J, MACROMOL. SCL-CHEM., A17(4), pp. 689-703 (1982)

Concepts of Trapping Topologically by Shell Molecules

MIECZYSŁAW MACIEJEWSKI

Institute of Organic Chemistry and TechnologyWarsaw Technical UniversityWarsaw, Poland

ABSTRACT

Concepts of the synthesis of shell topological compounds, whichconsist of a guest molecule (or molecules) trapped by a hostmolecule with a spacial, egg shell-like structure are discussed.Generally, both constructing the shell molecule in the presenceof a guest molecule and constructing the guest molecule In thepresence of the shell (host) are ways to "shell" topological com-pounds. The preparation of shell molecules may consist of thecompletion of "preshell" molecules or of obtaining cascadebranched oligomers and polymers. Cyclodextrins and aub-stances like triquinance are considered to play a role in preshellmolecules. Shell molecules may also be obtained by polyreactionof a monomer of the XRY type, which results In a cascadebranched molecule of shell structure (spherical form).When the polyreaction is continued, the cascade branched mole-cule becomes a "cast" one. E is theoretically possible to enclosea guest molecule inside the shell during the cascade branchingprocess if there is a good solvent (of high expansion coefficientvalue) iii respect to the growing branches, A spacially developedmolecule of both "empty" and "cast" structure may be obtainedalso by the known "step by step" cascade branching process whichInvolves, for instance, a repeated cyanoethylation-reductionreaction.

689

690 MACiEJEWSKI

Some kinds of compounds with topological bonds [ e.g., Rcfs. 1-7]are known, and methods for their synthesis are available. However,up to now three types of the compounds, (catenanes, rotaxanes, andknots) have only been examined as their polymer derivatives. Thesehave been based on macrocyclic molecules.

In the present paper new kinds of topological compounds and con-cepts of the synthesis of them are discussed. The topological com-pounds just mentioned consist of a guest molecule (or molecules)trapped by a host molecule, which is a spacially developed structureof completely closed form, like an egg shell. The term "shelltopological compounds" adequately reflects such a type of structure.The molecular geometry of any solid figure, which is empty inside,can play the role of the host molecule in shell compounds. In thesimplest case it would be a molecule of spherical structure.

One can draw at least two pathways which should lead to thesynthesis of shell topological compounds. One of them includes thepreparation of shell molecules in the presence of guest ones. It canbe assumed that some guest molecules will be trapped inside. On theother hand, the preparation of guest molecules in the presence of anavailable shell is another pathway to the synthesis of shell topologicalcompounds. In this procedure, the shell molecules used must exhibitselective permeability. They should be impermeable in respect to guestmolecules and penetrable for substrate molecules suitable for syn-thesis. Such a situation allows the substrate molecules to penetrateinside of the shell and react there in special conditions to result inguest molecules. The latter are combined with the shell topologically.Both statistical and directed methods seem to be available for thesynthesis of shell topological compounds. However, the preparationof shell molecules alone remains the most important problem in thissynthesis. Two concepts of the synthesis of shell molecules will bediscussed. The first one consists of the completion of the moleculargeometrical form which can be considered as an initial part of theshell. These can be called preshell molecules. The second usesoligomer or polymer compounds of spacially developed structures.Low molecular preshell molecules will be useful in the synthesisof rather simple shell topological compounds (Fig. la, lb, lc), andthe polymers will result in products of higher complexity (Fig. Id,le).

Sokolov [ 8] has perceived the possibility of the synthesis of shelltopological compounds by dimerization of triquinacene [9] as a com-plex with metals. Sokolov believes that this reaction would directlygive the topological compounds of pentagonal dodecahedrano (up tonow it has not been obtained) with metal atoms remaining in the freeinternal space of this spherical molecule. Besides that, it seems thereis no information in the literature in which the synthesis of shell topo-logical compounds is described [ 8]. It is very probable that the syn-thesis of pentagonal dodecahedrane will be accomplished shortly as aresult of intensive investigations made by Paquette et al. [ 10-13j onderivatives of this compound which, however, do not have a complete

TRAPPING łiY SHELL MOLECULES 091

FIG. 1. Schemes of shell topological compounds: (—-) externalcontours of shell molecules, (—) internal contours of shell molecules,( u ) guest molecules.

spherical structure. This would give the possibility of the synthesisof topological compounds based on dodecahedrane. We can hope thatother polyhedranes will be available for topological synthesis in thefuture.

