+ Effects of Long-Chain Branches on the Degradation Kinetics of Polymers CH3 R (4) The deuteration pattern of the amines obtained indicates that the reaction proceeds, as previously suggested, via an immonium formate, which is then reduced by deuteride transfer to the amine. c =o DCOOO <&a Procedure A solution of 3-(p-tert-butylphenyl)-2-methylpropanol (10.2g, 0.05mol) in toluene (70ml) is treated with cis-2,6dimethylmorpholine (6 g). After azeotropic removal of the water with toluene (which distills over until an internal flask temperature of ca. 120°C is reached), 2.5g of (2) in 5ml toluene is slowly added and the mixture of amines (3) and ( 4 ) finally distilled at 142--145"C/0.3 torr. In the case of ( 6 ) and (7) the {'HJ-noise-decoupled I3C-NMR spectra show a triplet at 6=64.77, and in the case of (9) a triplet at 6=31.82; in all cases by coupling with the deuterium nucleus. (3) and ( 4 ) each show two triplets at 6=64.53 and 31.71. The 'H-NMR spectra of ( 6 ) and (7) with signals at 7.3 (2, d), 7.1 (2, d), 3.7 (2, t), 2.8 (1, m), 2.7 (1, m), 2.35 (1, m), 2.2 (1, m), 2.15 (1, m), 2.0 (1, m), 1.7 (2, m), 1.3 (9, s), 1.15 (6, d) and 0.85 (3, d) confirm this assignment by the changing signal splitting; ( 3 ) and ( 4 ) as well as ( 6 ) and (7) are present as 40: 60 mixtures. Received: January 31, 1979 [Z 184 IE] German version: Angew. Chem. 91, 341 (1979) CAS Registry numbers: ( I ), 69668-13-9;(2), 920-42-3;(3), 69668-14-0;(4), 69743-83-5;( 5 ) , 91771-5; ( 6 ) , 69668-15-1 ; (7), 69743-84-6;( S ) , 925-94-0;(9), 69668-16-2; 3-(p-terr-hutylphenyI)-2-methylpropanal, 80-54-6;cis-2,6-dimethylmorpholine, 6485-55-8 [1] P. de Benneuilk, J. Macartney, J. Am. Chem. SOC. 72, 3073 (1950). [2] 13C-NMR (Bruker WH-270, CDCl3, TMS int.): 6=148.19 (I, s), 137.77 (1, s), 128.90 (2, d), 124.80 (2, d), 71.53 (2, d), 64.99 (1, t). 60.09 (1, t). 59.98 (1, t), 40.75 (1, t). 34.20 (1, s), 32.04 (1,d), 31.47 (3, q), 19.12 (2,4). 18.04 (1, 4). [3] N. J . Leonard, R . R . Sauers, J. Am. Chem. SOC. 79, 6210 (1957); J . J . Panouse er a/., Bull. SOC.Chim. Fr. 1963, 1753. By Klaus H . Ebert, Hanns J . Ederer, and Arno M a x Basedow"] Dedicated to Professor Horst Pornrner on the occasion of his 50th birthday Experimental investigations on the kinetics of the hydrolytic degradation of dextran in solution[' showed that small molemles are formed more frequently than should be the case in a random reaction. O n assuming, firstly that the dextran molecules are unbranched, and secondly that the "individual" degradation constants ( K J along the polymer chain vary according to a parabolic function, we could establish the curvature of this parabola as b =0.4 from experimentally determined molecular-weight distributions via the combined polydispersity ratio CPR = A?$/@,, .M,) by mathematical simulation. This means that the polymer bonds at the ends of the molecule are about three times more reactive than in the center of the molecule. Freudenberg, Kuhn, et u/.['I likewise deduced a non-random degradation from the acid hydrolysis of cellulose and starch. The assumption that the dextrans are unbranched is especially critical, since the experimentally determined molecularweight distributions of the degradation products can in principle also be explained by long-chain branching and random degradation (see ['I). Relatively little is known about branching in dextranL3.'I. Dextran obtained enzymatically from Leuconostoc Mesenteroides B 512 F has, at most, branching on 5 % of its repeating units[51.Of these at most 15 % are longer than two glucose unitsL6],so that the proportion of