On the Shape of a Diels-Alder Ladder Polymer** By Brittu L. Schurmann,* Volkev Enkelmann,* Mattliiiis Liiffler, and Arnulf-Dieter Schluter* We have developed a new generation of double-stranded (ladder) polymers, which have poly-Diels-Alder addition reactions as a basis for their synthesis.['l Polymers f and 2 were studied extensively as representatives of this group of polymers and found to be extremely soluble in common organic solvents. Not only was their double-strandedness unambiguously proven.['] but for the first time in the history of ladder polymers. comprehensive information on the molecular weights,[31the nature of end groups,[31and configurational and conformational was also obtained. In addition. ;I model for the shape of polymer 1 was proposed, according to which. the polymer attains the structure of a three-dimensional In this paper. we mostly provide 1 n 2 n theoretical evidence that certain ladder polymers in solution may attain the unprecedented shape of a two-dimensional coil, as is illustrated by the computer-generated structure of polymer 2 (Fig. 1). The formulas of I and 2 suggest that both double-stranded polymers have a symmetry plane ((TJ perpendicular to the plane sketched here, which cuts the bonds that connect the two strands. However, for 1. model studies clearly show that this is not the case. In constrast to the endo-configurated unit (see 3). the cyclohexene ring of the exo-configurdted repeat units exists in one of the two possible staggered conformations,lsl which are both nonsymmetrical about (T,~. Figure 2 a shows the (published[41)molecular structure of model compound 3 in the crystal to visualize the consequences for the shape of 1 . Whereas the endo-unit has plane symmetry, the em-unit does not. It is this unit that forces the backbone of I into the third dimension. [*] Dr. 8. Schurmann. Dr habil. V. Enkelmann, Prof. Dr. A.-D. Schluter.'" Dip1.-Chem. M. Loffler[+' Max-Planck-Institut fur Polymerforschung Postfxh 31 48. D-W-6500 Mainz (FRG) [ + ] Neh Address: lnstitut fur Organische Chemie der Freien Universitiit, Taku.;trasse 3. D-W-1000 Berlin 33 (FRG) [**I Fig. 1. Top and sidc view of a computer-generated structure of 2 (iilkyl sabstituents omitted) with a statistical sequence of \iw and mici-oriented oxygen bridges. This work was supported by the Bundesministerium fur Forschung und Technologie and the Fonds der Chemischen Industrie. We are grateful to Prof. G Wegner. Maim. for his interest in and support of this work. Fig. 2. ORTEP representations of the structures In the crystal o f 3 (a). aIlLsiw6 (b). and all-uwi-6 and cv7:uniii~yn-6(mixed crystal) (c). The structural characteristics of polymer 2 differ distinctly from those of 1, even though its backbone also consists of linearly annulated, a l k d r b o n , six-membered rings. However, all these rings are now conformationally rigid and have the proper symmetry elements for the polymer to show plane symmetry. Compound 6, a model for 2, was selected to demonstrate this point. The three diastereoisomers, all-mti6. all-syn-6, and syn/anti/syn-6were synthesized by reacting the bisdienophile 4[61with two equivalents of a precursor for isobenzofuran (5);'' single crystals were grown, and the structures in the crystal determined. All-anti-6 and syw/cinti/ R Ph R Ph 5 4 R I 7 1 5 R selected as a model for 2.['6* The M D studies were carried out a) with two different starting conformations of 7 (A and B) to avoid a dependence of the result upon the initial structure and b) in the presence of solvent molecules (benzene), since polymer/solvent effects have considerable influence on the conformation of a polymer chain.