Ulm, Federal Republic of Germany. polymkres 132, Ch. de Bellerive, 1007 Lausanne, Switzerland. Federal Republic of Germany.FISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE 27 So, for example, one of the main arguments for assuming a “ bundle ” structure is based on packing c o n ~ i d e r a t i o n s ~ ~ ~ * ~ ~ which should be applicable to paraffin melts as well as to polymers. Fig. 1 shows schematic drawings of the two extreme cases of models for the struc- ture of a melt of short-chain molecules. The problem of “ order ” in paraffin melts FIG. 1 .-Models of the structure of n-alkane melts. (a) Unperturbed molecular conformations as in solution, (b) liquid-crystal-like structures.l’ has already been studied by many authors both experimentally and from a theoretical point of view.l2-I7 We used the experimental techniques summarized in Table 1, and the results of these experiments will be reported and discussed in the following sec- tions, where we also will refer to previous investigations utilizing these methods.The problem has also been attacked by other types of measurements such as diamagnetic susceptibility,ll Brillouh calorimetric 25 n.m.r. relaxa- tion2”28 and the Kerr effect.29 We will discuss some of these results later. TABLE 1 .-EXPERIMENTAL METHODS USED methods informat ion obtainable depolarized light scattering (d.p.s.) magnetic birefringence (m.b.) small angle neutron scattering (SANS) Raman scattering (R.s.) wide-angle X-ray scattering (WAXS) segmental orientation correlation segmental orientation correlation conformation of single chains t- and g-population short-range order 1.DEPOLARIZED LIGHT SCATTERING (D.P.S.) Light scattering is a sensitive probe with regard to optical inhomogeneities in the sample under investigation. The polarized component of the scattered light is effected by density fluctuations, whereas the depolarized Rayleigh ratio H, is due to fluctua- tions in the optical anisotropy tensor. If one only takes into account the elastically28 LOCAL ORDER IN N-ALKANE LIQUIDS scattered radiation and if the internal field is approximated by the Lorenz-Lorentz relation, the depolarized component is given by 30-33 where & is the wavelength of light in vacuo, n is the refractive index, Ncm3 is the number density of molecules.d2 is the effective mean-squared optical anisotropy of the molecule, which in a liquid is in general different from the intrinsic mean-squared optical anisotropy 8; of a single isolated molecule. The differences are due to inter- molecular orientational correlations and therefore the ratio p = d2/d; (2) yields a convenient quantity for describing the extent of the orientational " order '' in the n-alkane liquids. The meaning of the order parameter p can be further elucidated if (under some simplifying assumptions) an orientation correlation function fe(r) = ( 3 (3 cos20ij - 1) ) (3) is introduced, where Oij is the angle between the axes of the scattering units i and j , which are a distance r apart.The depolarized component H, is proportional to the Fourier transform off0 (r). In the case that the correlation length 4 is much smaller than i, i.e. if no angular dependence of the scattered light is found, one can still measure the value Vc of the so-called correlation volume (4) which is related to the order parameter p by: In the case of flexible chain molecules it may sometimes be convenient to use a com- bined order parameter describing the orentational correlation of monomer units with an optical anisotropy r2. Then pll describes the intramolecular correlation and p12 is related to the correla- tion between units in different chains. One problem in measuring the correlation volume Vc arises from the fact that the depolarized scattering also contains an inelastic component which is due to (i) inter- molecular collisions (AHvl), (ii) correlated collision induced anisotropies (AH,"), and (iii) conventional Raman-scattering (AHV1I1). One example of the spectral decompo- iti ion^^ is shown in fig.2. In fig. 3 the integrated values of the inelastic ~cattering~~ are plotted. They depend strongly on both the temperature and the chain length and have to be subtracted from the measured depolarized intensity. The correction can be up 30% of the measured intensity. The effective anisotropy d2 of n-alkanes in solution exhibits a strong increase with in- creasing c~ncentration~~ as already described by several a ~ t h o r s . ~ ~ ~ ~ ~ So, for example, in the case of C16H34 in CC14 d2 increases from 5.8 A6 at x = 0.5 to 27.8 A6 at x = 1.0.This effect clearly indicates that there exists an orientational correlation between the axes of the polarizability tensors of neighbouring molecules. In order to determine the order parameter p defined by eqn (2) and (5) liquid n-alkanes were investigated by d.p.s. to determine their dependence on temperature and chain length.33.34 Fig. 4 P = P11 PlZ = d 2 K 2 (6)FISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE 1.6 - -i 1 . 