the inventive chiral photoisomerizable compounds are mesogenic or liquid crystalline , i . e . they can induce or enhance mesophase behaviour for example in a mixture with other compounds or exhibit one or more mesophases themselves . it is also possible that the inventive compounds show mesophase behaviour only in mixtures with other compounds , or , in case of polymerizable compounds , when being ( co ) polymerized . mesogenic inventive compounds are especially preferred . they can easily be synthesized , also on large scale of several hundred grams , with a broad range of derivatives using standard methods that are known from the literature , the starting materials can be obtained commercially or synthesized cheaply using methods known from the literature they can be prepared enantiomerically pure as compounds of different handedness ( left handed and right handed ), enabling both left and right handed helices to be formed in a nematic host , the availability of both helices is a considerable advantage , e . g . for the use in security applications , as it enables the production of chiral films or coatings reflecting circularly polarized light of a single handedness , they exhibit a high htp , they exhibit a good solubility in liquid crystalline mixtures , they exhibit broad liquid crystalline phases , when inventive compounds are used as chiral dopant in a liquid crystalline mixture , due to their high solubility higher amounts of dopant can be used to produce a high twist (= a low pitch ), in case high amounts of dopants are needed , due to the broad liquid crystalline phases of the inventive dopants the liquid crystal phase of the host mixture is less negatively influenced , due to their high htp , lower amounts of inventive dopants are needed to achieve a high pitch , and thereby the liquid crystalline properties of the mixture are less negatively affected , liquid crystalline mixtures comprising one or more inventive dopants show a considerably improved low temperature stability , nematic liquid crystalline mixtures comprising one or more inventive dopants show a reduced temperature dependence of the threshold voltage when used in electrically switchable displays , preferably the compounds of formula i comprise one or more polymerizable groups . x 1 , x 2 , x 3 , x 4 , x 5 and x 6 are selected from a ) h or straight chain or branched alkyl with 1 to 20 c atoms wherein one or more ch 2 groups can also be replaced by — o —, — s —, — co —, — nr 0 —, — ch ═ ch —, — c ≡ c — in such a manner that o and / or s atoms are not linked directly to one another and wherein one or more h - atoms can also be replaced with f or cl , b ) — b -( sp ) n - g , and c ) — b -( sp ) n -( m 1 - z 1 ) i -( pi ) k -( z 2 - m 2 ) i — r , wherein two of x 1 , x 2 , x 3 , x 4 , x 5 and x 6 may also form together a cyclic group with up to 40 c atoms that is optionally substituted with one or more groups r , and x 1 ≠ x 2 ≠ x 3 and x 4 ≠ x 5 ≠ x 6 , r 0 is h or alkyl with 1 to 4 c atoms , g is an aliphatic or aromatic carbocyclic or heterocyclic group with 3 to 40 c atoms that may also comprise fused rings and may also be substituted with one or more groups r , r is h , halogen , no 2 , cn , scn , sf 5 , straight chain , branched or cyclic alkyl with 1 to 25 c atoms wherein one or more ch 2 groups can also be replaced by — o —, — s —, — co —, — nr 0 —, — ch ═ ch —, — c ≡ c — in such a manner that o and / or s atoms are not linked directly to one another , and wherein one or more h - atoms can also be replaced by f or cl , or p -( sp ) n -, p is a polymerizable group , sp is a spacer group with 1 to 20 c atoms , n is 0 or 1 , b is — o —, — s —, — nr 0 —, — o — co —, — nr 0 — co —, — o — coo —, — och 2 —, — s — co —, — s — coo — or a single bond , pi is a photoisomerizable group that may in addition be mesogenic , m 1 and m 2 are independently of each other a mesogenic group , i , k and l are independently of each other 0 or 1 , z 1 and z 2 are independently of each other — o —, — s —, — co —, — coo —, — oco —, — co — nr 0 —, — nr 0 — co —, — ch 2 ch 2 —, — cf 2 cf 2 —, — ch 2 cf 2 —, — och 2 —, — ch 2 o —, — sch 2 —, — ch 2 s —, — cf 2 o —, — ocf 2 —, — ch ═ ch —, — cf ═ cf —, — ch ═ cf —, —( ch 2 ) 4 —, — ch ═ ch — coo —, — oco — ch ═ ch —, — c ≡ c — or a single bond , and at least one of x 1 , x 2 , x 3 , x 4 , x 5 and x 6 is — b - sp -( m 1 - z 1 ) i -( pi ) k -( z 2 — m 2 ) i - g , ( pi ) k —( z 2 — m 2 ) i - g , and k in at least one of those groups is 1 . particularly preferred are compounds of formula i comprising one to six , in particular one to four , very preferably one or two polymerizable groups p . further preferred are compounds of formula i comprising one to four , in particular one or two photoisomerizable groups pi . further preferred are compounds of formula i wherein x 1 = x 6 , x 2 = x 5 and x 3 = x 4 further preferred are compounds of formula i , wherein one or more , in particular one or two of x 1 to x 6 are selected from the groups as defined in a ). very preferably these groups are selected from h , alkyl , alkenyl , alkoxy , alkenyloxy , alkylcarbonyl or alkylcarbonyloxy with 1 to 12 c - atoms that is optionally fluorinated , or have one of the meanings of p . further preferred are compounds of formula i , wherein one or more , in particular one or two of x 1 to x 6 are — b -( sp ) n - g , wherein b is a linkage group , sp a spacer group and g a cyclic group as defined in formula i , and n is 0 or 1 . in these compounds b is preferably — o —, — coo —, — o — coo — or a single bond , very preferably — coo — or a single bond , and n is preferably 0 . the cyclic group g is preferably selected from cyclobutane , cyclo - pentane , 3 -( 1 , 1 ,- dimethylcyclopentane ), 2 - tetrahydrofuran , 1 - pyrrolidine , 2 - furan , 2 - pyrrol , 2 - thiophene , 2 - oxazole , 2 - thiazole , 2 - imidazole , 3 - pyrrolidin - 2 - one , cyclohexane , 1 - cyclohexene , 2 - tetrahydropyran , 1 - piperidine , 3 - tetrahydrothiopyrane , 4 -( 1 , 3 - dioxane ), 1 , 4 - dioxane , 2 -( 1 , 3 ,- dithiane ), 1 , 4 - dithiane , 2 - oxathiane , 4 - thiomorpholine , 4 - morpholine , phenylene , 2 - pyridine , 2 - pyrimidine , 2 - pyrazine , 4 - bicyclohexane , 4 ′- bicyclohexyl - 2 - ene , 1 - cyclohexane - 1 , 4 - dione , 1 - bicyclo [ 2 , 2 , 2 ] octylene , 3 - cyclohexenone , 3 - hexahydro - furo [ 3 , 2 - b ] furan , 2 -( 1 , 4 - dioxa - spiro [ 4 . 