["] The starting structure A of model 7 was constructed by using bond lengths and angles from the X-ray structures of 6 and the AMBER data bank which gives it plane ~ymmetry."~. 19] Conformation B is an equilibrated structure (after 30 ps) which was created from A by performing a M D calculation in vacua. During the calculation (without solvent) the initially two-dimensional coil starts to deviate significantly from planarity, which is initiated by higher fluctuations of the termini. This can be seen from the values of the moments of inertia ( I x , I,.. I,) about the .Y, y , and 2 axes which remain similar and constant (over 65 ps) after equilibrium is reached (Fig. 3a). Both initial structures were placed in a box of constant volume filled with benzene molecules of realistic density at 300 K, and the molecular dynamics were simulated under periodic boundary conditions.[201The results are as follows: Conformation A keeps its two-dimensional shape over the entire period of simulation (1 30 ps). This was derived from the dependence of I,. I,. and Iz on time. As is required for a nonspherical structure, the values of I, and I, are significantly larger than those of I , (Fig. 3 b). Visualization of the molecular dynamics in a movie showed that the structure, on a time average, retains the symmetry plane onr. To avoid the local minimum problem, the cakulations were repeated at 4 6 4 , 6 : R = (CH&-CH, sy7-6 are unique cases because they form mixed crystals with statistical disorder."] As can be expected, all isomers have a symmetry plane in which the oxygen atoms lie (Fig. 2b. c ) . [ ~ -' 'I These structures, however. and the vague description of the fragments of 2 as being rigid are not sufficient to lead to the conclusion that 2 attains the shape of a (snakelike) two-dimensional coil. This would depend upon the degree of anisotropy of the flexibility of 2 in the plane and out of the plane.[121All-atom molecular dynamics (MD) is an appropriate method to gain information on the fluctuations of the atoms' positions in molecules. It takes into account the chemical structure as well as all the interactions between each two particles of a given ensemble. Hence, we applied this method (AMBER program['31) to help solve the problem of the shape of polymer 2 in solution. An assessment of the reliability of this method has been published, in which structural predictions based on M D are compared with results obtained from, for example, 2D N M R or X-ray invesitgations.[l4] Polymer 7. which consists of seven repeat units carrying no alkyl chains" and terminated by benzene rings, was b) 2.5~10~~ 5.0xlOL 0 0 10 20 - 50 60 70 30 LO f Ips1 0 20 LO - 80 100 120 110 60 f [PSI z 1.0~10~ Ikg A218.0x10' 6.0~10~ 5.0~10~ 0 0 20 7 10 f - 60 [PSI 80 100 0 20 60 LO f Ips1 80 100 120 Fig. 3. Dependence of the moments of inertia *, I , (0).and 1: ( 0 ) about the Y. and z axes on time (i) of the two different starting conformations A and B (see text) of compound 7. a) B obtained from A in vacuo, and b) A in benzene (both runs at 300 K alter equilibrium ia reached). c) B at 700 K during equilibration. and d) B at 300 K after heating to 700 K (d). /A 400. 