Investigations on the ordering of five p, p'-di-n-alkyloxy-azoxybenzenes in their nematic phases by proton NMR

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Investigations on the ordering of five p,

p’-di-n-alkyloxy-azoxybenzenes in their nematic phases by proton NMR

St. Limmer, M. Findeisen, H. Schmiedel, B. Hillner

To cite this version:

St. Limmer, M. Findeisen, H. Schmiedel, B. Hillner. Investigations on the ordering of five p, p’-di-n-

alkyloxy-azoxybenzenes in their nematic phases by proton NMR. Journal de Physique, 1981, 42 (12),

pp.1665-1671. �10.1051/jphys:0198100420120166500�. �jpa-00209364�

Investigations ^{on the} ordering ^{of five p,} p’-di-n-alkyloxy-azoxybenzenes

in their nematic phases by proton ^NMR

St. Limmer, ^M. Findeisen, ^H. Schmiedel and B. Hillner

Sektion Physik ^der Karl-Marx-Universität, ^DDR-7010 Leipzig, ^Linnéstr. 5, Germany

(Reçu ^{le 31 mars} 1981, révisé le 3 juillet, accepté ^{le Il août} 1981)

Résumé.

On présente les résultats de l’étude de l’ordre dans la phase nématique ^de cinq membres de la série

homologue des p, p’-di-n-alkyloxy-azoxybenzènes par RMN. Les difficultés associées à la détermination de la valeur exacte du paramètre d’ordre par RMN des protons ^{sont discutées} critiquement. ^{Les résultats sont} comparés

à ceux obtenus par d’autres méthodes (0394~, ^rayons X). ^Les formes des raies de quatre substances mésogènes ^{ont été} calculées théoriquement, permettant de tirer des conclusions concernant la mobilité et/ou ^l’ordre intramoléculaire.

Abstract.

We present the results of proton ^NMR investigations ^{of the} ordering ^of five members of the homo-

logous ^series of the p, p’-di-n-alkyloxy-azoxybenzenes ^{in their nematic} phases. ^The difficulties connected with the determination of the accurate absolute value of the order parameter by ^{NMR is} critically discussed. The results are

compared ^to those obtained by other methods (0394~-measurements, X-ray diffraction analysis). ^The lineshapes ^of

four compounds ^are calculated theoretically permitting the derivation of conclusions concerning intramolecular

mobility and/or ^order.

Classification

Physics ^Abstracts

61. 30

76. 60

1. Introduction.

In this paper ^{we want to} present

some further investigations ^{on the} problem ^{of deter-} mining ^{the value of the} orientational order parameter S (= Szz) of (nematic) liquid crystals by ^NMR.

We performed proton ^NMR experiments ^{on the} third, fifth, sixth, seventh, ^and eighth members of the

homologous series of the _p, p’-di-n-alkoxy-azoxyben-

zenes (transition points ^are given ^{in table} I). ^Addi- tionally, ^we computed ^the spectral lineshapes ^{of thèse} compounds ⁱⁿ their nematic phases (except ^{for the} eighth member) employing ^the calculation procedure

described earlier [1, 2]. ^Detailed results and discussion of the first two members of this series, ^PAA [2], ^and

PAP [3], ^{have been} published ^elsewhere.

We chose this well-known homologous ^{series to}

discuss the difficulties and uncertainties connected with an accurate determination of the absolute value of the orientational order parameter ^S by ^NMR.

Another aim of this study ^{is to} check how reliable

our computer simulations of the lineshape ^{can be} expected ^to be, ^{and what} assertions can be derived from them with some accuracy.

2. Proton NMR stu ° s.

2. 1 GENERAL FEATURES OF THE PROTON NMR SPE RA. - ^The most obvious characteristic of the spectra o he different compounds

consists in a loss of structur going from the first

(PAA [2]) and second (PAP [3]) ^{to the} eighth ^member

Table 1.

Transition points of ^the investigated ^com- pounds [17] (TM-melting point, T cN-transition point

smectic C-nematic, TNI-clearing point).

