Theoretical Model of Polymer Network Chain Formation under Strain

Yong Yu; Shunping Yan; Ye Fang; Qinshu He; Huyi Wang; Yong Qiu; Qiang Wan

doi:10.1021/acsomega.8b01748

Effect of Adsorption on Reinforcement of Filled Polyurethane

Rubber Chemistry and Technology ◽

10.5254/1.3535147 ◽

1977 ◽

Vol 50 (2) ◽

pp. 333-341 ◽

Cited By ~ 10

Author(s):

J. Seto

Keyword(s):

Glass Transition ◽

Transition Temperature ◽

Glass Transition Temperature ◽

Physical Adsorption ◽

Random Coil ◽

Chain Formation ◽

Network Chain ◽

Effective Network

Abstract The effective network chains, ns formed at the polyurethane-particle interface are brought about by physical adsorption of the polymer from solution. The relation between ns and adsorption, Γs, is given as Equation (3). The coefficient K is evaluated as 10. This value supports multicontact adsorption and agrees with random coil dimensions. The pretreating of powder by a surfactant (oleate) brings about neither adsorption nor network chain formation. The glass transition temperature increases with increasing amount of adsorption.

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Thermoelasticity

Structures and Properties of Rubberlike Networks ◽

10.1093/oso/9780195082371.003.0011 ◽

1997 ◽

Author(s):

Burak Erman ◽

James E. Mark

Keyword(s):

Equation Of State ◽

Elastic Deformation ◽

Additional Assumption ◽

Polymer Network ◽

Ideal Gas ◽

Absolute Temperature ◽

Constant Volume ◽

Conformational Energy ◽

Network Chain ◽

Constant Deformation

The important postulate that intermolecular interactions are independent of extent of deformation leads directly to the conclusion that such interactions cannot contribute to an energy of elastic deformation ΔEel at constant volume. In the earliest theories of rubberlike elasticity, it was additionally assumed that, intramolecular contributions to ΔEel were likewise nil. In this idealization that the total ΔEel is zero, the elastic retractive force exhibited by a deformed polymer network would be entirely entropic in origin. At the molecular level, this would correspond, of course, to assuming all configurations of a network chain to be of exactly the same conformational energy and thus the average configuration to be independent of temperature. Under these circumstances, the dependence of stress on temperature is strikingly simple, as shown, for example, by the equation . . . f* = υkT/V (〈r2〉i/〈r2〉0)(α – α-2) . . . . . . (9.1) . . . that characterizes a polymer network in elongation where, it should be recalled, 〈r2〉i3/2 is proportional to the volume of the network. This additional assumption that 〈r2〉0 is independent of temperature would lead to the prediction that the elastic stress determined at constant volume and elongation α is directly proportional to the absolute temperature. Such network chains would be akin to the particles of an ideal gas, which would obey the equation of state p = nRT(1/V) and thus exhibit a pressure at constant deformation (1/V) likewise directly proportional to the temperature.

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Hysteresis Contributions in Carbon Black-Filled Rubbers Containing Conventional and Tin End-Modified Polymers

Rubber Chemistry and Technology ◽

10.5254/1.3538495 ◽

1998 ◽

Vol 71 (4) ◽

pp. 637-667 ◽

Cited By ~ 13

Author(s):

J. D. Ulmer ◽

W. L. Hergenrother ◽

D. F. Lawson

Keyword(s):

Carbon Black ◽

Loss Modulus ◽

Average Molecular Weight ◽

Polymer Network ◽

Linear Polymers ◽

Network Chain ◽

Modified Polymers ◽

Rubber Compounds ◽

Effective Network ◽

Tan Δ

Abstract A methodology was developed to estimate individual hysteresis contributions arising from the carbon black network, polymer free chain ends and effective polymer network chains. The estimation technique was applied to rubber compounds formulated with linear polymers of varied number-average molecular weight (Mn) from each of three different series. The three series corresponded to polymers modified with either zero, one or two tin ends per chain. In general, the relative hysteresis contributions depend on strain amplitude and Mn. For unmodified polymers at strain amplitudes from 0.02 to 0.07, and with Mn in the neighborhood of 150 kg/mole, each of the three hysteresis sources contributes about one-third of the total tan δ. With respect to shear loss modulus (G″), the carbon black network contributes about 60%, while free chain ends and the effective polymer network chains each contribute about 20%. At the same Mn and strain conditions, tin end-modified polymers reduce G″ and tan δ by as much as 60%, in comparison to their unmodified counterparts. The benefit is achieved primarily through reductions of up to 85% in the carbon black network contribution to hysteresis. Since the hysteresis contribution from free chain ends is not reduced so much by tin end-modification, the greatest potential for additional tan δ benefits lies in further free chain end reduction. In addition, it was found that tin end-modification has no measurable effect on the hysteresis contribution from effective network chains. Further, the analysis showed that an ineffective polymer network chain provides approximately ten times the hysteresis and one-half the elasticity of an effective network chain, at the test conditions of the current study. In general, the quantitative results, and some qualitative results as well, will change with compound composition and with temperature. Consequently, the development of a methodology, one that allows estimation of individual hysteresis contributions from different sources, is a major component of the present study.