4 - 5 r. k , 1 . 2 - h - a, t .- u 1 . 0 - =Ti' a 29 80 60 40 20 0 20 40 60 80 FIG. 2.-Spectral decomp~sition~~ of depolarized scattered light due to intermolecular collisions. Broad component AH:, narrow component AH:'. 3 / c m-1 0 20 40 60 80 100 120 T /'C FIG. 3.-Integrated inelastically scattered intensity AH: + AH:' + AHFaman as a function oo temperature for various chain lengths.34 @, C12; 0, c16; A, C18; 0, G o ; A, (224; ., c36, shows the results obtained from the suitably calibrated intensities and after subtraction of the inelastic components.Similar results were obtained by Patterson et aZ.36 and C a r l ~ o n . ~ ~ In the case of C36H74 an increase in scattering intensity at small angles was found, indicating that some heterogeneities remain after p~rification.~~ There- fore for the further analysis of the data a constant background scattering of 1.4 x cm6 was subtracted. This value was estimated from the data of Carlson, but using our own methods of evaluation.* * The methods differ mainly with regard to refractive index and the amount of collision-induced depolarization.30 LOCAL ORDER I N N-ALKANE LIQUIDS First we discuss the effects of the number n, of C-C bonds in the n-alkane. The effective anisotropy d2/n, increases with nc for all temperatures but there seems to be a saturation effect so that the order parameter p tends towards a constant value.For a temperature of 80°C the ratios d2/St are plotted against l/nc in fig. 5, which clearly indicates a chain-end effect. The extrapolation to p = 1 (no orientational correlation 9 - 8 . 7.6 5 4 lD E r. * 9 3 2 .m 2 1 0 .i; A c 24 c20 C1B c16 c12 I I I I I I I I 1 I 1 1 . 0 10 20 30 40 50 60 70 80 90 100 120 140 T / O C FIG. 4.-Temperature dependence of the effective optical anisotropy d2 of various n-alkane in the melt) leads to a critical chain length no ~8 9.For the case of C6HI4 the effective anisotropy S2 in the melt 33 agreed completely with the value measured in solution.30 Thus one has to conclude from fig. 5 that the chain ends act as a perturba- tion of the orientational ordering and that a minimum chain length of x8 9 bonds is required in order to establish some weak intermolecular orientational correla- tions. Remarkably, the same chain length is found using Raman spectros~opy~~ as a limit above which the abundance of an all-trans conformation is vanishingly small. The consequences of this observation will be discussed later. The excess anisotropy due to intermolecular order depends not only on n, but also on the temperature, as one would expect from general thermodynamic reasons. The temperature dependence of d.p.s.as demonstrated in fig. 4 cannot be explained by changes in S,", which are much smaller in the temperature range under investigation. On the contrary, one must conclude that the decrease in the effective anisotropy d2FISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE 31 with rising temperature is due to a decreasing orientational correlation, i.e. the corre- lation volume Ve or the order parameter p depend on temperature. In order to find a suitable quantitative description of the experimental results the similarity between the behaviour of the paraffin melts and the isotropic phase of 0 0.05 0.1 1.5 1 /nc FIG. 5.-Ratio of effective anisotropy d2 in the melt at 80°C to the calculatedJo anisotropy 8% of the single chain as a function of l/nc.nc = number of C-C-bonds. nematic liquid-crystal systems can be used. As an example fig. 6 shows the results 39940 of d.p.s. for the case of 4-butyl-N-(p-methoxy-benzylidene) aniline (MBBA) in the isotropic phase, i.e. a temperature above the nematic-isotropic transition. The changes in p for this case are much larger, of course, i.e. at p E 500 just above the nematic-isotropic transition temperature and p = 80 at 55°C. Because of the similarity it has been proposed 9*33934736 that the temperature effect in alkane melts can be interpreted along the same lines as in the case of MBBA, where the temperature dependence of p can be explained in terms of the general theory of orientational cor- relations in isotropic liquids developed by de C e n n e ~ .