5 ] decane ), 2 - naphthalene , 2 - decahydronaphthalene , 5 -( 1 , 2 , 3 , 4 - tetrahydronaphthalene , 2 - anthracene and 9 - phenanthrene . with r having the meaning of formula i and s being 0 , 1 , 2 , 3 , 4 or 5 . further preferred are compounds of formula i wherein one to five , in particular one to four of x 1 to x 6 denote h , cyclohexyl , phenyl that is optionally substituted with 1 to 4 groups l as defined in formula ii , or —( coo ) o — s with o being 0 or 1 and s being alkyl with 1 to 4 c atoms . further preferred are compounds of formula i wherein two of x 1 to x 6 , in particular the groups x 1 and x 6 or the groups x 2 and x 5 or the groups x 3 and x 4 are h . further preferred are compounds wherein two of x 1 to x 6 , in particular the groups x 1 and x 6 or the groups x 2 and x 5 or the groups x 3 and x 4 are cyclohexyl or phenyl that is optionally substituted with 1 or 2 groups l as defined in formula ii . further preferred are compounds wherein one of x 1 to x 6 is h and one of x 1 to x 6 is cyclohexyl , phenyl that is optionally substituted with 1 to 4 groups l as defined in formula ii , or —( coo ) o — s with o being 0 or 1 and s being alkyl with 1 to 4 c atoms , in particular those wherein one of x 1 and x 6 or one of x 2 and x 5 or one of x 3 and x 4 is h and the other is cyclohexyl , phenyl or —( coo ) o — s . further preferred are compounds , wherein two of x 1 , x 2 , x 3 , x 4 , x 5 and x 6 together form a cyclic group with up to 40 c atoms . preferred compounds of this type are selected from the following formulae x 7 and x 8 are independently of each other halogen , no 2 , cn , scn , sf 5 , straight chain or branched alkyl with 1 to 25 c atoms wherein one or more ch 2 groups can also be replaced by — o —, — s —, — co —, — nr 0 —, — ch ═ ch —, — c ≡ c — in such a manner that o and / or s atoms are not linked directly to one another , and wherein one or more h - atoms can also be replaced by f or cl , or denote a cycloalkyl , phenyl , benzyl or fused carbocyclic or heterocyclic aliphatic or aromatic group with up to 25 c atoms that is optionally substituted with one or more groups r as defined in formula i , or p -( sp ) n , p is in each case independently 0 , 1 , 2 or 3 , and r is in each case independently 0 , 1 , 2 , 3 or 4 . in the above formula , two substituents x 7 or x 8 in neighboured positions on a phenyl ring can also form a fused carbocyclic or heterocyclic aliphatic or aromatic group with up to 25 c atoms , like for example in the following compounds wherein the aromatic rings may also be mono - or polysubstituted with r as defined in formula i . particularly preferred are compounds of formula i wherein one to six , in particular one , two , three or four , very preferably one or two of x 1 to x 6 denote — b -( sp ) n -( m 1 - z 1 ) i -( pi ) k -( z 2 - m 2 ) i — r . very preferred compounds of this type are those wherein two of x 1 to x 6 , in particular the groups x 1 and x 6 or the groups x 1 and x 5 denote — b -( sp ) n -( m 1 - z 1 ) i -( pi ) k -( z 2 - m 2 ) i — r , especially those wherein the two groups — b —( sp ) n -( m 1 - z 1 ) i -( pi ) k -( z 2 - m 2 ) i — r are identical . the compounds of formula i comprise at least one mesogenic group , which can be a photoisomerizable group pi that is in addition mesogenic , or a separate mesogenic group m 1 or m 2 . the mesogenic groups m 1 and m 2 are preferably of formula ii a 1 and a 2 are independently of each other selected from a ) 1 , 4 - phenylene in which , in addition , one or more ch groups may be replaced by n , b ) 1 , 4 - cyclohexylene in which , in addition , one or two non - adjacent ch 2 groups may be replaced by o and / or s , c ) 1 , 3 - dioxolane - 4 , 5 - diyl , 1 , 4 - cyclohexenylene , piperidine - 1 , 4 - diyl , 1 , 4 - bicyclo -( 2 , 2 , 2 )- octylene , naphthalene - 2 , 6 - diyl , decahydro - naphthalene - 2 , 6 - diyl , 1 , 2 , 3 , 4 - tetrahydronaphthalene - 2 , 6 - diyl or indane - 2 , 5 - diyl , it being possible for all these groups to be unsubstituted , mono - or polysubstituted with l , l is halogen , cn , scn , no 2 , sf 5 or an alkyl , alkoxy , alkylcarbonyl or alkoxycarbonyl group with 1 to 4 c atoms , wherein one or more h atoms may be substituted with f or cl , z has in each case independently one of the meanings of z 1 in formula i , and m is 0 , 1 , 2 or 3 . alternatively a 1 and / or a 2 can have one of the above meanings of g . the mesogenic groups m 1 and / or m 2 preferably incorporate two or three five - or six - membered rings . a smaller group of preferred mesogenic groups of formula ii is listed below . for reasons of simplicity , phe in these groups is 1 , 4 - phenylene that may also be substituted with 1 to 4 groups l as defined in formula ii , cyc is 1 , 4 - cyclohexylene and z has one of the meanings of formula ii . the list is comprising the following subformulae as well as their mirror images particularly preferred are the subformulae ii - 1 , ii - 2 , ii - 3 , ii - 4 , ii - 5 , ii - 7 and ii - 10 . z is preferably — coo —, — oco —, — ch 2 ch 2 — or a single bond . very preferably the mesogenic groups m 1 and m 2 are selected from the following formulae and their mirror images wherein l and r have the above meanings , and r is preferably 0 , 1 or 2 . with l having each independently one of the meanings given above . particularly preferred are the subformulae iid , iig , iih , iii , iik and iio , in particular the subformulae iid and iik . l is preferably f , cl , cn , no 2 , ch 3 , c 2 h 5 , och 3 , oc 2 h 5 , coch 3 , coc 2 h 5 , cooch 3 , cooc 2 h 5 , cf 3 , ocf 3 , ochf 2 or oc 2 f 5 , in particular f , cl , cn , ch 3 , c 2 h 5 , och 3 , coch 3 , cf 3 or ocf 3 , most preferably f , cl , ch 3 , och 3 or ocf 3 . the compounds of formula i comprise at least one photoisomerizable group pi . the photoisomerizable group pi can be every group that is known to the skilled in the art for this purpose , as for example disclosed in john c . coyle , “ introduction to organo photochemistry ” 1986 , john wiley ans sons , chichester , uk . d 1 and d 2 are independently of each other ch or n or a saturated c atom in a carbocyclic or heterocyclic 5 - or 6 - membered ring , and c 1 and c 2 are independently of each other a bivalent aliphatic or aromatic carbocyclic or heterocyclic group with 3 to 40 c atoms that may also comprise fused rings , c 1 and d 1 or c 2 and d 2 may also together form a 5 - or 6 - membered carbocycle or heterocycle , and c 1 may also denote a single bond . preferably c 1 and c 2 have independently of each other one of the meanings of a 1 as defined in formula ii , and d 1 and d 2 are independently of each other ch or n . further preferred are compounds wherein c 1 is a single bond . very preferably d 1 and d 2 denote ch . further preferred are compounds wherein d 1 and d 2 denote n . wherein d 1 and d 2 are ch or n , l has the meaning of formula ii , and r has the meaning given above . particularly preferred are groups iiid , especially those wherein d 1 and d 2 are ch . particularly preferred are compounds of formula i comprising at least one , preferably one or two groups — b -( sp ) n -( m 1 - z 1 ) i -( pi ) k -( z 2 - m 2 ) i — r , wherein b is — oco —, n and i are 0 , k is 1 and pi is of formula iiid , so that the rest — b -( sp ) n -( m 1 - z 1 ) i -( pi ) k - forms a cinnamate group . further preferred are compounds of formula i , wherein pi is of formula iii and c 1 and / or c 2 are a mesogenic group of formula ii . in case these compounds comprise additional mesogenic groups m 1 or m 2 , these may be the same or different as c 1 and / or c 2 . has one of the meanings of a 1 , 2 in formula ii and has one of the meanings c 1 , 2 in formula iii , and are preferably selected from groups a ) and b ) of formula ii , x 1 , x 2 , x 6 , z , d 1 , d 2 , p , r and s have one of the meanings given above , b 1 and b 2 have independently of each other one of the meanings of b given above , r 1 , r 2 , r 3 , r 4 , r 5 and r 6 have independently of each other one of the meanings of r given above , x 9 is straight chain or