(All temperatures ^are given ⁱⁿ degrees centigrade/°C).

of the series. Before all the separation between the central component and the main doublet peaks ^is increasingly ^{« smeared out » with} rising (odd) ^C-atom

number in the chain. Moreover, there is also a loss of structure both in the doublet wings and in the central component (cf. Fig. 1). ^{For instance, in the} spectra ^of Prop-OAB ^three peaks ^{can be resolved} in each of the doublet side wings, whereas for Hept-OAB the doublet

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198100420120166500

1666

Fig. ^1.

Characteristic proton ^NMR spectra ^of a) Prop-OAB, b) Pent-OAB, c) Hex-OAB, d) Hept-OAB, ^and e) ^Oct-OAB.

wings ^{are broad,} structureless and hardly separable

from the central peak.

Besides, ^{there can} be observed the intensity-alter-

nation of the central line of the spectra ^{with the intensi-} ty being large ^for odd C-atom numbers in the chain,

and small for even ones what has already ^{been des-}

cribed and interpreted by ^Weber [4].

A plausible explanation ^{of the} origin ^{of the weake-} ning ^{of the structure can be found} by regarding ^the

number of interacting protons ^and proton groups, resp. In the case of PAA and PAP only ^benzene ring protons, ^one methyl, ^{and one} methylene group (for PAP), resp., ^are present ^so that there is no quasi-

continuous distribution of the strengths ^of dipolar

interactions (as ^for large molecules with long aliphatic tails) but rather some distinguished ^main interactions

giving rise, ^for example, ^{to the} well-structured PAP- spectrum.

In some cases (especially for Pent-OAB and Hex-

OAB) ^distinct humps ^{at the outer} wings ^{of the} spectra

can be observed. They ^should be attributed to the interaction of (chiefly) ^{the outer benzene} ring protons and the protons ^{of the first} (neighbouring) methylene

group what could be derived from the computer simulations of the lineshape (cf. ^{[3], see} also section 3).

2.2 TEMPERATURE DEPENDENCES OF THE DOUBLET SPLITTINGS AND SECOND MOMENTS.

In figures ^{2 to 6}

the temperature dependences of the main doublet

peak splittings along ^{with the} square ^root of the second moments are displayed where the second moment data have been fitted to the corresponding

curves of the peak splittings ^{with the} fitting points being ^indicated by ^arrows.

Fig. ^2.

Temperature dependences ^{of Av} (0), Mi ^{( x ), and}

A x (*) [15] along with the scales for the order parameters ^derived from the different measurements (see right hand side of the diagram).

S’ refers to the NMR dipolar splittings ^for (a supposed) rB

^2.45 Á,

S" to NMR for rB

2.39 Á, ^and _{S~x to} the ~~-measurements [15].

Provided that the molecules undergo rapid ^reorien-

tations (compared ^{to times} characteristic of NMR)

the spectrum fs(co) ^at any given temperature ^{could be} derived frôm the (hypothetical) spectrum f1(w) ^for

order parameter ^S

¹ by ^a simple scaling procedure

if only ^{the order} parameter S( T) ^{at this} temperature ^is known. Then one obtains [2, 3]

and similarly

where M’ ^{second moment for the spectrum with S = 1,}

and M2-second ^{moment of the} spectrum ^{at a certain} value S. Thus, M2 ^{should vary with} temperature ^as the order parameter ^S. Indeed, ^{this seems to be true for}

all samples keeping ^{in mind the} experimental ^errors, although ^{there are some} deviations (Pent-OAB, ^Hex- OAB, ^see figures ^{3 and 4,} resp.) ^at higher ^S-values (as

has been already reported ^{for PAP} [3]). ^However, relating ^{to this we are} here just ^at the limits of reliable assertions. Maybe ^{a more proper choice of the} fitting points ^could improve ^the agreement.

As to the determination of absolute values of the order parameter ^{it must be} noticed that the _accuracy of this procedure strongly depends ^{on the} knowledge ^of

which points (distance) ^{in the} spectra ^{reflect the}

interaction between the ortho protons ^{of the} phenyl

rings since this interaction is normally ^{assumed to be}

Fig. ^3.

