Stiff-Chain Behavior of Poly(isophthaloyl-trans-2,5-dimethylpiperazine) in Dilute Solution

Abstract

ABSTRACT:For narrow-distribution fractions of poly(isophthaloyl-trans-2,5-dimethylpiperazine) (PIDP) with weight-average molecular weights M w from 3. 7 x I 0 3 to 2.4 x 10 6 g mol-1 , z-average mean-square radii of gyration (S 2 ), and intrinsic viscosities ['1] in trifluoroethanol (TFE) and m-cresol were measured at 25oC. From the ['1] data for Mw<l0 5 gmol-1 , which exhibited the expected stiff-chain behavior, the persistence lengths of PIDP in m-cresol and TFE were determined to be 4.9±0.3 nm and 3.1 ±0.2nm, respectively, using YamakawaFujii's theory for unperturbed wormlike cylinders and assuming the ML and d values estimated previously by Motowoka et a/. for poly(phthaloyl-trans-2,5-dimethylpiperazine) and poly-(terephthaloyl-trans-2,5-dimethylpiperazine) in various solvents including m-cresol and TFE. Here ML is the molar mass per unit contour length and dis the diameter of the cylinder. Doublelogarithmic plots of (S 2 )! 12 and ['1] against Mw in the region of higher Mw exhibited features usually observed with flexible polymers in good solvents. This result can be explained by the fact that, though semiflexible, the PIDP chain in solution suffers excluded-volume effects if its length exceeds a certain value. In terms of the number of Kuhn's statistical segments, this critical chain length for PIDP is about 50 in TFE and !50 in m-cresol.KEY WORDS Poly(isophthaloyl-trans-2,5-dimethylpiperazine) I Wormlike Chain I Persistence Length I Dilute Solution I Light Scattering I MeanSquare Radius of Gyration I Intrinsic Viscosity I Excluded-Volume Effect I Expansion Factor I Motowoka et a/. 1 • 2 concluded from measurements of dilute solution properties that poI y(p h thaloy 1-trans-2, 5 -dimethy I piperazine) (PPDP) and poly(terephthaloyl-trans-2,5-dimethylpiperazine) (PTDP), two of the three polyamide isomers shown in Figure I, behave like an unperturbed wormlike chain in solution and that PTDP is 1.5 times as stiff as PPDP if the stiffness is expressed in terms of the persistence length. To estimate the persistence length of the remaining one of the three isomers, i.e., the meta-linked poly(isophthaloyltrans-2,5-dimethylpiperazine) (PIDP), we measured z-average mean-square radii of gyration (S 2 )z and intrinsic viscosities [ry] of narrow-distribution samples of this polymer over a range of weightaverage molecular weight Mw from 3.7 x 10 3 to 2.4 x 10 6 g mol-1 • This maximum M w was several times as large as any one of those treated in Motowoka's studies on PPDP 1 and PTDP. 2 Except at relatively low Mw, the data exhibited features usually observed for long flexible polymers in good solvents. In this paper, we report these experimental results and consider their significance in the study of semiflexible polymers in dilute solution. EXPERIMENTAL SamplesHigh-molecular-weight samples of PIDP were prepared by interfacial polycondensation of isophthaloyl chloride and trans-2,5-dimethylpiperazine, according to the method of Katz. 3 The isophthaloyl chloride was recrystallized from hexane; and the trans-2,5-dimethy...

New method for estimating the parameters of the wormlike chain model from the intrinsic viscosity of stiff-chain polymers

“…Despite this discrepancy, the values of ((Rq)/M)" give evidence of pronounced solvent effects on the chain conformation and confirm the effect of the structure of the phthalic acid isomers (cf. ref 36). The values of ML and d estimated by means of eq 24 for PTDP are in good correspondence with those reported by Motowoka et al 35 and with those estimated, in a different way, by Yamakawa and Yoshizaki.37 For PPDP, the agreement with the results in ref 37 is very good but is less good with those in ref 17. As follows from eq 24, the value of ML calculated from A" depends to some extent on the value of 0 ".…”

Stiff-Chain Nature of Poly(1-phenyl-1-propyne) in Dilute Solution

“…4 • 5 Nagai 15 was the first present a theory for the optical anisotropy factor of a wormlike chain with cylindrical symmetry. For relatively flexible wormlike chains, his expression can be written (6) where £ is defined by (7) with a 1 and a 2 being respectively the lon- in Figure 9, which reproduces the inverse proportionality predicted by the leading term of eq 6 with reasonable accuracy; we note that the O(qML/M) term in eq 6 does not exceed 0.012 in the Mw range studied. The values of I£ I are estimated to be 2.1 and 2.4 for cyclohexane and toluene, respectively.…”

Chain stiffness and excluded-volume effects in dilute polymer solutions. Poly(isophthaloyl-trans-2,5-dimethylpiperazine)

“…From eq 12 with (S2)0" = qM/3ML, we have (S2)/M = 1.53( /3 )(3/2 )3/5 2/5( /29 ,)1/6 z -*• «> (13) which predicts that, in the asymptotic limit (nK, z -°°), (S2)/M varies in proportion to M1/5. Figure 9 shows our (S2)z data for Mw above 5 X 104 to bear out the predicted linearity.…”

“…Sedimentation Equilibrium. Weight-average molecular weights of five fractions, f-l, f-2, ..., f-5, were determined by sedimentation equilibrium in a Spinco Model E ultracentrifuge, with NMP at 25 °C as the solvent (see ref 13 for the experimental details). Ratios of Mz (the 2-average molecular weight) to Mw were also estimated by the method17 described elsewhere.…”