branched alkyl with 1 to 25 c atoms wherein one or more ch 2 groups can also be replaced by — o —, — s —, — co —, — nr 0 —, — ch ═ ch —, — c ≡ c — in such a manner that o and / or s atoms are not linked directly to one another , and wherein one or more h - atoms can also be replaced by f or cl , or denotes a cycloalkyl , phenyl , benzyl or fused carbocyclic or heterocyclic aliphatic or aromatic group with up to 25 c atoms that is optionally substituted with one or more groups r or l as defined in formula i , or p -( sp ) n , a is 0 , 1 , 2 or 3 , and b is 0 , 1 or 2 . a 1 and a 2 are cyclohexyl or phenyl that may also be substituted with one to four , preferably one or two groups l as defined above , z is — coo —, — oco —, — ch 2 ch 2 — or a single bond , c 1 and c 2 are cyclohexyl or phenyl that may also be substituted with one to four , preferably one or two groups l as defined above , d 1 and d 2 are ch , x 1 and x 2 are h , b 1 is coo and b 2 is oco , r 1 and r 2 are f , cl , cn , alkyl or alkoxy with 1 to 10 c atoms , or p -( sp ) n — one or both of r 1 and r 2 denote p -( sp ) n -, r 3 and r 4 have of the meanings of l given above or denote p -( sp ) n -, and preferably are f , cl , cn or optionally fluorinated alkyl or alkoxy with 1 to 3 c atoms , p , r and s are each independently 0 , 1 or 2 , r 5 and r 6 are alkyl or alkoxy with 1 to 4 c atoms or denote p -( sp ) n -, and preferably are methyl , ethyl or propyl , x 9 is straight chain , branched or cyclic alkyl or alkyloxy with 1 to 12 c atoms , or phenyl that is optionally substituted with one , two or three groups l as defined above , a is 0 or 1 , b is 1 . wherein r 1 , r 2 , z , a 1 , a 2 , a and b have the meanings given above , in particular those wherein a and b are 0 and r 1 and r 2 are p - sp . if r in formula i is an alkyl or alkoxy radical , i . e . where the terminal ch 2 group is replaced by — o —, this may be straight - chain or branched . it is preferably straight - chain , has 2 , 3 , 4 , 5 , 6 , 7 or 8 carbon atoms and accordingly is preferably ethyl , propyl , butyl , pentyl , hexyl , heptyl , octyl , ethoxy , propoxy , butoxy , pentoxy , hexoxy , heptoxy , or octoxy , furthermore methyl , nonyl , decyl , undecyl , dodecyl , tridecyl , tetradecyl , pentadecyl , nonoxy , decoxy , undecoxy , dodecoxy , tridecoxy or tetradecoxy , for example . especially preferred is straight chain alkyl or alkoxy with 1 to 8 c atoms . oxaalkyl , i . e . where one ch 2 group is replaced by — o —, is preferably straight - chain 2 - oxapropyl (= methoxymethyl ), 2 -(= ethoxymethyl ) or 3 - oxabutyl (= 2 - methoxyethyl ), 2 -, 3 -, or 4 - oxapentyl , 2 -, 3 -, 4 -, or 5 - oxahexyl , 2 -, 3 -, 4 -, 5 -, or 6 - oxaheptyl , 2 -, 3 -, 4 -, 5 -, 6 - or 7 - oxaoctyl , 2 -, 3 -, 4 -, 5 -, 6 -, 7 - or 8 - oxanonyl or 2 -, 3 -, 4 -, 5 -, 6 -, 7 -, 8 -, or 9 - oxadecyl , for example . r in formula i can be a polar or an unpolar group . in case of a polar group , it is preferably selected from cn , no 2 , halogen , och 3 , scn , cor 8 , coor 8 or a mono - oligo - or polyfluorinated alkyl or alkoxy group with 1 to 4 c atoms . r 8 is optionally fluorinated alkyl with 1 to 4 , preferably 1 to 3 c atoms . especially preferably polar groups are selected of f , cl , cn , no 2 , och 3 , coch 3 , coc 2 h 5 , cooch 3 , cooc 2 h 5 , cf 3 , c 2 f 5 , ocf 3 , ochf 2 , and oc 2 f 5 , in particular of f , cl , cn , och 3 and ocf 3 . in case of an unpolar group , it is preferably alkyl with up to 15 c atoms or alkoxy with 2 to 15 c atoms . r in formula i can be an achiral or a chiral group . in case of a chiral group it is preferably selected according to formula iv : z 3 is — o —, — s —, — co —, — coo —, — oco —, — ocoo — or a single bond , q 1 is an alkylene or alkylene - oxy group with 1 to 9 c atoms or a single bond , q 2 is an alkyl or alkoxy group with 1 to 10 c atoms which may be unsubstituted , mono - or polysubstituted with halogen or cn , it being also possible for one or more non - adjacent ch 2 groups to be replaced , in each case independently from one another , by — c ≡ c —, — o —, — s —, — nr 0 —, — co —, — coo —, — oco —, — oco — o —, — s — co — or — co — s — in such a manner that oxygen atoms are not linked directly to one another , q 3 is halogen , a cyano group or an alkyl or alkoxy group with 1 to 4 c atoms different from q 2 . in case q 1 in formula iv is an alkylene - oxy group , the o atom is preferably adjacent to the chiral c atom . preferred chiral groups are 2 - alkyl , 2 - alkoxy , 2 - methylalkyl , 2 - methylalkoxy , 2 - fluoroalkyl , 2 - fluoroalkoxy , 2 -( 2 - ethin )- alkyl , 2 -( 2 - ethin )- alkoxy , 1 , 1 , 1 - trifluoro - 2 - alkyl and 1 , 1 , 1 - trifluoro - 2 - alkoxy . particularly preferred chiral groups are 2 - butyl (= 1 - methylpropyl ), 2 - methylbutyl , 2 - methylpentyl , 3 - methylpentyl , 2 - ethylhexyl , 2 - propylpentyl , in particular 2 - methylbutyl , 2 - methylbutoxy , 2 - methylpentoxy , 3 - methylpentoxy , 2 - ethylhexoxy , 1 - methylhexoxy , 2 - octyloxy , 2 - oxa - 3 - methylbutyl , 3 - oxa - 4 - methylpentyl , 4 - methylhexyl , 2 - hexyl , 2 - octyl , 2 - nonyl , 2 - decyl , 2 - dodecyl , 6 - methoxyoctoxy , 6 - methyloctoxy , 6 - methyloctanoyloxy , 5 - methylheptyloxycarbonyl , 2 - methylbutyryloxy , 3 - methylvaleroyloxy , 4 - methylhexanoyloxy , 2 - chlorpropionyloxy , 2 - chloro - 3 - methylbutyryloxy , 2 - chloro - 4 - methylvaleryloxy , 2 - chloro - 3 - methylvaleryloxy , 2 - methyl - 3 - oxapentyl , 2 - methyl - 3 - oxahexyl , 1 - methoxypropyl - 2 - oxy , 1 - ethoxypropyl - 2 - oxy , 1 - propoxypropyl - 2 - oxy , 1 - butoxypropyl - 2 - oxy , 2 - fluorooctyloxy , 2 - fluorodecyloxy , 1 , 1 , 1 - trifluoro - 2 - octyloxy , 1 , 1 , 1 - trifluoro - 2 - octyl , 2 - fluoromethyloctyloxy for example . very preferred are 2 - hexyl , 2 - octyl , 2 - octyloxy , 1 , 1 , 1 - trifluoro - 2 - hexyl , 1 , 1 , 1 - trifluoro - 2 - octyl and 1 , 1 , 1 - trifluoro - 2 - octyloxy , for example . in addition , compounds of formula i containing an achiral branched group r may occasionally be of importance , for example , due to a reduction in the tendency towards crystallization . branched groups of this type generally do not contain more than one chain branch . preferred achiral branched groups are isopropyl , isobutyl (= methylpropyl ), isopentyl (= 3 - methylbutyl ), isopropoxy , 2 - methylpropoxy and 3 - methylbutoxy . another preferred embodiment of the present invention relates to compounds of formula i wherein r is denoting p -( sp ) n . r 0 in formula i is preferably h or ch 3 , in particular h . the polymerisable group p is preferably selected from ch 2 ═ cw 1 — coo — ch 2 ═— o —, ch 3 — ch ═ ch — o —, ho — cw 2 w 3 —, hs — cw 2 w 3 —, hw 2 n —, ho — cw 2 w 3 — nh —, ch 2 ═ cw 1 — co — nh —, ch 2 ═ ch —( coo ) k1 - phe -( o ) k2 —, phe - ch ═ ch —, hooc —, ocn — and w 4 w 5 w 6 si —, with w 1 being h , cl , cn , phenyl or alkyl with 1 to 5 c - atoms , in particular h , cl or ch 3 , w 2 and w 3 being independently of each other h or alkyl with 1 to 5 c - atoms , in particular methyl , ethyl or n - propyl , w 4 , w 5 and w 6 being independently of each other cl , oxaalkyl or oxacarbonylalkyl with 1 to 5 c - atoms , phe being 1 , 4 - phenylene and k 1 and k 2 being