branching points with sidechains longer than ten monomer units can be assumed to be about 0.1 %, i.e. for every 1000 structural moieties there is one long-chain branch. Short-chain branches (side-chain lengths < five monomer units) do not influence the molecular weight distribution of the degradation products. We have investigated the influence of long-chain branching on the product distribution in a random degradation reaction by mathematical simulations of various branched model molecules, which were generated by a Monte Carlo method. The results are expressed in terms of the dependence of KS,l on 1. Here K s , l is the rate constant for the cleavage of a molecule having a degree of polymerization s into two fragments with degrees of polymerization 1and s-1. For unbranched molecules, Ks,l is a measure of the probability of cleavage at site 1. These diagrams are identical with the molecular weight distributions obtained, assuming every molecule has undergone a simple chain rupture. Our model calculations are based on molecules having a degree of polymerization of 1000 (Table 1). Model 1 is for singly branched molecules in which the length and position of the side-chain are randomly distributed. In models 2 and 3 the number of long-chain branches is increased respectively to three and seven, while the lengths and positions of the side chains are again randomly distributed; however, only one side chain can branch at each position of the main chain. Figure 1 a shows that the curvature of the curves increases with increasing number of branches. The effect is very pronounced even with one side chain; the curve is almost parabolic with b=0.8. The unbranched molecule gives a straight line parallel to the abscissa at 1. [*]Prof. Dr.K. H. Ehert, Dr. H. J . 321 Anqew Chem I n t Ed Engl 18 (1979) N o 4 0 Verlag Chemie, GmbH, 6940 Weinheim, 1979 Ederer. Dr. A. M. Basedow Institut fur Angewandte Physikalische Chemie und SFB 123 der Universitat Im Neuenheimer Feld 253, D-6900 Heidelberg 1 (Germany) 0570-0833/79,0404-0321$ 02.50/0 Table I . Parameters of model molecules. s=degree of polymerization = 1000, h=length of the main chain, u,=length of the side chain ( i = 1 ... z ) , z=number of side chains, p, = position of the branch i on the main chain, rnd. (x ...y ) = random choice within interval (x . . . j )R,E = residue of s not used in the selection process. - 2 Model 1 4 3 5 6 7 to 10 10 - h G; . md. (1 . ..s - 1 } rnd. {3.. .s - 31 md. {X.. ,s -8) vl=~-h u I = m d . (1 ...s - 1) UI u2 = rnd. { l ... RE - 1 } =RE Z 1 p, rnd. { I Fig. 1a . ._h - 1 } =rnd. (1 ...s -h} ui = m d . (1 ...RE-(2-i)} s / 2 = 500 ui=rnd. /30 ... 80; G, =rnd. {20...220} u1 = m d . { 1 .. . %(s-h)) RE rnd. distributed RE c o x . like 4 over ui v 2 - 8 = md. ( 1 ... RE,} for 1 i i i 7 v,=RE u1 = m d . { 1 ... s -h} L ) v g = RE ~ = - ~rnd. (1 . _ 2 ./3 RE,] =RE 3 7 9 9 9 9 rnd. { l .. .h - 1 } each pi selectable only once rnd. like 2 md. like 2 i i i la la Ib lb Ic Ic - of the products in degradation reactions. From the shape of the distributions, quantitative information can be gained about the number of branches and lengths of the side chains, and sometimes also about the main chain. Thus, e. g., from our experiments on dextran it can be concluded, assuming random probability of cleavage, that the number of long-chain branches lies below 0.2 %.-For a more accurate analysis of the long chain branching, the shape of the K S , ,curve should be determined from the experimental molecular weight distributions, and not only from molecular weight averages and the CPR. R 1 Idl h 3!