Cyclodextrins molecules are another type of preshell compound.They can place in their free spaces not only atoms but also moleculesof many compounds, especially organic ones. Inclusion compoundsof cyclodextrin are very well known. Cylindrical cyclodextrin mole-cules have two crowns of hydroxyl groups on their ends, and intra-molecular cross-linking of each crown separately ("darning" of holes)can mean the completion of the shell. If guest molecules are putinside cyclodextrin ones, molecules of shell topological compoundwill be obtained as in Fig, 2, The small number of compounds avail-able for the initial shell structure (practically, only the hoinnl.ijis ofcyclodextrins, alpha, beta, and gamma, are now available) significantlylimits the possibility of the eventual development of low molecularshell topological compounds. It seems that there are possibilities of

692 MACIEJEWSKI

HO- \W\\\\\\

\W\\\\\W

OH

2RX-

-OH 0-

R * 4HX

-0

FIG. 2. Intramolecular cross-linking ("darning" of holes) ofcyclodextrin molecule. Only 4 OH groups are shown instead of 18,21, or 24 (for alpha-, beta-, or gamma-cyclodextrin, respectively).

the synthesis of more complex shell compounds in the field of poly-mers. This problem will be discussed.

The approach to the synthesis of macromolecular shell topologi-cal compounds does not include cross-linked systems. Topologicalcompounds, which exist In the form of separate molecules, seemto be most Interesting and will be discussed below. The mainproblem here Is the synthesis of a shell molecule alone.

The protein cyst coating a virus nucleic acid is a very well knownnaturally occurring polymer shell "molecule" of almost full shellstructure. This protective coat is this nucleic acid. It seemsunlikely that we will soon be able to synthesize a polymer shellmolecule with such a thin-wall structure. A special molecularmatrix is surely needed for this purpose.

As will be shown below, a way to synthesize a macromolecu-lar shell molecule or a macromolecular shell topological compoundmay consist of the synthesis of a macromolecule having a geometryof a cast space figure, e.g., ball, cylinder, cone.

The only way to synthesize cast macromolecules is by a poly-reaction which is accompanied by an intensive chain branchingprocess unless the reaction product is cross-linked. The well-knownstar or comb polymers are not adequate; it is necessary to synthesizecascade branched polymers.

There is a kind of polyfunctional monomer (more than two func-tional groups) which does not result in cross-linked polymers evenat a high degree of polyreaction. These monomers have the generalformula XRY In which the polyreaction can be carried out only be-tween different functional groups, "n" is a whole number greater than 1.In such monomers X can be, for instance, either a hydroxyl or carboxylgroup, and Y can be either a corresponding carboxyl or hydroxyl group.The greater "n," the greater the degree of branching in the polymerchain.

Flory [ 14, 15] was first to pay attention to such monomer types,and he derived some statistical relations in polyreaetkm.s of them.

TRAPPING BY SHELL MOLECULES 093

He also indicated several examples of cascade branched polymers inthe literature. Cascade branched structures, described mainly mathe-matically (theory of branching processes, graph theory), have servedfor many years as models (tree-like) to explain network formationand properties of cross-linking systems [e.g., Refs. 15-24].

From monomers of simplest type XRY2, two kinds of polymerstructure can be obtained in extreme cases.

a. Linear Structure

X-R-Z-R-Z-R- R-Yi i i I

Y Y Y Y

where Z is a new group resulting from the reaction between X andY.

b. Cascade branched structure shown below is the initial poly-reaction product

R R

x-<z

RNY ' Y

The creation of a linear structure will be preferable in this case whenthe Y groups in the monomer molecule have different reactivities. The;equivalence of all Y groups will give rise to the predominance of thebranched structure. A perfect cascade branched structure would havethe polymer molecule growing in all directions at the same rate. De-viation from a perfect cascade branched structure will be of statisticalnature as well as coming from the steric isolation of the reacting groups.In many cases it seems possible to determine the cascade structurecontent in the reaction product by chemical analysis and spectros-copy. The cascade structure content can be express by the relation

^ Y Zof the amount of -R C -, groups (when n = 2) to the amount of - R ;' ^

694 MACIEJEWSKI

groups. The first formula represents a cascade branched structureand the second represents a linear one. In many cases both kinds ofgroups should be distinguishable chemically and spectroscopically.A perfect cascade branched structure will be represented only by

-R C Y groups distant from the initial mer of the polymer chain by

the same amount of chemical bonds. Analogously, one can considerthe situation for monomers of n more than 2.