~ ~ The application of such a theory to paraffin melts has also been treated by Bend1er.l’ 40 45 50 55 60 6 5 T / O C FIG. 6.-Vv and H, components for MBBA as a function of temperat~re.~32 LOCAL ORDER I N N-ALKANE LIQUIDS It has been shown by de Gennes that in the case of a short-range orientational order above a nematic-isotropic transition point T, the intensity of d.p.s. is propor- tional to kT 2A H, w - (7) where A is the coefficient of the quadratic term in the Landau expansion of the free energy in powers of the order parameter. A can be written as A w (T - T+)Y (8) where y is a critical exponent, which is y = 1 in a mean field theory, and T+ is a tem- perature slightly below T,. Physically T+ is the temperature at which the correlation length 5 would become infinite, if the isotropic phase were still stable below T,.Neglecting this small difference the mean field approximation yields that the order parameter p in eqn (2) is given by T p = - T - T, (9) where T, is a hypothetical transition temperature for the transition from the isotropic to the nematic state. Naturally, T, is located below the melting temperature T, of the n-alkanes, since in the whole temperature range of the melt no indication of a nematic transition exists. Pure speculations ''J* about such a transition for T > T, are proved to be wrong by the results of d.p.s. Applying de Gennes' theory to polymethylene chains the questions arises, what are the units which are subjected to orientational correlation? Clearly, in the case of long chains the optical anisotropy y2 of the units correlated to each other is not identi- cal with the intrinsic anisotropy & of a whole single molecule.Due to the rotational freedom of the members of a chain, the intermolecular ordering is not expected to per- sist for the entire chain length. Therefore we adopt the concept of the " segmental orientation correlation " introduced by Bendler l2 and leave the apparent anisotropy { y i ) of such a correlated segment as an adjustable parameter which can be determined experimentally. Because of the perturbing effect of the chain ends, ( y i } depends on nc. According to eqn (9) one may assume This equation was tested by plotting nJd2 against 1/T and the results of a linear re- gression calculation are given in table 2. TABLE 2.-HYPOTHETICAL TRANSITION TEMPERATURES T, AND APPARENT ANISOTROPIES ( y: ) ACCORDING TO EQN (10) melting point transition temp.regression coefficient n-a1 kane Tm/K Tc/K < 3, )/A6 r2 ClZ 263.6 21 1 0.339 0.990 C16 291.3 223 0.408 0.984 C18 301.3 21 4 0.527 0.963 C 2 0 309.8 218 0.594 0.999 c 2 4 323.8 23 1 0.622 0.980 C36 349.1 226 0.720 0.990FISCHER, STROBL, DETTENMAIER, STAMM A N D STEIDLE 33 0.5- oz 0.4- 20.3- 0.2- 0.1- I D " h N v The values of T, are far below the melting temperature as already indicated quali- tatively by the temperature dependence shown in fig. 4. With regard to chain length, the temperature T, is almost constant; there is only a slight increase observed, see fig. 7. The apparent anistotropy { 7: ) depends strongly on chain length, however, and seems to approach a limiting value { & ) .One obtains (1 1) with { &, ) = 0.903 & 0.05 A6 no = 7.16 & 0.8. Again no is a minimum chain length below which no critical behaviour occurs; that means n-alkanes shorter than about C8H18 should not show a temperature dependent intermolecular correlation. 0.8 J h Y 230 2 22 0 21 0 O ! I I 1 I b 0 10 20 30 40 nC FIG. 7.-Transition temperatures T, and apparent segmental anisotropies < y t ) as a function of chain length. The value of ( & ) can be compared with the optical anisotropy per unit of an isolated chain as calculated by Patterson and F10ry.~' The ratio of these quantities is ~ 2 . 5 and tells us that, on average, segments of 2-3 monomer units are correlated with regard to their orientation.Just above the melting point the number of cor- related segments (or the correlation volume Vt divided by segment volume) is given by Tm/(Tm - T,) according to eqn (9) and amounts to z3 at most. So the orienta- tional correlation in the melt is extremely weak compared with that for nematic systems and the correlation length 4 is certainly < 10 A. The absolute value of T, is questionable, of course, since the validity of eqn (10) over a large extrapolation range is assumed. Thus it is remarkable that, in spite of this uncertainty, a quite different method, namely magnetic birefringence, see fig. 10, yields the same kind of results, with a value of T, which is not very different. Both methods clearly demonstrate that near their melting points all the n-alkanes under investigation are far above a hypothetical nematic-isotropic transition temperature and that such a transition does not take place in the melt.Conclusions from Bril- louin spectroscopy about such a transition18 are erroneous because they are based on34 LOCAL ORDER I N N-ALKANE LIQUIDS the assumption that there must be a linear temperature dependence of the hypersonic velocity u,(T). There are good reasons to believe that us is coupled to the order parameter p in the isotropic liquid and therefore the continuous change of p leads naturally to a slightly curved behaviour. 