independently of each other 0 or 1 . p is particularly preferably an acrylate , methacrylate , vinyl , vinyloxy , epoxy , styrene or propenyl ether group , in particular an acrylate , methacrylate , vinyl or epoxy group . as spacer group sp in formula i all groups can be used that are known for this purpose to the skilled in the art . sp is preferably a straight chain or branched alkylene group having 1 to 20 c atoms , in particular 1 to 12 c atoms , in which , in addition , one or more non - adjacent ch 2 groups may be replaced by — o —, — s —, — nr 0 —, — co —, — o — co —, — s — co —, — o — coo —, — co — s —, — co — o —, — ch ( halogen )—, — ch ( cn )—, — ch ( oh )—, —( cf 2 ) x —, —( cd 2 ) x —, — ch ═ ch —, — cf ═ cf —, — ch ═ cf — or — c ≡ c —, with x being an integer from 1 to 12 , and in which one or more h atoms may be replaced by halogen , cn or oh . typical spacer groups are for example —( ch 2 ) y , —( ch 2 ch 2 o ) z — ch 2 ch 2 —, — ch 2 ch 2 — s — ch 2 ch 2 — or — ch 2 ch 2 — nh — ch 2 ch 2 —, with y being an integer from 2 to 12 and p being an integer from 1 to 3 . preferred spacer groups are ethylene , propylene , butylene , pentylene , hexylene , heptylene , octylene , nonylene , decylene , undecylene , dodecylene , octadecylene , ethyleneoxyethylene , methyleneoxybutylene , ethylene - thioethylene , ethylene - n - methyl - iminoethylene , 1 - methylalkylene , ethenylene , propenylene and butenylene for example . especially preferred are inventive compounds of formula i wherein sp is denoting alkylene or alkylene - oxy with 2 to 8 c atoms . straight - chain groups are especially preferred . in another preferred embodiment of the invention the compounds of formula i comprise at least one spacer group sp that is a chiral group of formula v : q 1 and q 3 have the meanings given in formula iv , and q 4 is an alkylene or alkylene - oxy group with 1 to 10 c atoms or a single bond , being different from q 1 . in case q 1 in formula v is an alkylene - oxy group , the o atom is preferably adjacent to the chiral c atom . the inventive chiral compounds can be synthesized according to or in analogy to methods which are known per se , as described in the literature ( for example in the standard works such as houben - weyl , methoden der organischen chemie [ methods of organic chemistry ], georg - thieme - verlag , stuttgart ), to be precise under reaction conditions which are known and suitable for said reactions . use may also be made here of variants which are known per se , but are not mentioned here . further methods for preparing the inventive compounds can be taken from the examples . in particular , the inventive compounds can be prepared according to or in analogy to the following reaction schemes . a ) ( dhq ) 2 — phal , n - methylmorpholine n - oxide , t - butanol , potassium osmate ( vi ) dihydrate , r . t . ; b ) dcc , 4 -( dimethylamino )- pyridine , dcm , r . t . ; c ) dcc , 4 -( dimethylamino )- pyridine , dcm , r . t . ; d ) potassium t - butoxide , thf , − 5 ° c . a ) dcc , 4 -( dimethylamino )- pyridine , dcm , r . t . ; b ) dcc , 4 -( dimethylamino )- pyridine , dcm , r . t . ; c ) net 3 , 35 ° c . the inventive chiral compounds can be used in a liquid crystal mixture for liquid crystal displays exhibiting a twisted molecular structure of the liquid crystal matrix like , for example , twisted or supertwisted nematic displays with multiplex or active matrix addressing , or in displays comprising a liquid crystal mixture with a chiral liquid crystalline phase , like for example chiral smectic or chiral nematic ( cholesteric ) mixtures for ferroelectric or cholesteric displays . the inventive compounds , mixtures and polymers are especially suitable for cholesteric displays , like for example surface stabilized or polymer stabilized cholesteric texture displays ( ssct , psct ) as described in wo 92 / 19695 , wo 93 / 23496 , u . s . pat . no . 5 , 453 , 863 or u . s . pat . no . 5 , 493 , 430 , in particular for liquid crystal devices with variable pitch , like multi - domain liquid crystal displays as described for example in wo 98 / 57223 , or multicolour cholesteric displays as described for example in u . s . pat . no . 5 , 668 , 614 . the entire disclosure of the above mentioned documents is introduced into this application by way of reference . the inventive compounds of formula i are also suitable for use in photochromic liquid crystal media , which change their colour upon photoradiation . thus , another object of the invention is a liquid crystalline mixture comprising at least one chiral compound of formula i . yet another object of the invention are cholesteric liquid crystal displays comprising cholesteric liquid crystalline media containing at least one chiral compound of formula i . many of the inventive compounds are characterized by a good solubility in liquid crystalline host mixtures , and can be added as dopants to liquid crystalline hosts in high amounts without significantly affecting the phase behaviour and electrooptical properties of the mixture . undesired spontaneous crystallization at low temperatures is thereby reduced and the operating temperature range of the mixture can be broadened . furthermore , these chiral compounds can be used for the preparation of a highly twisted liquid crystal medium even if they have a low htp , because the dopant concentration can be increased to yield low pitch values ( i . e . high twist ) without affecting the mixture properties . the use of a second dopant , which is often added to avoid crystallization , can thus be avoided . many of the inventive chiral compounds of formula i exhibit high values of the htp . a liquid crystalline mixture with high helical twist , i . e . a low pitch , can be prepared by using these compounds as dopants , or a liquid crystalline mixture with moderate helical twist can be achieved by using these inventive compounds as dopants already in very small amounts . as mentioned above , the inventive compounds are furthermore advantageous because they are affecting the physical properti s of the liquid crystalline mixture only to a minor extent . thus , when admixing the chiral compounds of formula i for example to a liquid crystalline mixture with positive dielectric anisotropy that is used in a liquid crystal display , δε is being only slightly reduced and the viscosity of the liquid crystalline mixture is increased only to a small extent . this leads to lower voltages and improved switching times of the display when compared to a display comprising conventional dopants . a liquid crystalline mixture according to the invention comprises preferably 0 . 