The probability of creating of cast molecules in cascade branchingpolyreaction comes directly from so-called "Malthusian packingparadox" [21, 22, 24], E tells us that the space available for a cas-cade branched growing molecule (tree-like structure) cannot accom-modate all structural units when all functional groups react. TheMalthusian packing paradox, which is related to the gel of cross-linking systems, is reflected by the situation where the number ofstructural units at the r bond distance from a given unit in the gelstructure is proportional to y r , while the space available for these

units is proportional to r2 [ 2l] , y denotes the relative conversionwhich, exceeds 1, after the gel point then is r r / r 2 - °°. If shell topo-logical compounds are involved, it is useful to note how the relationof the volume needed for accommodating the structural units to thevolume available for them changes depending on the degree of polym-erization of a growing molecule.\ This relation will express thedensity of packing of a growing molecule in the space available for it.

Let a simple monomer X-CH C Y condense with a molecule X-Y

as a by-product of the reaction. A perfect cascade branched polymeris assumed to be created:

CH Y H ;CH : C H XCHNCH / H ,C

,CH X-tHCH CH S

This structure, shown schematically on the plane, is embedded inspace, of course. A cast molecule will be produced on condition thatthe structural units of the polymer (CH) fill a ball volume determined

TRAPPING BY SHELL MOLECULES 695

by a radius, which equals the length of a branch, being extended to amaximum. This volume is the largest that can be available for thatmolecule (the lengths of each branch are equal in a perfect cascadebranched molecule obtained by polyreaction of XRY ; one of them isindicated by boldfaced lypo in the formula.

Structural units of the polymer molecule must be considered asphysicalo bodies having real dimensions. The CH group takes a volumeof 10.9 AJ in the hydrocarbon molecule (25] , In Table 1 are resultsof calculations describing the perfect cascade branched polymer con-structed from CII units, depending on the polymerization degree m ofa branch of. the molecule. The m value corresponds lo the amount ofC-C bonds in a branch (m also corresponds to the conventionalnumbering of generations in the theory of branching processes), z(Column 2) denotes the amount of CH units in a whole polymer mole-cule. For a monomer XCHY2, 2 increases in a geometrical progres-sion during the polyreaction. For m equal to 1, 2, 3, 4, etc., z equals(1 + 2), t(2 x 2), +(2 x 2 x 2), +(2 x 2 X 2 x 2), etc., respectively. Thesum of such a progression is expressed by

1 - q2 = 1 + a 1

1 - q

where

a.i = q - 2

The equation is common for monomers of the XRY type and thena 1 - q = 11. In Column 3 there are length values K of a branch in itsmost extended position, t denotes the distance between the centerof a carbon atom in an initial mer and the center of a bond followingthe C1I group considered as the last one in the branch. For simplicitythe end groups (X and Y) have been neglected and the molecule con-sidered is assumed to be a ball section of radius 1 in respect to somegreater one, both being in concentric positions. This allows all bondsto be equivalent. On the base of m, z, and lvalues, the volume V t

(Column 4) of a ball determined by radius c and the volume V , which isthe sum of the volumes of all CH units within a ball section, can be cal-culated. In Hie perfect cascade branched molecule, no structure unitcan appear outside that ball section and then V will simply be equal to

zVp... The relation V /V expresses the density of packing k in the

molecule. In other words k indicates the extent to which structuralunits fill the volume available for a polymer molecule.