2. MAGNETIC BIREFRINGENCE (M.B.) When an external magnetic field B is applied to an isotropic liquid consisting of anisotropic molecules, these molecules will be slightly aligned producing a bire- fringence An which can be measured : An = nil - n 1 = A CmB2 (12) where A is the wavelength of light and Cm is the Cotton-Mouton constant.The effect is known to be extremely sensitive with regard to an orientational correlation of the m~lecules-~ and therefore it can be applied to the structure problem of liquid n-alkanes. The experimental set-up will be described in another paper.44 The measurements are rather difficult since the optical and diamagnetic anisotropies of paraffins are very Nevertheless the advantage of m.b. is that small amounts of heterogeneities in the samples do not play such an important role as in the d.p.s. measurements. If an order parameter p according to eqn (6) is introduced, the Cotton-Mouton constant of n-alkanes can be written to a first approximation as O6 cm = - 2n(n2 + 2)2 p L Actm kT AXm P 135 a M, where p is the density, L Avogadro’s number and Mm the molecular weight of a monomer unit.Am, and Axm are the optical and diamagnetic anisotropy of these units, respectively. jT describes both the intra- and the inter-molecular order. The linear dependence on p” is due to the fact that both Act and Ax per correlated segment are proportional to p , and also M = M,. The dependence of Cm on the volume fraction VJV of n-alkane in solution was first studied for C12H26, C16H34 and C20H42. A typical result is shown in fig. 8. According to theory,47 the n-weighted Cm-constants should be additive : and without intermolecular orientation correlation a straight line is expected. Fig.8 shows that in agreement with the results of d.p.s. measurements a dependence of C, on concentration is observed indicating an increase in segmental correlation with increasing concentration. According to the light scattering experiments we should expect that C , of the paraffin melts depends much more strongly on temperature than E l/Taccording to eqn (13). This is indeed observed, as shown in fig. 9 for the longer chains. However, in the case of CSHIS, Cm can be approximated by C, FZ 1/T. The results are similar to those of fig. 4 and one may assume that the temperature dependence can be again described by eqn (9). In order to prove this hypothesis some of the temperature dependent quantities of eqn (13) were eliminated by the use of Cm(T) = [n2(T) + 212 p ( T )FISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE 35 and one obtains, with eqn (6), K T - T, c,' = - where 2nNAu,Axm 135 A M,k '''* K = 3.0 f 0 0.2 0 .4 0.6 0.8 1.0 V l / v FIG. 8.-Concentration dependence of the Cotton-Mouton constant C,,, of C16H34 in CC14 solution; (-) expected behaviour without intermolecular correlations. FIG. 9.-The a function of \c - 4 . 0 1 I E N I ; -2.04 - - 1 . o - - t -n k I ] ? , , , I , , , , b 0 40 80 120 160 200 T/OC Cotton-Mouton constant of various 9-alkanes and of a polyethylene (M, temperature. 0 , PE; .A, c 3 6 €374; A , c 2 4 H ~ o ; 0, CI, H34; 0, CIZ H26; c5 Hl2. 53 000) as , C8H18 a, The quantity K is supposed to depend only slightly on temperature and the intra- molecular correlation pI1 involves (as does ( y ; } ) information on the size of the segments which are subjected to orientational correlations. Eqn (1 6) has been tested for the case of CI6Hs4 and the results are shown in fig.10. A hypothetical transition temperature of T, = 215 K was obtained in good agreement with the results of d.p.s., see table 2.36 LOCAL ORDER IN N-ALKANE LIQUIDS 7 6 5 Y 4 E u wl t- u) " 3 -1.2 \ 2 1. 0 -60 0 60 120 r/ OC FIG. 10.