1 to 30 %, in particular 1 to 25 % and very particularly preferably 2 to 15 % by weight of chiral compounds of formula i . a liquid crystalline mixture according to the invention preferably comprises 1 to 3 chiral compounds of formula i . in a preferred embodiment of the invention the liquid crystalline mixture is consisting of 2 to 25 , preferably 3 to 15 compounds , at least one of which is a chiral compound of formula i . the other compounds are preferably low molecular weight liquid crystalline compounds selected from nematic or nematogenic substances , for example from the known classes of the azoxybenzenes , benzylidene - anilines , biphenyls , terphenyls , phenyl or cyclohexyl benzoates , phenyl or cyclohexyl esters of cyclohehexanecarboxylic acid , phenyl or cyclohexyl esters of cyclohexylbenzoic acid , phenyl or cyclohexyl esters of cyclohexylcyclohexanecarboxylic acid , cyclohexylphenyl esters of benzoic acid , of cyclohexanecarboxylic acid and of cyclohexylcyclohexanecarboxylic acid , phenylcyclohexanes , cyclohexylbiphenyls , phenylcyclohexylcyclohexanes , cyclohexylcyclohexanes , cyclohexylcyclohexenes , cyclohexylcyclohexylcyclohexenes , 1 , 4 - bis - cyclohexylbenzenes , 4 , 4 ′- bis - cyclohexylbiphenyls , phenyl - or cyclohexylpyrimidines , phenyl - or cyclohexylpyridines , phenyl - or cyclohexylpyridazines , phenyl - or cyclohexyldioxanes , phenyl - or cyclohexyl - 1 , 3 - dithianes , 1 , 2 - diphenyl - ethanes , 1 , 2 - dicyclohexylethanes , 1 - phenyl - 2 - cyclohexylethanes , 1 - cyclohexyl - 2 -( 4 - phenylcyclohexyl )- ethanes , 1 - cyclohexyl - 2 - biphenyl - ethanes , 1 - phenyl2 - cyclohexylphenylethanes , optionally halogenated stilbenes , benzyl phenyl ether , tolanes , substituted cinnamic acids and further classes of nematic or nematogenic substances . the 1 , 4 - phenylene groups in these compounds may also be laterally mono - or difluorinated . the liquid crystalline mixture of this preferred embodiment is based on the achiral compounds of this type . the most important compounds that are posssible as components of these liquid crystalline mixtures can be characterized by the following formula wherein l ′ and e , which may be identical or different , are in each case , independently from one another , a bivalent radical from the group formed by - phe -, - cyc -, - phe - phe -, - phe - cyc -, - cyc - cyc -, - pyr -, - dio -, - b - phe - and - b - cyc - and their mirror images , where phe is unsubstituted or fluorine - substituted 1 , 4 - phenylene , cyc is trans - 1 , 4 - cyclohexylene or 1 , 4 - cyclohexenylene , pyr is pyrimidine - 2 , 5 - diyl or pyridine - 2 , 5 - diyl , dio is 1 , 3 - dioxane - 2 , 5 - diyl abd b is 2 -( trans - 1 , 4 - cyclohexyl ) ethyl , pyrimidine - 2 , 5 - diyl , pyridine - 2 , 5 - diyl or 1 , 3 - dioxane - 2 , 5 - diyl . g ′ in these compounds is selected from the following bivalent groups — ch ═ ch —, — n ( o ) n —, — ch ═ cy —, — ch ═ n ( o )—, — c ≡ c —, — ch 2 — ch 2 —, — co — o —, — ch 2 — o —, — co — s —, — ch 2 — s —, — ch ═ n —, — coo - phe - coo — or a single bond , with y being halogen , preferably chlorine , or — cn . r ′ and r ″ are , in each case , independently of one another , alkyl , alkenyl , alkoxy , alkenyloxy , alkanoyloxy , alkoxycarbonyl or alkoxycarbonyloxy with 1 to 18 , preferably 3 to 12 c atoms , or alternatively one of r ′ and r ″ is f , cf 3 , ocf 3 , cl , ncs or cn . in most of these compounds r ′ and r ″ are , in each case , independently of each another , alkyl , alkenyl or alkoxy with different chain length , wherein the sum of c atoms in nematic media generally is between 2 and 9 , preferably between 2 and 7 . many of these compounds or mixtures thereof are commercially available . all of these compounds are either known or can be prepared by methods which are known per se , as described in the literature ( for example in the standard works such as houben - weyl , methoden der organischen chemie [ methods of organic chemistry ], georg - thieme - verlag , stuttgart ), to be precise under reaction conditions which are known and suitable for said reactions . use may also be made here of variants which are known per se , but are not mentioned here . a preferred use of the inventive compounds is the preparation of polymerizable liquid crystalline mixtures , anisotropic polymer gels and anisotropic polymer films , in particular polymer films that exhibit a helically twisted molecular structure with uniform planar orientation , i . e . wherein the helical axis is oriented perpendicular to the plane of the film , like oriented cholesteric films . anisotropic polymer gels and displays comprising them are disclosed for example in de 195 04 224 and gb 2 279 659 . oriented cholesteric polymer films can be used for example as broadband reflective polarizers , colour filters , security markings , or for the preparation of liquid crystal pigments . broadband cholesteric reflective polarizers are described for example in ep 0 606 940 , wo 97 / 35219 or ep 0 982 605 . colour filters are described for example in ep 0 720 041 or ep 0 685 749 and r . maurer et al ., sid 1990 digest , 110 – 113 . liquid crystal pigments are described for example in ep 0 601 483 , wo 97 / 27251 , wo 97 / 27252 , wo 97 / 30136 or wo 99 / 11719 . for the preparation of anisotropic polymer gels or oriented polymer films , the liquid crystalline mixture should comprise at least one polymerizable compound , preferably a polymerizable mesogenic compound . thus , another object of the invention are polymerizable liquid crystalline mixtures comprising at least two compounds , at least one of which is a chiral compound of formula i and at least one of which is a polymerizable compound . the polymerizable compound can be said at least one compound of formula i or an additional compound . examples of suitable polymerizable mesogenic compounds that can be used as co - components in the polymerizable mixture are disclosed for example in wo 93 / 22397 ; ep 0 , 261 , 712 ; de 195 , 04 , 224 ; wo 95 / 22586 and wo 97 / 00600 . the compounds disclosed in these documents , however , are to be regarded merely as examples that shall not limit the scope of this invention . preferably the polymerizable mixture comprises at least one polymerizable mesogenic compound having one polymerizable functional group and at least one polymerizable mesogenic compound having two or more polymerizable functional groups . examples of especially useful monoreactive chiral and achiral polymerizable mesogenic compounds are shown in the following list of compounds , which should , however , be taken only as illustrative and is in no way intended to restrict , but instead to explain the present invention : wherein , p has one of the meanings given above , x is an integer from 1 to 12 , a is 1 , 4 - phenylene or 1 , 4 - cyclohexylene , v is 0 or 1 , y 0 is a polar group , r 7 is an unpolar alkyl or alkoxy group , ter is a terpenoid radical like e . g . menthyl , chol is a cholesteryl group , and l 1 and l 2 are each independently h , f , cl , cn , oh , no 2 or an optionally halogenated alkyl , alkoxy or carbonyl group with 1 to 7 c atoms . the polar group y 0 is preferably cn , no 2 , halogen , och 3 , ocn , scn , cor 8 , coor 8 or a mono - oligo - or polyfluorinated alkyl or alkoxy group with 1 to 4 c atoms . r 8 is optionally fluorinated alkyl with 1 to 4 , preferably 1 to 3 c atoms . especially preferably the polar group y 0 is selected of f , cl , cn , no 2 , och 3 , coch 3 , coc 2 h 5 , cooch 3 , cooc 2 h 5 , cf 3 , c 2 f 5 , ocf 3 , ochf 2 , and oc 2 f 5 , in particular f , cl , cn , och 3 and ocf 3 . the unpolar group r 7 is preferably an alkyl group with 1 or more , preferably 1 to 15 c atoms or an alkoxy group with 2 or more , preferably 2 to 15 c atoms . examples of useful direactive chiral and achiral polymerizable