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Assignment of Effective Network Chains in Cured Rubbers Derived from Chemical Crosslinking, Entanglements, Polymer End Linking to Carbon Black and Filler Interaction: VII. Tensile Retraction Measurements

Rubber Chemistry and Technology ◽

10.5254/1.3547941 ◽

2006 ◽

Vol 79 (2) ◽

pp. 338-365

Author(s):

William L. Hergenrother ◽

J. D. Ulmer ◽

Christopher G. Robertson

Keyword(s):

Carbon Black ◽

Volume Fraction ◽

Polymer Network ◽

Polymer Chains ◽

Network Chain ◽

End Groups ◽

Individual Contributions ◽

Cross Links ◽

Effective Network ◽

The Individual

Abstract The individual contributions to effective network chains from chemical cross-links and from trapped polymer chain entanglements were estimated for gum rubber compounds using Tensile Retraction (TR). In addition, the influences of carbon black and of polymers with functional end-groups, on the character of the polymer network in filled compounds were explored. The effective network chain contributions were established for gum vulcanizates through an entanglement model and an independent estimate of the polymer molecular weight between entanglements, Me. It was found that Me was related closely to the extrapolated γ intercepts obtained from the TR of cured gums. The gum compounds were used to further estimate the effects of fillers and functional end-groups on the total number of effective network chains. Comparing an α,ω-difunctional SBR with its non-functional counterpart enabled the assessment of the effects of functional end-groups. The comparison allowed for the determination of the probability, π, that a functional end group reacts with carbon black. The π was seen to increase as the volume fraction of filler increased, and π2 provided an estimate of the fraction of functional polymer chains that react with carbon black at both ends.

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Freeze-etch TEM of aqueous polymer gel network morphology

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100145327 ◽

1986 ◽

Vol 44 ◽

pp. 796-797

Author(s):

J. A. N. Zasadzinski ◽

R. K. Prud'homme

Keyword(s):

Metal Ion ◽

Polymer Network ◽

Polymer Gels ◽

Polymer Gel ◽

Deformation History ◽

Crosslinked Polymer ◽

Aqueous Polymer ◽

History Of ◽

Gel Network ◽

Network Morphology

The rheological and mechanical properties of crosslinked polymer gels arise from the structure of the gel network. In turn, the structure of the gel network results from: thermodynamically determined interactions between the polymer chain segments, the interactions of the crosslinking metal ion with the polymer, and the deformation history of the network. Interpretations of mechanical and rheological measurements on polymer gels invariably begin with a conceptual model of,the microstructure of the gel network derived from polymer kinetic theory. In the present work, we use freeze-etch replication TEM to image the polymer network morphology of titanium crosslinked hydroxypropyl guars in an attempt to directly relate macroscopic phenomena with network structure.

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A theoretical model for understanding dentists' behavior in treating patients with AIDS

Journal of Dental Education ◽

10.1002/j.0022-0337.1991.55.11.tb02589.x ◽

1991 ◽

Vol 55 (11) ◽

pp. 708-716 ◽

Cited By ~ 1

Author(s):

MS Chen

Keyword(s):

Theoretical Model

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A Model for Analyzing Suicide Prevention

Crisis ◽

10.1027//0227-5910.21.2.80 ◽

2000 ◽

Vol 21 (2) ◽

pp. 80-89 ◽

Cited By ~ 3

Author(s):

Maila Upanne

Keyword(s):

Risk Factors ◽

Theoretical Model ◽

Protective Factors ◽

Suicide Prevention ◽

Suicide Risk ◽

Practical Work ◽

Individual Risk ◽

Self Assessment ◽

Prevention Project ◽

Individual Risk Factors

This study monitored the evolution of psychologists' (n = 31) conceptions of suicide prevention over the 9-year course of the National Suicide Prevention Project in Finland and assessed the feasibility of the theoretical model for analyzing suicide prevention developed in earlier studies [ Upanne, 1999a , b ]. The study was formulated as a retrospective self-assessment where participants compared their earlier descriptions of suicide prevention with their current views. The changes in conceptions were analyzed and interpreted using both the model and the explanations given by the subjects themselves. The analysis proved the model to be a useful framework for revealing the essential features of prevention. The results showed that the freely-formulated ideas on prevention were more comprehensive than those evolved in practical work. Compared to the earlier findings, the conceptions among the group had shifted toward emphasizing a curative approach and the significance of individual risk factors. In particular, greater priority was focused on the acute suicide risk phase as a preventive target. Nonetheless, the overall structure of prevention ideology remained comprehensive and multifactorial, stressing multistage influencing. Promotive aims (protective factors) also remained part of the prevention paradigm. Practical working experiences enhanced the psychologists' sense of the difficulties of suicide prevention as well as their criticism and feeling of powerlessness.

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