It must be emphasized that there is a specific packing densitydependence on the degree of polymerization. With the exception of

696 MACIEJ EWSKI•4-1

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TRAPPING BY SHELL MOLECULES 697

TABLE 2. Packing Density of Structural Units for Different Polym-erization Degrees in the Case of XCYa Monomera

m

1

2

3

4

5

6

z

1,

4

13

40

121

364

093

1

1.875

3.125

3.375

5.625

6.875

8.125

V

1,

2,

1

27.

127.

350

744

,358

,242

55

5

V =P_22

71

221

669

193

6,044

.12

.9

.2

k = V /Vj

0.80

0.56

0.63

0.9

1.4

2.7

M

1

4

13

48

156

480

,452

,368

,116

Meaning o^ symbols see Table 1.bV = 5.53 A3 | 25],

the case in which the molecule consists of three structural units andprobably its shape strongly differs from a ball, the packing density issmall and CH groups fill only 50% of the available volume at lowdegree of polymerizations (m = 2/5). When m increases, the packingdensity becomes larger and larger and reaches quickly a value whichis larger than the theoretically possible one. At m = 8 (k = 1.11) theperfect cascade branched molecule is indeed a cast one. It is certainthat the polymer molecule becomes a cast ball even earlier than inthis case because substances never reach a packing density equal to1, even in the crystalline state. A packing density of 0.80 is thelimit, and this is not attained by crystalline polymers | 26). It seemsreasonable to accept this value (in the absence of another) as a limitwhich a cast molecule may approach. One can also calculate themolecular weight desired for the cast molecule to occur. In theabove case the polymer has reached a cast structure by m = 7(molecular weight about 3300).

Table 2 contains data on the perfect cascade polyreaction of amonomer with a larger number of the functional groups (3Y groups).In this case the reaction product surpasses the limiting value of pack-ing density by m = 4 (molecular weight 1452) when X—Y moleculesevolve as by-products. By the way, the reaction product is a varietyof "diamond" structure (if the endgroups are neglected). As indiamonds, only quaternary carbon atoms are present in the molecule(angles and distances are neglected). Undoubtedly it would be interest-ing to obtain and determine the properties of such a "diamond" poly-mer.

In any case, the perfect cascade branching process is possiblefor monomers XRY only up to real limiting value of packing density.

698 MACIE.JEWSKI

guest molecules cascade branchedmolecule

FIG. 3. Approximate distribution of packing density in a growingball molecule.

The cascade process of some branches will be interrupted above thislimit because of crowding. However, the molecule can continue todevelop centrically in the form of a growing macroball while remain-ing a part of functional groups in its interior. One must rememberthat functional groups Y crowd mainly on the surface of the macro-ball in a growing molecule. This introduces a disturbance into thebranching process. If the Y group volume is greater than thai of thestructural unit, the mathematical description of the branching processwill be more complex.

Coming back to molecules with a low degree of polymerization (atlow numbers of generations), it is easy to see that there is a situation

TRAPPING BY SHELL MOLECULES 699

at favorable conformation:.;, when a partially unfilled bail moleculecomes into being at the beginning ot the reaction (see k values atdifferent values). This molecule becomes more and more filledwith structural units (mainly in its periphery) in the next steps ofthe reaction, so that to be completely full at last. Before the mole-cule has become a cast one, there must be a moment at which themolecule has a cast structure only in its periphery, thus creating ashell which encloses a partially unfilled interior (Fig. 3). That is, ashell molecule has been obtained. Such an "empty" molecule can existonly hypothetical^, of course, because the growing cascade brancheswill also fill the initial free space. It is, however, theoretically pos-sible for space unfilled with structural units to remain if this spaceis filled with guest molecules before the shell is completed. Thenit is possible to obtain a shell topological compound directly. Therewill be especially favorable conditions if the cascade polyreaetionproceeds in the presence of guest molecules which are a good solventfor the polymer. A good solvent means a solvent with a sufficientlygreat so-called average expansion coefficient, in such a condition thegrowing branches will take an expanded conformation and the solventmolecules attracted by the polymer segments will be closed by theexternal shell of the growing ball (Fig. 3). This seems to be a veryreal pathway to the synthesis of shell topological compounds of thespherical type.