^{The same as in} figure 2 for Pent-OAB. The denotations have their former meanings.

Fig. ^4.

^{Same as in} figure 2 for Hex-OAB (labelling ^as before).

Fig. ^5.

^{Same as in} figure ^{2 for} Hept-OAB. Labelling ^{as before} except that there is now a scale refering ^{to the} X-ray ^data (0) [16]

marked by Sx instead of the scale for S ",

responsible for the appearance of the main doublet

peaks (see, ^e.g. [4]). ^{In view} of the wealth of interactions

(among ^{them even} fairly large ^ones from other proton groups) ^{it is somewhat} surprising that indeed these main peaks originate from the interactions between the phenyl protons ^{and their} splittings compare well to the values expected theoretically ^{for a} two-spin system.

This was revealed by ^the computer simulations of the

lineshapes (with ^a given ^molecular geometry) omitting

all except ^the phenyl protons ^at hrst, ^{and afterwards} taking ^{into account} distinct other groups always watching ^the position ^{of the} phenyl proton peaks.

It turned out that in all cases discussed here (and certainly ^{in most other} cases) it is well justified ^to

consider the main peaks ^as proceeding ^{from ortho} phenyl proton interactions.

Having ^{overcome this} problem there emerges the next one : for an accurate determination of the absolute value of S the exact atomic co-ordinates of at least the phenyl ring protons necessarily ^{must be}

known.

Normally, ^a distance rB

2.45 A of the ortho

phenyl protons is assumed. From X-ray crystallo- graphic investigations of mesogen compounds [5] ^one

has to conclude that the mean phenyl carbon-proton

distance is around 1.00 Á and therefore ortho proton distances have been found between about 2.36 Á and 2.48 Á, ^{with an} accumulation around 2.38, ..., ^2.40 Á

(see ^also [3]).

The influence of the angle ^{cp between the} long

molecular axis and the para axis of the benzene ring

on the calculation of S has been ignored in the fol-

lowing ^because of its smallness.

So we have given ^{in the} diagrams ^for Prop-OAB, Pent-OAB, and Hex-OAB besides the two scales for the

splittings ^{and the square roots} of the second moments also two further scales for the order parameter ^values calculated for rB

^{2.45 Á} and rB

^2.39 À, resp.

The values of S computed such differ by ^{a factor of} 1.077, ^i.e. by nearly eight per cent, only ^{from an uncer-} tainty ^{in the exact} knowledge ^{of the inter} proton distance that is probably ^still greater (see below) !

To compute S from the second moment data requires

to know the magnitude ^of M2. ^In principle, ^{it could}

be obtained assuming ^a certain molecular geometry ^as it has been done in ^our computer simulations (see

section 3). ^The uncertainty, however, ^{is the same} (if

not greater) ^{as for the} determination of S from Av.

The second moments M 2 1 ^{for the} computed spectra generally ^would yield ^S-values clearly ^too high ^com- pared ^to those derived from ^the splittings Av (if

rB

2.47 A as it was assumed in the computer ^simu- lations). Very probably ^the theoretical second ^mo- ments for S

1 are too low due to the relative large

C-H bonds used in the computer programme leading

to rB

2.47 Á. However, ^these S-values derived from

M2 agree fairly ^{well with S-values} from other methods

(see below). The values for S from Av and Mi, ^resp.,

would converge if Av increased with decreasing rB (as ^{the most} important distance) slower than the square ^root of the second moment or, ^on the other hand, ^{Av decreased with} increasing ^rB slower than

~MS2.

This could be possibly ^realized by slight changes ⁱⁿ

the conformational parameters and/or specihc ^varia-

tions (within reasonable limits) ^{of bond} lengths ^and angles. ^{The best} way is, ^{of course, a} complete X-ray crystallographic analysis ^{of the} compound ⁱⁿ question

what generally yields very good ^and consistent results

as e.g. for TBBA [6] ^and nitrophenyl-octyloxyben-

zoate [7].

1668

Hex-OAB shows a fairly strong temperature ^varia- tion of Av and M2 ⁱⁿ comparison ^{to the other}

substances.

