Elastically Ineffective Cross-Links in Rubbers

Tonelli, Alan E.; Helfand, Eugene

doi:10.1021/ma60037a012

Cited by 42 publications

(35 citation statements)

References 2 publications

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“…These structures hardly contribute to an increase in G′. [14][15][16] The viscous modulus G′′, on the other hand, is a measure of energy dissipation per cycle of sinusoidal deformation 13 and represents the viscous behavior of the system under investigation. The viscosity is known to be sensitive to the molecular weight of polymer chains.…”

Section: Resultsmentioning

confidence: 99%

Inulin hydrogels as carriers for colonic drug targeting. Rheological characterization of the hydrogel formation and the hydrogel network

Vervoort

Vinckier

Moldenaers

et al. 1999

Journal of Pharmaceutical Sciences

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Free radical polymerization converts aqueous solutions of methacrylated inulin into cross-linked hydrogels. The purpose of this work was to study the hydrogel formation and to characterize the fully cured hydrogels. The gelation process of aqueous solutions of methacrylated inulin was monitored as a function of time by means of linear oscillatory shear measurements, at a fixed frequency and amplitude. The fully cured inulin hydrogels were characterized by measurement of the frequency-dependency of the linear elastic modulus G'. The effects of the degree of substitution and feed concentration of methacrylated inulin on both the gelation kinetics and the rigidity of the obtained hydrogels were determined. The effect of the concentration of the initiators of the radical polymerization reaction has been studied as well. The weight fraction of polymer which was not incorporated in the hydrogel networks was determined using the anthrone reaction, and physical chain entanglements were determined by solution viscosity measurements. The gelation kinetics and the elastic modulus were proportional to the degree of substitution and feed concentration of methacrylated inulin. Increasing concentrations of radical-forming compounds also accelerated the hydrogel formation, but lowered the elastic modulus of the obtained hydrogels. The amount of polymer chains incorporated in the hydrogel network seemed to be especially influenced by the degree of substitution of the derivatized inulin, and for a feed concentration of 27% w/w of methacrylated inulin, entanglements have to be accounted for. The gelation kinetics and the elastic modulus of inulin hydrogels are not only affected by the degree of substitution and the feed concentration of methacrylated inulin, but also by the concentration of the initiators of the free radical polymerization reaction.

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Section: Resultsmentioning

confidence: 99%

Inulin hydrogels as carriers for colonic drug targeting. Rheological characterization of the hydrogel formation and the hydrogel network

Vervoort

Vinckier

Moldenaers

et al. 1999

Journal of Pharmaceutical Sciences

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“…In ref 2 we document the case that short loops, let us say ten or less units, make .the major contribution to p1 and 0 2 . However, the added factor of k in eq 8 for a L has a profound effect in shifting weight to longer loops.…”

Section: (5)mentioning

confidence: 98%

“…It was this fraction, f, which was calculated in the previous paper. 2 In total, the fraction q of units involved in elastically effective cross-links is the sum of (i) the units with nonsterile intermolecular cross-links, and (ii) the units with intramolecular cross-links that are not elastically ineffective Let us consider that a cross-link can occur between a unit located a t what we will designate the origin and another unit a distance L away ( Figure 4). L is a characteristic of the type of cross-linking bridge used; we present results below for L = 6 h;.…”

Section: Theorymentioning

confidence: 99%

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Elastically Ineffective Polymer Chains in Rubbers

Helfand¹,

Tonelli²

1974

Macromolecules

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Chain ends and certain intramolecular loops in a rubber are not elastically effective, because they are tied to the network at only one point. An estimate is made of the fraction of the polymer contained in such defect portions of the rubber. Also some minor improvements are made on our previous calculation of the number of cross-links which close elastically ineffective loops.In a rubber, cross-links tie together macromolecules into a network, resulting in a group of chains which bear the stress ( i e . , have increased free energy) when the network is strained. There occur in the network two types of defects. By this we mean parts of polymer chains which are capable of relaxing when strained and so do not contribute to equilibrium elasticity. One example, chain ends (cf. Figure I), was first discussed by Floryl in 1944. In that paper he alluded to another type of defect, intramolecular loops (Figure 2). Both end and loop defects are elastically ineffective by virtue of being tied to the network by only one crosslink (the sol has no links to the network). In Figure 3 we see that some intramolecular loops can be elastically effective, viz., those loops which have another elastically effective cross-link along their length. We have not been completely rigorous about such pairs of cross-links, but we believe our estimates to be very good in most cases.In our previous report2 an estimate was provided of the fraction of cross-links which closed elastically ineffective loops. The present calculation is aimed a t determining the fraction of polymer contained in these loops. Results are also presented for the fraction of polymer in chain ends. In this paper, too, the effect of chain ends is treated in the manner of Scanlan3 rather than F1ory.lThe earlier work contained an indication that short loops make an important contribution to the total number of elastically ineffective loops which form. This can be attributed to the fact that short polymer chains have a greater probability of returning to the neighborhood of the origin and also that longer chains have an increased chance of containing elastically effective cross-links along their length. The contribution of longer loops we shall find not to be negligible, however.To summarize the results in general terms, let us say: (i) the number of cross-links closing elastically ineffective intramolecular loops is a small but nonnegligible fraction for dry state curing and quite a large fraction for curing in a 10% rubber solution; (ii) the effect of this wastage of crosslinks is most notable in the amount of polymer contained in chain ends; and (iii) the fraction of polymer contained in the loops is quite small except for the case of solution curing.We have previously2 speculated that the elastically ineffective portion of the polymer acts like a diluent in decreasing the Mooney-Rivlin deviations from ideal elastic behavior, even when all solvent has been removed. These calculations make clear how much unstrained rubber is present to serve in this manner. TheoryThe basic con...