The analysis of the possibility of the synthesis of spherical topo-logical compounds in the polymer field has been carried out for thesimplest types of monomers. However, in practice the availablemonomers are usually more complex, and the functional groups aredistant from each other. Some monomers with a more real structurewill now be discussed. Data in Table 3 shows that if the functionalgroups of a monomer are distant, the limiting value of packing densitywill be reached by a polymer with a higher degree of polymerization.With 3,5- Diaminobenzoic acid (or acid chloride) as a monomer( t - 6.04 A), the limiting packing density will not be surpassed

until m - 13. On the other hand, the polymer can become a castmolecule at a lower m if the volume of a monomer molecule increasesalthough t remains constant. Suitable substituents can be introducedfor this purpose either into a monomer molecule or into a polymermolecule. 3,5-diaminotrimellitic acid will give a cast structureat m = 11. Thus there are many possibilities for the synthesis ofcast ball polymers with various chemical structures and molecularweights.

It is rather hard to predict theoretically what part of a "cast"macromolecule will constitute free space and be taken by guestmolecules. In the shell topological compound, part of the packingdensity will be due to the guest molecules, and then limiting valueof the density calculated as above will be attained at lower degree ofpolymerization (V will be decreased by the total volume of the guestmolecules). fc

700 MACIEJEWSKI

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TRAPPING BY SHELL MOLECULES 701

Cast macromolecules as well as shell topological compoundsshould exhibit some shape stability and undergo neither contractionnor expansion. For such molecules obtained in real conditions, themolecular weight distribution as well as the molecular shape dis-tribution will be characteristic. Introduction of the term "averageshape" for these molecules seems necessary. When the product of aperfect cascade polyreaction of XRY is ball-shaped, that can be the

average shape only in real conditions. The shape distribution ofcascade branching molecules will be complex because of the possibilityof the reaction of growing molecules with each other in addition to thereaction between growing molecules and the monomer.

However, there is the possibility of the synthesis of model spheri-cal compounds of strictly ball shape by way of a "step by step" re-action. Low molecular weight cascade branched molecules, whichhave topologically shaped cavities or pseudo-cavities obtained inthis way, have been described I 27]. The authors guess they haveproperties of cryptands and are capable of binding ionic guests ormolecules (as complex or inclusion compounds). According to Ret". 27,cascade branched molecules have been obtained by several repetitionsof two reactions: cyanoethylation of am ino groups (each amino groupcan be substituted for by two cyanoethyl groups), and reduction ofnitrile groups to amino functions. As a result of repeated reactions,polyaza molecules with "increasingly growing cavity size" (as theauthors say) are obtained. What the authors really obtained underthe conditions they used can be calculated. If even the largest polyazamolecules (n = 2, m = 3, £ .. = 4.7, V .f = 49.71) are involved,' ' unit ' unit 'their packing density (0.063) is very far from that of cast structureand the molecules can be considered only as the octopus type [ 27],However, the pathway indicated by the authors must lead to cast mole-cules at higher degrees of polymerization. It can be calculated forthis system that the cast structure will be reached at m = 13 (k - 0.85).This means that the cyanoethylation reduction reactions would have tobe repeated 13 times. This is a very laborious, time-consuming path-way to cast structures, but the only one if a perfect cascade branchedstructure is to be obtained. This is because no more than one mono-mer unit can be annexed on each branching chain at each step of thereaction. On the other hand, a very high yield reaction can be chosenwhich allows the units to be annexed by (practically) all the brandlingchains at each reaction step. Under these conditions the cast mole-cules of perfect balls form or the corresponding topological compoundwill be obtained after the real limiting density packing value is readied.The "step-by-step" concept of the synthesis of cast macromoleculesis also useful in respect to the variety of geometrical forms of mole-cules created depending on the shape of the starting molecule. Alast instance is a linear polymer with functional groups along thecham. If a polyvinylamine molecule undergoes repeated cyanu-ethylation-reduction reactions, a cast molecule of cylinder form will