500, 600, and 700 K["] followed by cooling to 300 K, which yielded results in full agreement with those obtained at 300 K . For starting structure B, the simulation in benzene at 300 K did not lead to any significant change of the gross conformation even at extended simulation time (200 ps). Therefore, the system was heated to 700 K in steps of 100 K. After each run had equilibrated, the system was cooled to 300 K . Finally, in the 700 K case for this conformation, a change in a plane-symmetrical geometry takes place. Figure 3 c shows that the moments of inertia about the three axes split into two sets of values (Z~y, I,., and Zz), which are retained upon cooling (Fig. 3d).12Z1 As in the case of conformation A. the visualization of the molecular motion revealed that conformation B was not spherical anymore but, in fact, two-dimensional and disc-like (on a time average). However. the end-to-end distance was now smaller by a factor of approximately 2 and did not converge within 100 ps to that of the equilibrated conformation A. Undoubtedly. this is due to the large time scale within which the backbone is stretched out. Regardless of the starting conformation, 7 in benzene solution equilibrates to a two-dimensional conformation, which indicates a unique structural feature of 2 and other ladder polymers of comparable rigidity and symmetry. It is important, however, to realize that this calculation does not account for other effects which might play a roleduring synthesis of the polymer. It may well be the case that. as the polymer chain grows. larger fragments of the Same polymer chain overlap each other irreversibly o r that iiitermolecular effect5 (for example: formation of entanglements) prevent the polymer from relaxing into a two-dimensional geometry. Small-angle X-ray scattering is an appropriate method with which one can approach this problem Esper-iritmtcil Procedure A suspension ofa niixture ofrinti-4 and .vri7-4  (3.0 g, 7.9 mmol) and 5 (8.38 g. 15.X nimol) in toluene (80 m L ) is heated at reflux for 24 h under nitrogen. whereupon the solvent is removed. The crude material obtained is chroinatogriiphed through silica gel with petroleum ether (60:40):ethyl acetate (9. I ) iis eluent t o remove 1 .'.3.4-tetraphenylbenzene. A mixture of at least four o f the six possible diartercomeric adducts ( N M R ) is then recovered from the column hy using T H F as eluent. Yield' 4.37 g (90%). Correct elemental analysis. Fracilli~ationfrom chloroform affords pure all-mri-6. whose solubilits is the lowest of d l diastereoiners obtained. pure all-.\w-6. as well as mixed crystals or ;ill-un/i-6 and . \ ~ . i r . a r i r r ' . s ~ n - 6' H . N M R (300 MHz. CDC1,): all-unii6: (5 = 2.3X. 2.49 (2m. 4 H : n-CH?), 2.64 (dd. J , = 3.2, Jz = 1.7 Hz: 4 H . H-5a. Xa. 1421. 1 7 ~ )4.61 . ( a . 4 H . H-6.8. 15. 17). 5.25 (dd. J , = 3.2..1, =1.7 Hz:4H. H-5. -9. -14. -1X); all-.\~w6:6 =1.87 (s, 4 H . H-5a. 8 a . 14a. 17a). 2.57 (t. J =1.6 HI. 4 H . z - C H ~ ) .5.39 (s; 4 H . H-5, 9. 14. 18). 5.40 ( s : 4 H : H-6. 8. 15, 17). .si'ir unii 5rii-6: d =1.95 (s: 4 H . H-52. Xa. 143. 17a). 2.45-2.67 (m: 4 H . 7-CHJ. 5.44. 5.46 ( I s : 8 H : H-5. 6. 8. 9, 14. 15. 17. 18). Received. July 4. 1992 [Z 5446 IE] German version: A n g a r . Clioir. 1993. 105, 107 [I] A,-D Schliiter. A r k . Muter. 1991.3.284:for more recent. related work. see U . Schcrf. K . Mullen, Swr1ie.vi.s 1992. 23.  K. Blatter. A,-D. Schluter. Mu~ror,iok,cirir.s 1989, 22. 3506: T. Vogel. K. Blatter, A.-D. Schluter. Mrrkrornol. CIii~r77.Rupid Coinii~rrr~. 1989, 10. 427: A. Godt. A.-D. Schliiter. A n g a r . C/iern. 1989. I O I . 1704. Ang[w C % P I I I . I n / . Ed. Engl. 1989, 78, 1680.  A. Godt. A.-D. Schluter, Mukrontol. C/i<wi.1992. /Y3. 501.  A. Godt, V. Enkelmann. A.-D. Schluter. ('hem E P ~1992. . 125. 433. [S] E. L. Eliel. Siereochemrstr~ of Curhon Con7pou17d5 McCruw-Hill. New York. 1962.  K. Blatter, A,-D. Schluter, Cl7rm. Ber 1989. 172. 1351.  In analogy to L. F. Fieser, M. J. Haddadin, Cm. J. Clin,? 1965. 43. 