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“…Here A and B are the terminal vectors specifying the states of the terminal units defined by A=(auM,;Up,;) B=( ~) (4) where a and b measure the relative preference of the right-handed helix in the first and final monomer units, respectively. The average number nM of monomer units in the right-handed helical conformation is calculated from…”

Section: Theorymentioning

confidence: 99%

Molecular Mechanisms for the Optical Activities of Polyisocyanates Induced by Intramolecular Chiral Perturbations

Sato

Teŕamoto

et al. 1997

Polym J

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ABSTRACT:Molecular mechanisms were proposed to account for extraordinary optical activities of polyisocyanates containing chiral moieties (chiral monomer or initiator fragment) reported by Green et al. and by Okamoto et al., where the polyisocyanate molecule was modeled by a helical chain consisting of an alternating sequence of right-handed and left-handed helices with helix reversals in between. Theoretical predictions based on this model were consistent with remarkable dependence of optical rotation on monomer composition for random copolyisocyanates of chiral and achiral monomers and enantiomorphous copolymers and chain length dependence of optical rotation for achiral polyisocyanates with a chiral initiator fragment on the chain end. The helix reversal was shown to be the key factor for all the cases and more frequent for aromatic sidechain polymer poly(m-methyl phenyl isocyanate) than for aliphatic side chain polymers such as poly(butyl and hexyl isocyanate)s.KEY WORDS Chiral / Optical Activity / Polyisocyanate / Helical Conformation / Helix Reversal / Statistical Mechanics / Copolymer / Amide bonds of partial double-bond nature in a polyisocyanate chain tend to be coplanar, but they are distorted in a helical conformation due to steric interactions between the main chain and side chains. 1 -1° For this reason the global conformation of the polymer chain is well modeled by wormlike chains. 7 -9 • 11 -18 However the sense of the helix is not determined for an achiral polyisocyanate because both the right-handed and lefthanded helices are symmetric. This symmetry is broken by a subtle chiral perturbation within a given molecule and this molecule becomes optical active. [19][20][21][22][23][24][25] showed that incorporation of a very small amount of chiral monomers into an achiral polyisocyanate in a random fashion gives rise to remarkable optical activity, which increases disproportionately with the mole fraction of chiral monomer. A similar disproportionate change in optical activity has been found in copolymers of enantiomorphous isocyanates (R-S copolymers). 25 On the other hand Okamoto and collaborators 26 • 27 introduced a chiral perturbation into polyisocyanate chains in a different way; they synthesized polyisocyanates with chiral initiators, which were attached to a chain end, and showed that those polyisocyanates exhibited optical activity changing remarkably with length and temperature. The present study was motivated by these findings and tries to explore the molecular mechanisms behind the optical activities in these particular polymers. Green et al. 20 called chiral entities sergeants and achiral entities soldiers. Thus we here deal with sergeants-soldiers polymers. Theoretically these polyisocyanates are regarded as typical linear cooperative systems just as chiral polyisocyanates and a-helical polypeptides. Therefore we analyze their conformational properties including optical activity by the well-established statistical mechanical procedures based on the matrix method. 28 -30 A preliminary...

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Elastically Ineffective Cross-Links in Rubbers

Cited by 42 publications

References 2 publications

Inulin hydrogels as carriers for colonic drug targeting. Rheological characterization of the hydrogel formation and the hydrogel network

Inulin hydrogels as carriers for colonic drug targeting. Rheological characterization of the hydrogel formation and the hydrogel network

Elastically Ineffective Polymer Chains in Rubbers

Molecular Mechanisms for the Optical Activities of Polyisocyanates Induced by Intramolecular Chiral Perturbations

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