702 MACIEJEWSKI

be obtained. For such a molecule to be obtained it is enough for eaclimer of the polymer chain to be cascade branched to an extent whichallows a unit cylinder (of a height equal to the mer length and radiusequal to O to be filled by the branches. If polyvinylamine is involved,simple calculations show that the packing density of the resultingpolymer will pass the limiting value at m = 6. Theocast macromole-cule created will have a cylinder form of about 50 A diameter. Inthis case there is a theoretical possibility of the tiynthesis of thetopological compound which is represented by the polymer geometryof a pipe (as a shell molecule) filled with guest molecules by analogyto the compound geometry of the ball. The branching process mustbe carried out, of course, up to the moment when the ends of polymerpipe have been closed by the creation of the respective hemispheres.However, open pipe molecules would also be very interesting struc-tures from the inclusion chemistry point of view. Similar modifica-tion of polymers can also be carried out by polyreaction of monomerXRY in the presence of a polymer which has Y functions of the same

(or higher) chemical activity. However, as a result, a mixture of amodified starting polymer and spherical ones (created by the poly-reaction of XRY alone) will be most promising.

Following the procedure described above, one can synthesize manypolymer structures based on copolymers as well as normally branchedchains such as star and comb polymers. Many other low molecularweight and polymer structures are suitable as base substrates.

Experimental studies of these structures are underway.

R E F E R E N C E S

l] E. Wasserman, J. Am. Chem.Soc, 82, 4433 (1960).2] G. Schill, Chem. Ber., _1007^521 "t 1967T; Habilitation Thesis,

University of Freiburg, T564.[3] G. Schill, Catenanes, Rotaxanes, and Knots, Academic, New

York, 19717"[4] B. Hudson and J. Vinograd, Nature (London), 2N5, 647 (1967).[ 5] G. Karagounis and J. Pandi-Agathokli, Prakt. Akad. Athenon,

pp. 118-126 (1970).[6] M. Maciejewski and G. Smets, Paper Presented at 2nd Confer-

ence on Modification of Vinyl Polymers, Wroclaw, Poland,1973; Sci. Papers Inst. Org. Technol. Piast., Wrocław Tech.Univ., ,16, 57 (19747;_Chenu_Abstr.,_83, 43826e (1975).

[7] M. Maciejewski, Habilitation Thesis, Warsaw TechnicalUniversity, 1980.

I 8] V. J. Sokolov, Vviedeniye v teoreticheskuyu stereokliimiyu,"Nauka," Moscow, 1970, p. 176.

TRAPPING BY SHELL MOLECULES 703

[9] R. B. Woodward, T. Fukunada, and R. C. Kelly, j^Am^Client.Soc., 86, 3162 (1964).

[ 10] L. A. Paquette, M. J. Wyvratt, O. Schallner, J. L. Muthard,W. J. Begley, R. M. Blankenschip, and D. Bulogh, J. Org. Chem.,44, 3616 (1979).

[ 11] L. A. Paquette, W. J. Begley, D. Balogh, M. J. Wyvratt, andD. Bremner, Ibid., 44, 3030 (1979).

[ 12] R. L. Sobczak and L. A. Paquetle, Ibid^ 44, 4896 (1979).[ 13] L. A. Paquette, J. L. Muthard, and TTCynkowski, jJ^

Soc., 101, 6991 (1979).14] P. J . Flory, J . Am. Chem. Soc., 74, 2718 (1952).15] P. J. Flory, Principles of Polymer Chemistry, Cornell Uni-

versity Press, Ithaca, New York, 1953.16] W. H. Stockmayer, J^Cliem. Phys., 11, 45 (1943).17] I. J. Good, Proc. Cambridge Pliilos. Soc, 45X 360 (194a),

through Ref. 19.I. J. Good, Proc. R. Soc, A, 272, 54 (1963).G. R. Dobson and M. Gordon, J. Chem. Phys., 41, 2389 (1964).

1819 __20] M. Gordon and G. N. Malcolm, P r o c R. Soc, A,"295, 29 (1966).

[21] M. Gordon, T, C. Ward, and R. S. Withney, in PolymerNetworks_.Structure and Mechanical Properties (A. J. Chompff ancTsT New-man, eds.), Plenum, New York, 15*71.

[22] M. Gordon, Pure Appl. Chem., 43_, 1 (1975), through Ref, 24.[23] M. Gordon and'W. B^Temple, in Chemical Applications of Graj)h_

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Accepted by editor February 13, 1981Received for publication March 6, 1981