A kind of even-odd effect of the order parameter ^can be read from figure 7. The main peak splitting ^{and the}

square ^root of the second moment are plotted ^versus

the number n of carbon atoms in the alkoxy ^{chain for}

two different temperature distances from the clearing point. Obviously ^the splittings and second moments are greater ^{for even C} numbers. The change ^{in the} splittings and second moments, resp., going ^{from a}

certain n to n + 1 is most dramatic for low n (from ¹

to 2, ^{and 2 to} 3) and flattens toward larger ^{C atom}

numbers.

The absolute values of the order parameter ^S (which ^{has been} determined assuming effective uniaxia-

lity ^{of the} molecules) ^{and its} temperature ^variation

can be compared ^{to the} results obtained by ^other

methods such as measurements of ^the anisotropy ^of

the diamagnetic susceptibility [15]. ^{In such studies,} however, the açcuracy of the absolute S-values also

crucially depends ^{on the} knowledge ^of the molecular

anisotropy ^data (from single crystals) ^{which are}

available within this series only for PAA. Therefore

a fit of the susceptibility ^{data to} the NMR results

(and ^vice versa) should be well feasible as has been demonstrated in figures ^{2 to 6} where the S-values calculated from AX - ^data [15] ^are plotted ^{such to} produce ^a good ^{fit to the} temperature dependence ^{of S}

from NMR (a ^scale indicating the S-values from A x

is additionally given ⁱⁿ figures ^{2 to} 4). However, ^the absolute values of S using the molecular anisotropy

data of PAA (Xlm - Xtm

^{61.2 x 10-6 cm3 mol-1} [15])

for the investigated compounds prove ^to be fairly large compared ^{to our NMR results. A} good agreement could be attained only assuming ^an ortho benzene proton distance between about 2.46 A and 2.50 A (cf. Figs. ^{2 to 6). A} slight increase of the magnitude ^of

the molecular anisotropy (what ^{should be} quite acceptable ⁱⁿ consideration of the fact that de Jeu and Claassen conceded that the use of the PAA-value might

« lead to an underestimation of Xm - Xtm ^{for the} higher members of the series » [15]).

Otherwise the absolute S-values for Hept-OAB

Fig. ^6.

^{Same as in} figure 5 for Oct-OAB.

Fig. ^7.

Even-odd effect of a) the square ^root of the second moment, and b) ^the peak splitting.

from Ax-studies [15] ^and X-ray diffraction investi-

gations [16] ^agree fairly ^well suggesting rB ~ ^{2.49 A}

to obtain a satisfactory accordance of our NMR data with the other results. Clearly this is in contradiction to the assumptions necessarily ^{made to} explain ^the extraordinarily large splittings ^{of the} PAP-spectra [3].

For Oct-OAB (Fig. 6), ^however, distinctly ^smaller

S-values are derived from Ax-data than from the

X-ray analysis [16].

In figures ^{5 and 6 we have} plotted the data of the

Ax-measurements together with the results of the

X-ray analysis [16] ^{as well as of our NMR} investiga-

tions. There are given ^{two scales for} S, ^{one as deman-}

ded by ^the X-ray analysis, ^{the other} refering ^{to NMR} peak splitting supposing rB

^{2.45 A.} The S-values derived from ~~ apply ^to the scale used for X-ray ^data.

The magnitudes of the order parameters ^differ by ^a

factor of about 1.12 (i.e. ^{NMR values} being ^smaller by ^{more than ten} per cent) ^for Hept-OAB, ^{and 1.13}

for Oct-OAB.

Lying ^{as a} base for the S-determination the theoreti- cal second moments (cf. Fig. 8) ^better agreement ^{can be} gained (since ^there generally rB

^{2.47 A has been} used ; ^see also section 3.1). ^For example, ^from

for the second moment of the computed spectrum ^of Hex-OAB (see Fig. 8c) one’would ^{derive an S = 0.548}

for TNI - T

^{9 K} compared ^{to S = 0.555 from} AX-

data [15].

Fig. ^8.

Computed spectra ^of a) Prop-OAB, b) Pent-OAB, c) Hex-OAB, ^and d) Hept-OAB.

