Finite extensibility and orientational effects in rubbers. A physical interpretation of the ‘van der Waals equation’ for the elastic force

Vilgis, T. A.

doi:10.1007/bf01418188

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…The reason can be illustrated in the framework of the primitive path model, which provides a good description of the physics of a highly entangled network system. [5][6][7] Within this model, the primitive path is defined by entanglement points in the system and, instead of the contour length of a chain between crosslinks, the maximum extension of a chain, a max , is determined by the step length of the primitive path (corresponding to the distance between two successive entanglement points). Since this new-introduced step length is much smaller than the contour length in the highly entangled limit, a max will be decreased largely, which leads to the more importance of the finite-extensibility correction for this system.…”

Section: Resultsmentioning

confidence: 99%

Effect of Finite Extensibility on the Equilibrium Chain Size

Miao

Vilgis

Poggendorf

et al. 2010

Macro Theory & Simulations

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We investigate the finite‐extensibility effect on the equilibrium size of a single polymer chain by using a Flory‐type calculation. The finite extensibility of the chain is effectively taken into account by modifying the Gaussian stretching energy to a non‐Gaussian form which recovers the harmonic spring behavior in the limit of weak stretch and diverges when the chain extension approaches the total contour length. In general, the finite extensibility decreases the equilibrium size of the chain compared to that obtained from Flory's classic theory, due to a steeper free energy or effective potential of the chain generated by the finite‐extensibility effect. It is illustrated clearly that, for a chain with a short contour length and/or with strong repulsions between monomers, the finite‐extensibility correction is important and necessary to be taken into account. A typical system where the finite extensibility plays an important role is suggested to be the highly charged and highly crosslinked hydrogel.magnified image

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Section: Resultsmentioning

confidence: 99%

Effect of Finite Extensibility on the Equilibrium Chain Size

Miao

Vilgis

Poggendorf

et al. 2010

Macro Theory & Simulations

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“…It would be worthwhile to note here, for network systems like rubbers or hydrogels, the entanglement effect of the system will enhance further the necessity of the finite‐extensibility correction. The reason can be illustrated in the framework of the primitive path model, which provides a good description of the physics of a highly entangled network system 5–7. Within this model, the primitive path is defined by entanglement points in the system and, instead of the contour length of a chain between crosslinks, the maximum extension of a chain, $\alpha _{{\rm max}} $ , is determined by the step length of the primitive path (corresponding to the distance between two successive entanglement points).…”

Section: Resultsmentioning

confidence: 99%

“…From the point of view of statistical mechanics, the finite extensibility introduces a constraint on the phase space of the polymer system under consideration, by which those microstates with the end‐to‐end distance of the chain beyond the total contour length are excluded from the partition function. Therefore, the finite extensibility would generate many important effects on both static and dynamic properties of the polymer system 3–11…”

Section: Introductionmentioning

confidence: 99%

“…Among the theoretical developments of accounting for the finite‐extensibility effect of a polymer system, Vilgis and coworkers3–7 considered the finite‐extensibility effect in the context of the rubber elasticity theory for both the dilute limit and the highly entangled limit of the system in the framework of the so‐called van der Waals network model, where the finite extensibility of a chain was treated in a similar way as the finite volume of a molecule enters the van der Waals equation for gases. This treatment then went beyond the Gaussian elasticity theory of rubbers and a better fitting between experiments and theories was obtained, especially for the highly crosslinked and/or the highly entangled rubbers.…”

Section: Introductionmentioning

confidence: 99%

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Use of disposable reactors to generate inoculum cultures for E. coli production fermentations

Mahajan¹,

Matthews²,

Hamilton³

et al. 2010

Biotechnology Progress

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Disposable technology is being used more each year in the biotechnology industry. Disposable bioreactors allow one to avoid expenses associated with cleaning, assembly and operations, as well as equipment validation. The WAVE bioreactor is well established for Chinese Hamster Ovary (CHO) production, however, it has not yet been thoroughly tested for E. coli production because of the high oxygen demand and temperature maintenance requirements of that platform. The objective of this study is to establish a robust process to generate inoculum for E. coli production fermentations in a WAVE bioreactor. We opted not to evaluate the WAVE system for production cultures because of the high cell densities required in our current E. coli production processes. Instead, the WAVE bioreactor 20/50 system was evaluated at laboratory scale (10-L) to generate inoculum with target optical densities (OD(550)) of 15 within 7-9 h (pre-established target for stainless steel fermentors). The maximum settings for rock rate (40 rpm) and angle (10.5) were used to maximize mass transfer. The gas feed was also supplemented with additional oxygen to meet the high respiratory demand of the culture. The results showed that the growth profiles for the inoculum cultures were similar to those obtained from conventional stainless steel fermentors. These inoculum cultures were subsequently inoculated into 10-L working volume stainless steel fermentors to evaluate the inocula performance of two different production systems during recombinant protein production. The results of these production cultures using WAVE inocula showed that the growth and recombinant protein production was comparable to the control data set. Furthermore, an economic analysis showed that the WAVE system would require less capital investment for installation and operating expenses would be less than traditional stainless steel systems.

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“…Other problems include entanglements and the interpenetration of chains and junctions in a "real network". These excluded volume effects affect the fluctuations of the junctions [4] and constrain the chains [15].…”

Section: Introductionmentioning

confidence: 99%

The influence of finite extensibility of the chains on the orientation behaviour of a polymer network

Dietrich

Ortmann

Bonart

1988

Colloid & Polymer Sci

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The chains of a deformed polymer network can only be extended up to their contour length L. In this work, it is assumed that the chain vector initially undergoes an affine deformation, and then subsequently a pseudo-affi_ne rod orientation as soon as it is fully extended. The density distribution of the chain vectors Z for r < L is approximated by an affinely deforming Gaussian distribution. We calculate the proportion of fully extended chains, their orientation distribution, the Hermans' orientation factor of the segments for both the fully extended and the partially extended chains, and the strain birefringence for this phantom network model. We take into account that the lack of further extension of the fully extended chains results in an excess strain in the partially extended network chains. This leads to non-affine orientation behaviour, and relates the finite extensibility of the chains to the finite elasticity of the network.

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Finite extensibility and orientational effects in rubbers. A physical interpretation of the ‘van der Waals equation’ for the elastic force

Cited by 10 publications

References 13 publications

Effect of Finite Extensibility on the Equilibrium Chain Size

Effect of Finite Extensibility on the Equilibrium Chain Size

Use of disposable reactors to generate inoculum cultures for E. coli production fermentations

The influence of finite extensibility of the chains on the orientation behaviour of a polymer network

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