mesogenic compounds are shown in the following list of compounds , which should , however , be taken only as illustrative and is in no way intended to restrict , but instead to explain the present invention wherein p , x , a , l 1 and l 2 have one of the meanings given above and y is an integer from 1 to 12 the same as or different from x . the mono - and difunctional polymerizable mesogenic compounds of above formulae vi and vii can be prepared by methods which are known per se and which are described in the documents cited above and , for example , in standard works of organic chemistry such as , for example , houben - weyl , methoden der organischen chemie , thieme - verlag , stuttgart . in a preferred embodiment of the invention the polymerizable liquid crystalline mixtures comprise at least one inventive chiral compound of formula i , at least one monofunctional compound of formulae via – vim and at least one bifunctional polymerizable compound of formulae viia – viie . in another preferred embodiment the polymerizable liquid crystalline mixtures comprise at least one inventive chiral compound and at least two monofunctional compounds of formulae via – vim . another object of the invention is an anisotropic polymer film with an oriented chiral liquid crystalline phase obtainable by ( co ) polymerizing a liquid crystalline mixture comprising at least one chiral compound of formula i and at least one polymerizable mesogenic compound preferably selected of formula via – vim and viia – viie and / or at least one polymerizable chiral compound of formula i . the preparation of an anisotropic polymer film with twisted structure from a polymerizable mixture is generally described for example in d . j . broer , et al ., angew . makromol . chem . 183 , ( 1990 ), 45 – 66 . the cholesteric polymerizable mixture is coated onto a substrate , aligned into uniform planar orientation , and polymerized in situ by exposure to heat or actinic radiation , thereby fixing the uniform alignment . alignment and curing are carried out in the chiral liquid crystalline phase of the polymerizable mixture . actinic radiation means irradiation with light , like uv light , ir light or visible light , irradiation with x - rays or gamma rays or irradiation with high energy particles , such as ions or electrons . as a source for actinic radiation for example a single uv lamp or a set of uv lamps can be used . another possible source for actinic radiation is a laser , like e . g . a uv laser , an ir laser or a visible laser . for example , when photopolymerizing by means of uv light , a photoinitiator can be used that decomposes under uv irradiation to produce free radicals or ions that start the polymerization reaction . it is also possible to use a cationic photoinitiator , when curing reactive mesogens with for example vinyl and epoxide reactive groups , that photocures with cations instead of free radicals . as a photoinitiator for radical polymerization for example the commercially available irgacure 651 , irgacure 184 , darocure 1173 or darocure 4205 ( all from ciba geigy ag ) can be used , whereas in case of cationic photopolymerization the commercially available uvi 6974 ( union carbide ) can be used . preferably the polymerizable liquid crystalline mixtures comprising polymerizable chiral compounds of formula i and / or polymerizable mesogenic compounds of formulae vi and vii additionally comprise 0 . 01 to 10 %, in particular 0 . 05 to 8 %, very preferably 0 . 1 to 5 % by weight of a photoinitiator , especially preferably a uv - photoinitiator . preferably polymerization is carried out under an atmosphere of inert gas , preferably under a nitrogen atmosphere . as a substrate for example a glass or quarz sheet as well as a plastic film or sheet can be used . it is also possible to put a second substrate on top of the coated mixture prior to , during and / or after polymerization . the substrates can be removed after polymerization or not . when using two substrates in case of curing by actinic radiation , at least one substrate has to be transmissive for the actinic radiation used for the polymerization . isotropic or birefringent substrates can be used . in case the substrate is not removed from the polymerized film after polymerization , preferably isotropic substrates are used . preferably at least one substrate is a plastic substrate such as for example a film of polyester such as polyethyleneterephthalate ( pet ), of polyvinylalcohol ( pva ), polycarbonate ( pc ) or triacetylcellulose ( tac ), especially preferably a pet film or a tac film . as a birefringent substrate for example an uniaxially stretched plastic film can be used . for example pet films are commercially available from ici corp . under the trade name melinex . the polymerizable mixture is preferably coated as a thin layer on a substrate or between substrate , and aligned in its chiral mesophase , e . g . the cholesteric or chiral smectic phase , to give a planar orientation , i . e . wherein the axis of the molecular helix extends transversely to the layer . planar orientation can be achieved for example by shearing the mixture , e . g . by means of a doctor blade . it is also possible to apply an alignment layer , for example a layer of rubbed polyimide or sputtered sio x , on top of at least one of the substrates . alternatively , a second substrate is put on top of the coated material . in this case , the shearing caused by putting together the two substrates is sufficient to give good alignment . it is also possible to apply an electric or magnetic field to the coated mixture . in some cases it is of advantage to apply a second substrate not only to aid alignment of the polymerizable mixture but also to exclude oxygen that may inhibit the polymerization . alternatively curing can be carried out under an atmosphere of inert gas . however , curing in air is also possible using suitable photoinitiators and high lamp power . when using a cationic photoinitiator oxygen exclusion most often is not needed , but water should be excluded . an inventive polymerizable liquid crystalline mixture for the preparation of anisotropic polymer films comprises preferably 0 . 1 to 35 %, in particular 0 . 5 to 15 % and very particularly preferably 0 . 