Regularly alternating poly(amideimide)s containing pendent pentadecyl chains: Synthesis and characterization

Two new aromatic diamines containing preformed amide linkages, viz., N,N′-(4-pentadecyl-1,3-phenylene)bis(4-aminobenzamide) I and N,N′-(4-pentadecyl-1,3-phenylene)bis(3-aminobenzamide) II, were synthesized by reaction of 4-pentadecylbenzene-1,3-diamine with 4-nitrobenzoylchloride and 3-nitrobenzoylchloride, followed by reduction of the respective dinitro derivatives. A series of new poly(amideimide)s was synthesized by polycondensation of I and II with four commercially available aromatic dianhydrides, viz., pyromellitic dianhydride (PMDA), 4,4′-biphenyltetracarboxylic dianhydride (BPDA), 4,4′-oxydiphthalic anhydride (ODPA), and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6-FDA) in N,N-dimethylacetamide (DMAc) employing conventional two step method via poly(amic acid) intermediate followed by thermal imidization. Reference poly(amideimide)s were synthesized by polycondensation of N,N′-(1,3-phenylene)bis(4-aminobenzamide) and N,N′-(1,3-phenylene)bis(3-aminobenzamide) with the same aromatic dianhydrides. Inherent viscosities of poly(amideimide)s containing pendent pentadecyl chains were in the range 0.37-1.23 dL/g in N,N-dimethylacetamide at 30 ± 0.1 °C indicating the formation of medium to high molecular weight polymers. The poly(amideimide)s containing pendent pentadecyl chains were found to be soluble in N,N-dimethylacetamide, N,N-dimethylformamide, 1-methyl-2-pyrrolidinone and pyridine and could be cast into transparent, flexible and tough films from their N,N-dimethylacetamide solution. Wide angle X-ray diffraction patterns exhibited broad halo indicating that the polymers were essentially amorphous in nature. X-ray diffractograms also displayed sharp reflection in the small angle region (2θ ≈ 3°) for poly(amideimide)s containing pentadecyl chains indicating the formation of layered structure arising from packing of flexible pentadecyl chains. The glass transition temperatures observed for reference poly(amideimide)s were in the range 331-275 °C and those for poly(amideimide)s containing pendent pentadecyl chains were in the range 185-286 °C indicating a large drop in T_g owing to the “internal plasticization” effect of pentadecyl chains. The temperature at 10% weight loss (T₁₀), determined by TGA in nitrogen atmosphere, were in the range 460-480 °C indicating their good thermal stability.     

Flip-flop between soft-spring and hard-spring bistabilities in the approximated Toda oscillator analysis

We study theoretically the effect of truncating the nonlinear restoring force (exp(F)-1=?_n=1^￥Fⁿ/n!\exp (\Phi)-1={\sum}_{n=1}^{\infty}\Phi^{n}/n!) in the bistability pattern of the periodically driven, damped one-degree-of-freedom Toda oscillator that originally exhibits soft-spring bistability with counterclockwise hysteresis cycle. We observe that if the truncation is made third order, the harmonic bistability changes to hard-spring type with a clockwise hysteresis cycle. In contrast, for the fourth-order truncation, the bistability again becomes soft-spring type, overriding the effect of third-order nonlinearity. Furthermore, each higher odd-order truncation attempts to introduce hard-spring nature while each even-order truncation turns to soft-spring type of bistability. Overall, the hard-spring effect of every odd-order nonlinear term is weaker in comparison to the soft-spring effect of the next even-order nonlinear term. As a consequence, higher-order approximations ultimately converge to the soft-spring nature. Similar approximate analysis of Toda lattice has in recent past revealed remarkably similar flip-flop pattern between stochasticity (chaotic behaviour) and regularity (integrability).