3. Computation ^{of the} proton ^NMR spectra.

3.1 GENERAL REMARKS.

The spectra ^{have been} calculated using ^the approximative procedure ^des-

cribed in some detail in [1, 2]. ^A plane ^{all-trans confor-}

mation of the molecules has been taken ^{as a} basis of the simulation with bond lengths ^and angles given

in table II.

Though ^ortho proton distances of 2.47 A owing ^to

these bond data might ^{be too} large ^to yield ^realistic

S-values for all substances of this series (especially ^for

PAP [3]) ^{as discussed already} in section 2.2 a simu- lation of the proton ^NMR lineshape ^{can be} performed

Table II.

Bond lengths [14] ^and angles ^{used in the} computation ’if ^the proton ^NMR spectra.

successfully ^{since the} shape of the calculated spectrum is not too sensitive against little variations of the bond parameters ^within justifiable limits. So the overall appearance of the PAP spectrum ^didn’t change signi- ficantly ^on diminishing, ^for instance, the C-H bond

lengths ^for aromatic and methylene protons ^{to 1.00} A

and 1.03 A, resp., whereas naturally splittings ^and

second moment became correspondingly larger.

Thus for the purpose of the study ^{of how} suitable the spectra simulation _programme is for the analysis ^of

intramolecular order or mobility, ^{or in other} words,

how reliable it can produce lineshapes of mesogen

compounds ^{in their} mesophases under reasonable

suppositions, ^{the use of this set of molecular data}

seems to be justihed. ^{For an exact} determination of the absolute S-values by comparison of the theoretical and

experimental spectra, however, ^more specihc ^data

should be available (from X-ray crystallographic analysis).

Tentatively, there have also been chosen other than the plane all-trans conformations of the molecules as a basis of the computations, e.g. such ones with the

planes of the chain carbons being ^{rotated out of the}

benzene ring planes, ^{or the two benzene} rings being

twisted against each other.

Although by ^{such a} rotation of the chain planes ^a stronger decoupling ^{of the} interactions between

phenyl ^and methylene protons (of ^the neighbouring CH2-group) ^{can be obtained} giving ^{rise to a} disap-

pearance of the side humps ^{at the outer} wings ^{of the} spectra [3] the overall agreement ^between experimental

and theoretical spectra generally couldn’t be improved noticeably, ⁱⁿ many ^cases it was even clearly ^dete-

riorated. So the use of the above-described all-trans conformation seems to be well suitable for our inten- tions.

As described earlier [1-3] ^{the state of motion of a} given proton is characterized by ^{a so-called « confor-}

mational parameter » Sj designating ^the degree ^{of the}

reduction of the interaction of this proton ^{with some} other, i.e. the value of the dipolar interaction between two différent protons j ^{and k with} conformational

parameters Si ^{and Sk, resp., is reduced by a factor} Sj Sk ^{compared to the} perfectly rigid ^state (cf. [1-3]).

Normally ^the procedure ^{starts with the} spectrum of the totally rigid ^molecule (all Sj

^{1, no flips of the}

benzene rings, ^no methyl group rotation). ^Then methyl

group rotation or/and ^benzene ring flips (jumping

motion of the benzene ring planes ^{about their para}

axes by 1800) ^{are admitted.} Usually ^the resemblance

to the experimental spectrum ^{is still} poor. Therefore différent sets of Sj’S ^{are ascribed now to the distinct}

proton groups in the molecule (generally, e.g., Sj

¹

to the benzene protons) indicating their relative intra- molecular mobility ^{or order.} Hereby ^the strengths

of the interactions of the protons ^{involved are reduced} corresponding ^{to their} S/s ^{(see above).}

A more consistent method to describe the reduction

of Bo ^(dipolar interaction parameter ^of protons j

1670

and k in the absence of intramolecular motions) ^would require ^{to introduce a} conformational order _para- meter Sjk ^{for each} proton pair ^{in such a way that the} product Bh Sjk