5 to 5 % by weight of one or more polymerizable chiral compounds of formula i . polymerizable liquid crystalline mixtures are preferred that comprise 1 to 3 chiral compounds of formula i . the inventive polymerizable liquid crystalline mixtures can additionally comprise one or more other suitable components such as , for example , catalysts , sensitizers , stabilizers , inhibitors , co - reacting monomers , surface - active compounds , lubricating agents , wetting agents , dispersing agents , hydrophobing agents , adhesive agents , flow improvers , defoaming agents , deaerators , diluents , reactive diluents , auxiliaries , colourants , dyes or pigments . preferably the inventive polymerizable mixture comprises a stabilizer that is used to prevent undesired spontaneous polymerization for example during storage of the composition . as stabilizers in principal all compounds can be used that are known to the skilled in the art for this purpose . these compounds are commercially available in a broad variety . typical examples for stabilizers are 4 - ethoxyphenol or butylated hydroxytoluene ( bht ). it is also possible , in order to increase crosslinking of the polymers , to add a non mesogenic compound with two or more polymerizable functional groups , preferably in an amount of up to 20 % by weight , to the polymerizable mixture alternatively or additionally to multifunctional mesogenic polymerizable compounds . typical examples for difunctional non mesogenic monomers are alkyldiacrylates or alkyldimethacrylates with alkyl groups of 1 to 20 c atoms . typical examples for non mesogenic monomers with more than two polymerizable groups are trimethylpropanetrimethacrylate or pentaerythritoltetraacrylate . polymerization of inventive compositions comprising compounds with only one polymerizable functional group leads to linear polymers , whereas in the presence of compounds with more than one polymerizable functional group crosslinked polymers are obtained . for the preparation of anisotropic polymer gels , the liquid crystalline mixtures can be polymerized in situ as described above , however , in this case alignment of the polymerizable mixture is not always necessary . due to the presence of a photoisomerizable group in the compounds of formula i , the chirality of the inventive compounds and liquid crystalline mixtures can be changed by photoirradiation . photoirradiation can be achieved for example with irradiation by uv light or other high energy sources such as lasers . the photoisomerizable compounds of formula i are particularly suitable for the preparation of cholesteric films or layers with planar alignment . such layers or films show selective reflection of visible light that is circularly polarized , caused by interaction of incident light with the helically twisted structure of the cholesteric material . the central wavelength of reflection λ depends on the pitch p and average refractive index n of the cholesteric material according to equation ( 2 ) the bandwidth δλ of the reflected wavelength band depends on the pitch and the birefringence δn of the cholesteric material according to equation ( 3 ) the inventive compounds and mixtures can for example be used to prepare reflective cholesteric films wherein the optical properties , like the reflection wavelength λ and the reflection bandwidth δλ , can be varied easily . for example , cholesteric reflective films with a horizontal pattern comprising regions of different reflection wavelength λ , or broadband reflective films with a broad bandwidth δλ of the reflected wavelength band can be prepared . the preparation of such films is described for example in wo 00 / 34808 and in p . van de witte et al ., j . mater . chem . 9 ( 1999 ), 2087 – 2094 , the entire disclosure of which is incorporated into this application by way of reference . the preparation of patterned cholesteric films and of broadband reflective films is also exemplarily described below . a cholesteric film with variable wavelength can for example be prepared as follows : a thin layer of a cholesteric polymerizable mixture comprising an inventive chiral photoisomerizable compound of formula i is coated onto a substrate and aligned into planar orientation as described above . the coated and aligned layer shows selective reflection of a wavelength λ that is depending on the helical pitch p according to above equation ( 2 ). if the coated layer is exposed to photoradiation of a suitable wavelength , the photoisomerizable group ( s ) in the compound of formula i is isomerized . for example , in case the compound of formula i comprises a photoisomerizable group pi of formula iiia wherein d 1 and d are ch ( stilbene group ), the stilbene group will undergo e - z - isomerization if the wavelength of radiation is selected accordingly between 300 and 400 nm . this causes a shift of the htp of the photoisomerizable compound and , according to above equation ( 1 ), a change in the helical pitch p and thus in the reflection wavelength λ of the layer . the degree of isomerization and the shift of λ can be controlled by varying e . g . the irradiation time and / or the radiation dose . the structure of the layer is then fixed by in - situ polymerization . if only a part of the layer is exposed to photoradiation , the helical pitch and reflection wavelength will change only in th exposed parts , but remain unchanged in the non - exposed parts . this can be achieved for example by photoradiation through a photomask that is applied on top of the coated layer . afterwards , the cholesteric structure is fixed in those parts where the pitch has changed by polymerization , for example by in - situ photopolymerization through the photomask . if the above steps of photoisomerization and ( photo ) polymerization are then repeated for the previously non - exposed parts of the coated layer under different conditions , e . g . different irradiation time and / or radiation dose , a patterned cholesteric film is obtained with different regions showing different reflection wavelengths . such patterned films are suitable for example for use as colour filter in optical or electrooptical devices like liquid crystal displays or projectors . they can also be used for security markings , e . g . to identify or prevent falsification of credit cards , passports , bank notes or other documents of value . a broadband reflective cholesteric film can for example be prepared as follows : a layer of a cholesteric mixture with planar orientation comprising a photoisomerizable compound of formula i additionally comprises a dye having an absorption maximum at the wavelength where the isomerizable compound shows photoisomerization . for example , the mixture may comprise an isomerizable compound showing isomerization at a wavelength in the uv range together with a uv dye . if the mixture is exposed to uv radiation as described above , the dye will create a gradient in uv light intensity throughout the thickness of the layer . as a consequence , the isomerization is faster at the top of the layer than at the bottom and a pitch gradient is created , leading to a broadening of the reflected wavelength band . the pitch gradient and reflection bandwidth can be controlled for example by varying the film thickness , irradiation time , radiation dose and / or the concentration of the uv dye and the photoisomerizable compound . if the cholesteric mixture comprises one or more polymerizable components , the structure of the film can be fixed by in - situ polymerization . from the foregoing description , one skilled in the art can easily ascertain the essential characteristics of this invention , and without departing from the spirit and scope thereof , can make various changes and modifications of the invention to adapt it to various usages and conditions . without further elaboration , it is believed that one skilled in the art can , using the preceding description , utilize the present invention to its fullest extent . the following examples are , therefore , to be construed as merely illustrative and not limitative of the remainder of the disclosure in any way whatsoever . in the foregoing and in the following examples , unless otherwise indicated , all temperatures are set forth uncorrected in degrees celsius and all parts and percentages are by weight . the values of the helical twisting power htp of a chiral compound in a liquid crystalline host are given according to the equation htp =( p · c ) − 1 in μm − 1 wherein p is the pitch of the molecular helix , given in μm , and c is the concentration by weight of the chiral compound in the host given in relative values ( thus , e . g . a concentration of 1 % by weight is corresponding to a value of c of 0 . 