-Reciprocal value of the (negative) adjusted Cotton-Mouton constant C& of CI6H3., as a function of temperature. A more detailed analysis of the quantity K will be presented elsewhere.44 Pre- sently we are only interested in the chain length dependence of K, which is plotted in fig. 11. It shows behaviour very similar to (7:) in fig. 7 and proves that the concept of a critical behaviour according to eqn (16), combined with a perturbation effect of the chain ends, is well suited to the description of the m.b.results. The extent of orientational correlations is again very small. For example, in the case of CI6Hs4 at 20°C, the intra- and the inter-molecular correlation amounts to p" = 8.3, whereas a bundle of only 5 chains would result in a value of f j ~ 7 5 . It may be mentioned that the pretransitional ordering should also be reflected in the dynamic properties. According to de Gennes41 the relaxation time z of the order parameter varies as Where v is a transport coefficient and A is the quadratic term in the Landau expansion mentioned above. The results of flow birefringence and viscosity measurements 48 indicate such a behaviour at least qualitatively.A similar result is observed from Brillouin scattering2I by n-alkanes. The linewidth of the Brillouin peak which is proportional to the absorption coefficient of the liquid shows a temperature depen-FISCHER, STROBL, DETTENMAIER, STAMM A N D STEIDLE T 37 0 10 20 30 "C FIG. 1 1.-Chain length dependence of the proportionality constant K of eqn (16). dence which can be explained by eqn (18), just as in the case of MBBA observed by ultrasonic measurements .49 3. SMALL-ANGLE NEUTRON SCATTERING (SANS) In the light of the observations reported so far the very important question arises whether the n-alkane molecules in the bulk liquid state possess their unperturbed dimensions or whether the intermolecular interactions lead to a deviation from their 8-conformations. This problem can be studied either by small-angle neutron scatter- ing or by spectroscopic methods.SANS investigations of mixtures of deuterated and protonated n-alkanes have been carried out by Dettenmaier.50 The differential scattering cross-section of radia- tion scattered by N molecules per unit volume dispersed in a medium of different scattering power is given by dE/dQ = N(Ab)2P(K). (19) P(K) is the form factor of a molecule [ K = (4@)sin(B/2)] and Ab the difference in scattering lengths between the molecules and the surrounding medium. For small K the inverse of the form factor takes the form where R is the radius of gyration of an allowed conformation of the molecule and the average is taken over all conformations.According to this equation a plot of P" against ?c2 should give a straight line. From its slope ( R 2 ) can be evaluated, which is an important parameter in characterizing the conformation of the molecule. From experiment the following conclusions may be drawn:50 The radii of gyra- tion of the hexatriacontane and liexadecane molecules in the melt and in cyclohexane solution are close to each other, the difference being within experimental error. Both are in good agreement with the theoretical values calculated on the basis of rotational isomeric state theory,51 but are in strong disagreement with those for extended chains in an all-trans conformation. In addition the whole shape of the scattering curve is in good agreement with the theoretical results.In fig. 12 the experimental 50 and theoretical 52 scattering CUFVeS38 LOCAL ORDER IN N-ALKANE LIQUIDS 0.31 f/ 0 !8' (a) v I I 1 I * 0 0.1 0;2 OI3 OI4 K / P 0.94 0 7 0.4 0*3 0 0.1 0.2 FIG. 12.-Scattering functions F"(K) = nP(rc)lc2 for (a) n-C36H74 and (b) lt-C16H34 in the meIt (0) and in the cyclohexane solution (0) according to Dettenmaier." The drawn lines represent calculations per- formed by Yoon and FloryS1 for conformations with Ea = 600 cal mol-' and all-trans ones. are plotted against K. from the unperturbed state of the chain molecules. Within experimental error there is no indication of deviations 4. RAMAN SPECTROSCOPY The question of the effect of intermolecular forces on the conformations of indivi- dual chains can also be treated by Raman vibrational spectroscopy.Experiments can make use of the fact that the vibrational behaviour of a chain generally shows a sensitive dependence on its rotational isomeric state, being on the other hand only weakly affected by the molecular surroundings. The Raman spectrum of an n-alkane in the liquid state can thus be regarded as reflecting the statistical distribution of single chain conformations, Any modification of this distribution should lead to changes in the spectral shape. In considering the effect of intermolecular forces one can compare the spectra measured for the n-alkane melts with those of solutions in low molecular-weight com- pounds. Experiments of this type have been performed on mixtures of n-alkanes with carbon tetrachloride. Spectra were registered using an argon ion laser and triple monochromator (Coderg T 800).In order to locate the spectral ranges withFISCHER, STROBL, DETTENMAIER, STAMM A N D STEIDLE 39 high conformational sensitivity a temperature dependent measurement on pure n- hexane was first performed. Fig. 13 shows two spectra obtained at -90 and 77 "C, respectively. Changes in shape are clear in the range of the C-C stretching vibra- tions, 1000-1200 cm-l, and around 900 cm-l. The assignments included are those of Snyder .62 I I I I I 1 I I 1500 1400 1300 1200 1100 1000 900 800 V/c m-1 FIG. 13.