Bjk represents the value of the average dipolar interaction parameter in the presence of intramolecular motions. Thus in the case of N pro- tons we would have to consider the large ^{number of} N(N - 1)/2 conformational order parameters Sik’

However, the characteristic features of the proton NMR lineshape ^are mainly determined by ^{the values}

of the largest Bjk’S ^which correspond ^to neighbouring protons (in alkyl ^and alkyloxy chains, resp., these are

the proton pairs ^{of the} methylene groups). Therefore,

in simulating ^PMR lineshape, only ^the Sjk’s ^of neigh- bouring protons ^{will be} important. ^If B k ^{is already}

relatively ^small (e.g. if the distance between the protons is large) ^the dipolar interaction of spins j ^{and k has no} significant ^{influence on the PMR} lineshape ^{and the}

exact value B 0 Sjk ^is relatively meaningless. ^The simple

ansatz Sik = Si ^Sk that has been used by ^{us in the}

above described procedure ^of simulating ^{the PMR} lineshape yields ^{for the} important interaction between the protons of the k-th methylene group the value ’

SkkMethylene - Sk Sk (since Sk = Sk-) with Sk being a ^site

factor of the k-th segment of the chain of the _mesogen molecule. The value of Sk ^{should be} compared ^{to the} corresponding reduction of the quadrupolar splitting

in deuterium NMR [8, 9] ^{and to} the reduction of chemical shielding in 13C-NMR [10, 11] and has the

meaning ^{of an} intramolecular orientational order parameter of the chain segment ^{k. For more distant} protons ^{the ansatz made above accounts for a motional} reduction of B0jk ^{which is} proportional ^{to the} mobility

of the sites. To calculate the exact value of S jk ^{in this}

case would require ^{to have a} detailed model for the

complicated ^chain mobility. ^As pointed ^{out before}

the PMR lineshape ^is rather insensitive to relatively

small values of Bjlk and thus the use of the above- discussed ansatz appears ^to be justified.

In all cases studied here benzene ring flips ^{had to}

be supposed ^to yield the best fit to the experimental spectra. This is in accordance with the findings ^of 13C_NMR [10, 11]. Perhaps ^some kind of hindered rotation of the benzene rings would be conceivable what cannot be totally excluded, ^{at least} by ^our

measurements.

In contrast to this a good agreement ^between experimental ^and computed spectra ^{of PAP could} only ^{be attained} without 1800 benzene ring flips.

This seems to be supported by investigations ^{of the} interpair ^{second moments} [13] by ^{means of the} spin pair dipolar echo method [12].

Besides we had to assume rotating CH3-groups ^for

all substances ^as it should be.

3.2 RESULTS OF THE LINESHAPE COMPUTATIONS.

In figure ^{8 the} computed spectra ^of Prop-OAB, Pent-OAB, Hex-OAB, ^and Hept-OAB ^{are assorted}

which can be compared ^{to the} experimental ^ones (Fig. 1). ^{For each} spectrum ^{there are also} given ^the

conformational parameters Si ^{of the protons in}

different molecular parts used in the calculation of the

corresponding spectrum. ^In this a, 03B2, y, ^etc. denote the

first, second, third, ^etc. methylene groups after the

phenyl ring, methyl protons ^{are labelled} by ^the

letter ^« M ». One has to note that all benzene protons

are assumed to be rigid (relative ^{to a} molecule-fixed frame of reference), i.e. in all cases their S/s ^{are equal}

one. As to the methylene ^and methyl protons ^{it should} be noticed that the Sjs ^{of the protons within a certain}

group ^are identical.

In all cases best fit to the experimental spectra ^could be obtained assuming ^a stepwise ^{decrease of the} Sj’s along ^the chain towards the terminal CH3-group.

The values of the CH,-group parameters ^{show a} remarkable even-odd effect which in consideration of the above-discussed difficulties should be treated with some caution. From the same reasons the fact that the absolute Sj-value ^{of the CH3-group is partially}

greater than that of the preceding CH2-group (Hex- OAB, Hept-OAB) shouldn’t be too surprising.