1599  As a consequence, corresponding segments in a polymer cham can replace each other without altering the shape of the polymer. X-ray Structure data ofconipounds 6: Enraf-Nonius CAD-4 diffractometer, room temperature. Cu,, radiation. i = 1.5405 A. graphitc monochromator. The structure was solved by direct methods (MULTAN) and by vector search methods (DIRDIF). Empirical absorption correction. anisotropic temperatur factors for O and C. refinement ofthe H atoms in the "riding mode" with fixed isotropic temperature factors. All-un/1-6 (at 273 K ) : monoclinic. space group P2ir. ( I = 14.4470(9). h = 6.0272(8). 1' = 23.9443(15)A.p = 91.995(8). V = 2083.7A3.%= 4.0,,~,,,,= I 360gcm-' 3583 reflections. 2392 observed [ I > 3c(I)]. R = 0 05X. R, = 0.056. all51~6 (at 273 K): orthorhomhic. space group Pna2,. (/ = 14.2156(10). h = 10.673(2). c = 29.358(1), V =7588 A3. Z = 8. (1',,, r J = 1.225 g c m - " . 6369 reflections. 3092 observed [ I > 3 u ( I ) ] .R = 0.083. R, = O.OX5: .\)'I?r i n / i - . s ~ r i - 6 from a mixed crystal (at 195 K):monoclinic. space group PI, n. R = 13.671(1). h = 22.387(2), c = 5.6060(5). lj = 100.308(4). V = 16x8 k 3 . Z = 4. pcA,cd=1.210gcm-3. 2177 reflections, 1158 observed [ I > 3 u ( l ) ] . R = 0.068. R, = 0.070. Further details of the crystal structure investigations may be obtained from the Fachinformationszentrum Karlsruhe, Gesellschnlt fur x i s senschaftlich-technische Information mbH. W-7514 Eggenstein-Lcopoldshafen 2 on quoting the depository number CSD-56902. thc nameb of the authors. and the journal citation. All other stereoisomers should show plane symmetry. For this specific type of double-stranded polymers, a new theiiretical delinition of persistence length is required. S. J. Weiner, P. A. Kollman, D . A. Case, U. C . Singh. C . Ghio. G. Alagona. S. Profeta. P. Weiner. J. An?. Clirin. Soc. 1984. 106. 765. B. L. Schurmann. M. Depner. Mol. PI??.\. 1991. 74. 715; B. L. Schurmann. 6 . .lung, Lipid Cr:vsi. Mol. Ci:~.vt.1990. 1x5. 141. For reviews. see W. F. van Gunsteren. H. 1. C. Berendsen. Angeiir C / : P ~ .1990, 1 0 . 1020; Angviv. C h m . In!. 0 1 . Engl. 1990, 29. 991: H. FruhbeiD, R. Klein. H. Wallmeicr. i b i d 1987, 99, 413 and 1987. 26.403. The alkyl chains containing six C atoms iire expected to have only minor influence on the conformation of the backbone. The sequence of the relative configurations of neighboring oxygen bridges in 7 is unri.'untr;~jn'.vj.n.\~n!'.srniuntr.sy'unri.unri~antrs i x . s y i ( i n t i uiiii. The structure shown in Figure 1. though having all features required Tor the formation of a two-dimensional coil. could not be used for simulation\ in solution because of the large number of atoms. For example see M. Depner. B. L Schiirmann. J. C o ~ n p i ~(%mi?. i. 1992. 13. 1210. The partial charges used to describe Coulombic interactioiis were obtained from M N D O calculations and scaled by the empirical factor of 1.3. ii factor generally used to obtain consistency with the AMBER force field. [I 31 An appropriate distance (1.2 A) between the solvent and solute :nolecules was chosen to ensure the correct physical density of the solvent. For a more detailed description, see ref. [IS]. The heating was performcd to explore the conformational space in the sense that kinetic energy pumped into the ensemble is used to overcome the energy barriers separating the different local minima. Bond hreaking cannot occur because of the particular mathematical expression used for the potential. The I,. I,. and I= values of the two-dimensional coils obtained from stiirting conformations A and B. respectively (Fig. 3 b and d). var) due to differences in the shape of these coils as reflected by the differcni cnd-toend distances. G. Urban, M. Ballauff. Karlsruhe, private communication.