-Raman spectra of n-hexane measured at (a) -90 and (b) 77°C. Assignments according to Snyder.62 These changes can be compared with the behaviour observed at room temperature for a series of mixtures with carbon tetrachloride.The volume content of n-hexane has been varied between C = 1 and C = 0.125. Fig. 14 shows the spectra in the sensitive region around 900 cm-'. No modification at all can be detected. The occupation numbers of the different rotational isomeric states thus appear to be un- affected by the dilution process. A similar observation has been made for a dilution series of n-hexadecane (C16H34) in carbon tetrachloride. Results are shown in fig. 15. Again spectra do not show a concentration dependence. The conclusion to be drawn is similar to that derived from the SANS experiments : If there are any modifications in chain conformations initiated by intermolecular forces, they are very small and lie below the error range of the measurement.Com- pared to the effect of temperature, this influence is negligible. There is no indication for the occurrence of bundle-like structures with chain conformations different from a random coil. Another spectral region of interest is that below 500 cm-l. Fig. 16 shows mea- surements on melts of different n-alkanes with carbon numbers between n = 6 and 16. A prominent feature in this range is the chain-length dependent " longitudinal acoustical mode " (LAM) associated with an accordion-like deformation of all those chains which are in the stretched all-trans conformation. As is evident from fig. 16, this band becomes very weak above n z 9 indicating that for longer chains the all-40 LOCAL ORDER I N N-ALKANE LIQUIDS 900 850 (C 1 ( d 1 FIG. 14.-Raman spectra measured for various mixtures of n-hexane [volume content C = (a) 1.0 (b) 0.5, (c) 0.25 and ( d ) 0.1251 and carbon tetrachloride (2,4 and 8 spectra have been accumulated for C = 0.5, 0.25 and 0.125, respectively, in order to compensate for the increasing dilution).l ' ' ' ' l " ~ ~ l ~ " ~ 1 " ' ~ l ~ ' ~ ~ l ~ 1300 1200 1100 1000 900 800 ?/ern-' FIG. 15.-Concentration dependence of Raman spectra measured for C16H34 + eels mixtures. trans conformation becomes highly improbable. There remains only a very broad band, here called " pseudo-LAM ". It also appears in the spectrum of polyethylene with a shape very similar to that observed for CI6H3,, and seems to be characteristic for a random coil. It is interesting to note that the intermolecular orientation corre- lation effects become obvious only for chain lengths for which no measurable all-trans population is found.This clearly indicates that the orientational correlation is not caused by a nematic-like state of stretched molecules or larger segments.FISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE -LHM /\,,LAM LAM pseudo-LAM 41 I . I S * * ' I " ' " ' ' - , , * m , 500 400 300 200 v /c m-' - FIG. 16.--Chain-length dependent low-frequency Raman spectra of liquid n-alkanes, the accordeon- mode (LAM) being indicated. 5. WIDE-ANGLE X-RAY SCATTERING (WAXS) Several authors5s56 have claimed that the analysis of the X-ray or electron intensi- ties scattered by a polyethylene melt shows lateral order and therefore proves the validity of some kind of bundle model. In a careful study by Voigt-Martin et aZ.57 it was shown that, at least in the case of electron diffraction, this conclusion is untenable.Paraffin melts have been also studied by means of X-ray ~ c a t t e r i n g . ~ ~ . ~ ~ As an example in fig. 17(a) the reduced intensity curves si(s) for melts of polyethylene (at 160°C) and n-C12H26 (at 25 "C) are plotted.58 Only small differences are detected and42 LOCAL ORDER I N N-ALKANE LIQUIDS this is also true for other liquid paraffin^.^^.^^ On the other hand electron diffraction studies of gaseous n-C16H34 have been performed;59 the intensity curve used to cal- culate the atomic pair distribution function is plotted in fig. 17(b). There are still two peaks at 2.9 and 5.2 A-1, only the first peak at 1.4 A-l is missing.So there is no doubt that this peak is due to intermolecular interferences, as is also shown by the - 3 1 0 1 2 3 4 5 6 7 SIB;’ FIG. 17.