01 ). unless indicated otherwise , the htp values of the examples were determined in the commercially available liquid crystal host mixture mlc - 6260 ( merck kgaa , darmstadt , germany ) at a concentration of 1 % and a temperature of 20 ° c . the following abbreviations are used to illustrate the liquid crystalline phase behaviour of the compounds : c = crystalline ; n = nematic ; s = smectic ; n *, ch = chiral nematic or cholesteric ; i = isotropic . the numbers between these symbols indicate the phase transition temperatures in degree celsius . furthermore , mp . is the melting point , δn is the birefringence at 589 nm and 20 ° c . and δε is the dielectric anisotropy at 20 ° c . c * in a chemical formula denotes a chiral c atom . dcm is dichloromethane . “ conventional workup ” means : water is added if necessary , the mixure is extracted with methylene chloride , diethyl ether or toluene , the phases are separated , the organic phase is dried and concentrated by evaporation , and the product is purified by crystallization and / or chromatography . to a jacketed flask ( 1l ) 4 -( 4 - pentyl - cyclohexyl )- benzoic acid ( 6 . 31 g , 23 mmol ), s , s - 1 , 2 - dipheny - ethane - 1 , 2 - diol ( 5 . 00 g , 23 mmol ), 4 -( dimethylamino )- pyridine ( 0 . 24 g , 2 mmol ) and n , n ′- dicyclohexylcarbodiimide ( 5 . 16 g , 25 mmol ) were added , followed by the addition of dichloromethane ( 50 ml ), and the mixture stirred at ambient temperature overnight . solid material was then filtered , the organic layer washed with brine ( 2 × 25 ml ), dried ( mgso 4 ) and the solvent removed under vacuum . column chromatography ( on silica , ch 2 cl 2 as eluent ) gave 4 -( 4 - pentyl - cyclohexyl )- benzoic acid 2 - hydroxy - 1 , 2 - diphenyl - ethyl ester ( 1a ) ( 6 . 20 g , 13 mmol , 57 %), structure confirmed by 1 h , 13 c , gc - ms and ir . to a round bottomed flask ester ( 1a ) ( 3 . 00 g , 6 mmol ), ( e )- 3 -{ 4 -[ 6 -( 3 - chloro - propanoyloxy )- propyloxy ]- phenyl }- acrylic acid ( 2 . 13 g , 8 mmol )), 4 -( dimethylamino )- pyridine ( 0 . 12 g , 1 mmol ) and n , n ′- dicyclohexylcarbodiimide ( 1 . 44 g , 7 mmol ) were added , followed by the addition of dichloromethane ( 100 ml ), and the mixture stirred at ambient temperature for 42 h . triethylamine ( 1 . 25 ml , 9 mmol ) was then added and the mixture stirred at 35 ° c . overnight after which time the mixture was filtered , washed with brine ( 3 × 30 ml ), dried ( mgso 4 ) and the solvent removed under vacuum . column chromatography ( on silica , ethyl acetate and 40 – 60 petrol as eluent 1 : 9 ) gave 4 -( 4 - pentyl - cyclohexyl )- benzoic acid 2 -{( e )- 3 -[ 4 -( 6 - acryloyloxy - propyloxy )- phenyl ]- allanoyloxy }- 1 , 2 - diphenyl - ethyl ester ( 1 ) ( 2 . 0 g , 3 mmol , 43 %), structure confirmed by 1 h , 13 c , gc — ms and ir . to a round bottomed flask ester ( 1a ) of example 1 ( 5 . 00 g , 11 mmol ), 4 - formyl - benzoic acid ( 1 . 65 g , 11 mmol )), 4 -( dimethylamino )- pyridine ( 0 . 12 g , 1 mmol ) and n , n ′- dicyclohexylcarbodiimide ( 2 . 27 g , 11 mmol ) were added , followed by the addition of dichloromethane ( 50 ml ), and the mixture stirred overnight at 35 ° c . the reaction mixture was then filtered , washed with water ( 2 × 25 ml ), dried ( mgso 4 ) and the solvent removed under vacuum . column chromatography ( on silica , ch 2 cl 2 as eluent ) gave 4 -( 4 - pentyl - cyclohexyl )- benzoic acid 2 -( 4 - formyl - benzoic acid )- 1 , 2 - diphenyl - ethyl ester ( 2a ) ( 2 . 09 , 3 mmol , 43 %), structure confirmed by 1 h , 13 c , gc - ms and ir . ( 4 - n - butoxybenzyl ) triphenylphosphonium bromide ( 3 . 54 g , 7 mmol ) was added to a jacketed vessel ( 1 l ), dissolved in tetrahydrofuran ( 200 ml ) and cooled to 5 ° c . potassium t - butoxide ( 0 . 90 g , 8 mmol ) was then added and the mixture stirred for 30 min ., after which ester ( 2a ) ( 4 . 00 g , 7 mmol ) was added and stirred for a further 30 min ., before slowly increasing the temperature to 25 ° c . and stirring overnight . the reaction mixture was then washed with brine ( 2 × 50 ml ), the organic layer dried ( mgso 4 ) and the solvent removed under vacuum . after column chromatography ( on silica , 1 st with ch 2 cl 2 as eluent , 2 nd with ethyl acetate and petrol ( 40 – 60 ) as eluent 1 : 9 ) 4 -( 4 - pentyl - cyclohexyl )- benzoic acid 2 -( 4 -[( e )- 2 -( 4 - butoxy - phenyl )- vinyl ]- benzoic acid )- 1 , 2 - diphenyl - ethyl ester ( 2 ) was isolated as both the cis - ( 0 . 80 g , 1 mmol , 15 %) and trans - ( 1 . 00 g , 1 mmol , 19 %) isomers . the structures were confirmed by 1 h , 13 c , gc - ms and ir . the following compounds , wherein n is 3 or 6 , are prepared analoguously compound a 51 . 70 % compound b 12 . 95 % compound c 23 . 70 % compound d 9 . 30 % fx 13 1 . 16 % tpo 1 . 16 % 4 - methoxyphenol 0 . 03 % compounds ( a ), ( b ), ( c ) and ( d ) can be prepared according or in analogy to the methods described in d . j . broer et al ., makromol . chem . 190 , 3201 – 3215 ( 1989 ). fx13 ® is a polymerizable nonionic surfactant with a perfluoroalkyl group which is commercially available from 3m corp . tpo ( 2 , 4 , 6 - trimethylbenzoyl - diphenylphosphine oxide , trademark lucirin ® tpo ) is a commercially available photoinitiator ( from basf ag ). mixture m is dissolved in xylene to give solution s1 with a concentration of 50 % of total solids . 0 . 0395 g of compound ( 1 ) of example 1 are added to 0 . 9566 g of solution s1 to give solution s2 with the concentration of ( 1 ) being 7 . 94 % of total solids . thin films of the solution s2 are coated onto a substrate and isomerized in air for different periods of time , using 3 . 8 mw / cm − 2 radiation from a medium pressure hg lamp . immediately after isomerization each film was polymerized using approx . 15 mw / cm − 2 radiation from the same medium hg pressure lamp in an n 2 atmosphere . in this way , the following polymer films are obtained the reflection spectrum of the polymer films p1 – p5 are depicted in fig1 . it can be seen that the central wavelength of reflection is shifted towards higher values with increasing isomerization time . fig2 depicts the central wavelength of reflection of films p1 – p5 versus isomerization time . the preceding examples can be repeated with similar success by substituting the generically or specifically described reactants and / or operating conditions of this invention for those used in the preceding examples . from the foregoing description , one skilled in the art can easily ascertain the essential characteristics of this invention , and without departing from the spirit and scope thereof , can make various changes and modifications of the invention to adapt it to various conditions and usages .