Generally ^the Sj’S of the first (ring-neighboured ^or a-) CH2-group ^{are close} around 0.8 indicating ^a nearly equal degree ^of (minor) mobility of this group. Again only ^PAP requires greater ^values [3]. (Remark : ^the

S/s ^{can be} varied without significant ^loss of agreement

with the experimental spectrum within limits of about

± ¹⁰ %.) ^{The value of the next} (03B2) CH2-group generally

differs only little, ^{if at} all, ^from that of the _a-group.

The relative large values of the a-CH2-groups ^cause

the distinct humps ^{at the} wings ^{of the} computed spectra ^{due to} the interaction of the methylene ^and (outer) phenyl protons ^{as has been mentioned} already

before (cf. ^also [3]). ^{This can be} observed in the experi-

mental spectra, ^too (see ^section 2.1, Fig. 1) though

often much less pronounced.

The S/s chosen for the computed spectra ^{of all} investigated compounds yielding the best fit to the

experimental ^{ones are} compiled together in table III.

a, fi, y, ^etc. have their former meanings. The asterisks at certain S.-values indicate the corresponding ^group

to be a methyl group.

Table III.

Synopsis of ^{the sets} of conformational

parameters Si ^{used in the} computation of ^the spectra with the best fit to ^the experimental ^{ones. The numbers}

in parentheses ^{are the values} of ~Rj ^{obtained from}

13C-NMR [11].

As pointed ^out in section 3.1 the value of Sj2 ^{has the}

meaning ^{of an} intramolecular orientational order parameter of the chain segment j ^{and should be com-} pared ^{to the} corresponding ^reduction parameters Rj

from deuterium and 13C-NMR, resp. In table III for Pent-, Hex-, ^and Hept-OAB ^the S/s together ^with

the _square roots of the reduction parameters fiï ^as

obtained from 13C-NMR data of benzylidene ^anilines 50-n, 60-n, ^70-n (n ^{varies from 2 to} 7) in the nematic

phase [11] ^are displayed. In 13C-NMR Rj ^{is the ratio}

of the experimentally determined value of the aniso-

tropic ^shift (of the 13C-NMR line with respect ^{to its} value in the isotropic phase) ^{of the carbon atom in the} j-th ^{segment of the} alkoxy-chain ^{to the} theoretically expected ^{one for the case of a} rigid all-trans confor- mation of the molecule.

As can be seen from table III the agreement ^of Si

with ~Rj is rather good justifying such the inter-

pretation ^{of the} S/s ^as site order parameters.

Summarizing the results of the calculations it should be pointed ^out that it is possible ^{to obtain a} good ^fit

of the spectra calculated by ^{means of the} fairly simple approximative procedure [1, 2] under reasonable

suppositions ^even for relative large ^and complex

molecules. It can serve to derive conclusions about the state of internal mobility and/or ordering, espe-

cially ⁱⁿ mesophases.

Investigations ^{of the} ninth, tenth, ^and higher

members of this series including ^an analysis ^{of their}

smectic C phases ^are presently ^{under work.}

4. Expérimental.

^The samples ^{have been} syn- thesized by the Sektion Chemie der Martin-Luther- Universitât Halle, ^GDR.

The NMR experiments ^{have been} performed ^{on a}

Bruker Fourier Transform NMR spectrometer BKR 322s at resonance frequencies of 32 and 60 MHz.

All lineshape calculations were executed on the

mini-computer ^BNC-12 (Bruker-Nicolet).

Acknowledgments.

^{We are} obliged ^{to Dr. D.}

Demus, ^{Dr. G.} Pelzl, ^{and Dr. S. Diele} (Halle) ^for placing ^{at our} disposal ^the samples investigated ^here.

Useful discussions with Prof. Dr. A. Lôsche and Dr. S. Grande ^are gratefully acknowledged.

References

[1] SCHMIEDEL, H., HILLNER, B., GRANDE, S., LÖSCHE, A., ^LIM-

MER, St., ^J. Mag. ^{Res. 40} (1980) ^369.

[2] LIMMER, St., SCHMIEDEL, H., HILLNER, B., LÖSCHE, A., GRANDE, S., ^J. Physique ⁴¹ (1980) ^869.

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