--Seattering curves si(s) in arbitrary units: (a) measured from C12Hz6 (25°C) (i) and from polyethylene (160°C) (ii)”; (b) calculated for C16H34 in the gaseous state.” temperature dependence of the position of this peak.56*58 However, the two models of fig. 1 differ with respect to the long range correlation of segmental orientation and not with regard to packing density. For rather general reasons9 it is therefore quite obvious that WAXS cannot contribute to the solution of our problem in a straight- forward manner. The pair distribution function gcc(r) of C-atoms is rather insensitive with regard to the orientational correlation.6 . DISCUSSION The results of depolarized light scattering and magnetic birefringence showed the existence of a local orientational correlation of segments of the n-alkane molecules in the bulk liquid state. The extent of this correlation is very weak, the correlation volume Vc is certainly < (10 A)’. In spite of this correlation effect there is no change inFISCHER, STROBL, DETTENMAIER, STAMM AND STEIDLE 43 the average chain conformation, so far as neutron small-angle scattering and Raman spectroscopy can detect changes of conformation. The analogy between the isotropic phase of a liquid-crystal system and the alkanes has led us to the introduction of a hypothetical transition temperature T, far below the melting point of the alkanes. The temperature dependence of depolarized light scattering and magnetic birefringence can be described in terms of de Gennes’ theory41 of pretransitional orientation ordering in isotropic phases of anisotropic molecules. Some of the calorimetric data12*25 suggest a similar analysis, and the values of T, reported by Heintz et aZ.25 agree surprisingly well for C12 and C16 with our results.Two alternative explanations of the segmental orientation correlation may be mentioned. Lemaire and Bothorel 6o found by Monte Carlo calculations two ther- modynamically stable states of a C17H36 alkane. State I is composed of totally coiled conformations without molecular correlations ; state I1 is partially ordered and exhi- bits marked molecular orientational correlations between nearest-neighbour chains.The mean optical anisotropy of the two states was calculated and, so far as we can see, a temperature dependence of the value of d2 must be expected, in contrast to the observed behaviour. Since state I1 has a higher free energy ( ~ 6 0 0 cal mol-l) d2 should increase with rising temperature and not decrease, as it was observed to do. A second alternative approach is the explanation of ordering by the assumption of a heterophase fluctuation as has been discussed from a general point of view by Frenkel? In de Gennes’ treatment it was assumed that in a homogeneous phase only the correlation length increases with decreasing temperature without any phase boundaries. In contrast Frenkel treats the pretransitional ordering as a thermody- namic equilibrium in a system consisting of a large phase A and very small “ embryos ” of phase B, which are separated by a phase boundary with surface energy CT.The number N, of embryos consisting of z molecules can be written under some symplifying assumptions as where H, is the heat of fusion, T, is the melting point and 0’ is related to the surface energy 0. t 0 0.1 0.2 0.3 0.4 ( 7, - T, 1 / r , FIG. 18.-The excess anisotropy Aa2 = a2 - & at To = 80°C for various n-alkanes as a function of the relative superheating (To - Tm)/Tm.44 LOCAL ORDER I N N-ALKANE LIQUIDS For the case of the n-alkanes Carlson3’ and Fischer 34 tried an analysis based on these assumptions. A crude test of eqn (21) can be carried out by assuming that the excess depolarized scattering is given by Ad2 = d2 - 6; = N<,> ((~)6,)~ where 6, is the optical anisotropy of a segment incorporated in an average embryo of ( 2 ) segments.A plot of the values In AS2(To) measured at a constant temperature To(=8O0C) as a function of (To - Tm)/Tm where T, is a variable due to various chain lengths, yields surprisingly reasonable results, see fig. 18. The measured values are well represented by a straight line with a slope H, ( 2 ) = 5200 cal mol-I. This is approximately H, - nc x 600 cal mol-l and therefore the constant number of mono- mer units in an embryo is nc ( 2 ) - 8.6. We do not want to extend this analysis fur- ther at the present time. 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