\ Received: February 5, 1979 [Z 185 IE] German version: Angew. Chem. 91, 341 (1979) ~~ [l] A . M. Basedow, K . H . Ebert, H . J . Ederer, Macromolecules 11, 774 Fig. 1. Dependence of the rate constants Ks,, on the degree of polymerization 1 of the fragment (K*=experimental degradation constant). The curves are model 3; b) model symmetric about s/2. a) A model 1, 0 model 2, 4, model 5; c) model 6, model 7. Model 4 contains nine long-chain branches and the main chain is as long as the sum of the side chains; these were varied randomly between 30 and 80 monomer units. The branching points on the main chain were likewise randomly chosen. In model 5 the main chain was shortened to ten monomer units and the lengths of the side chains distributed randomly between 20 and 220. Model 4 can be regarded as a “comb”, model 5 as a “star”. Figure 1 b shows that shorter side chains lead to higher K,,,-values at small I-values; in the case of larger /-values (up to 4 2 ) longer side chains and the main chain are decisive. The models 6 and 7 are “stars” with a greater distribution in the length of the side chains. Model 6 permits a random choice of z/3 of the residual monomer units available in the generating process, in the case of model 7 the lengths of the side chains are chosen randomly (Fig. Ic) from the total number of the residual monomer units (Table 1). Model 6 contains more side chains with average degrees of polymerization; hence the curve falls more slowly at low /-values. In the random model 7 the number of large fragments is greater; hence the larger values near to the center of the molecule 42. Our models cover all polymer molecules without compound branches as well as all molecules in which double branching is peripheral. More strongly branched or crosslinked molecules require more complicated models. Our simultaneous show that long-chain branches have considerable influence on thedistribution of the molecular weights 322 (1 978). [2] K . Freudmberg, W Kuhn, W Diirr, F. Bolz, G . Steinhrunn, Ber. Dtsch. Chem. Ges. 63, 1510 (1930). [3] K . H . Eberr, M. Brosche, Biopolymers 5 , 423 (1967). [4] K . H . Eberr, G . Schenk, Adv. Enzymol. 30, 179 (1968). [ 5 ] K . Frombling, F. Patot, Makromol. Chem. 25, 41 (1957). 161 0. Larm, 8.Lmdbery, S. Szensson, Carbohydr. Res. 20, 39 (1971). tvans-Bis(l-alkynyl)-4B-metalPhthalocyanines[**l By Michael Hanack, Konrad Mitulla, Georg Pawlowski, and L. R. Subramanian[*I Dedicated to Professor Horst Pommer on the occasion of his 60th birthday Monomeric phthalocyanine derivatives of type ( 3 ) of elements of the 4th main group having two axial metal-carbon bonds are model substances for new polymer structures, which according to EHMO calculations ought to show pronounced electrical conductivity“]. Octahedral silicon phthalocyanines having one axial Si-C bond have already been reported[’]; and the tin phthalocyanine ( 3 ) , R = C6H5,has been synthesized, but only in 1% yieldc3]. Analogous meso-tetraphenylporphyrins were recently described14! We obtained trans-bis(1 -alkynyl)-4B-metal phthalocyanines ( 3 ) in yields of about 90 % by reaction of the corresponding [*] Prof. Dr. M. Hanack, Dip1.-Chem. K. Mitulla, DipLChem. G. Pawlowski, Dr. L. R. Subramanian Institut fur Organische Chemie der Universitat Auf der Morgenstelle 18, D-7400 Tubingen 1 (Germany) Part 3 of The Synthesis and Properties of Novel One-Dimensional Conductors.-Parts I and 2: [l]. [**I Angew. Chem. Int. Ed. Enyl. 18 (1979) No. 4 0 Verlag Chemie, GmbH, 6940 Weinlreim, 1979 0570-0833/79/0404-0322 $ 02.SOjO

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