Talk:Rubber elasticity

— Preceding unsigned comment added by Davidhanson471 (talk • contribs) 03:53, 3 December 2019 (UTC)

Arithmetic Problems

  This comment pertains to an early version of the article.  The text that it refers to is now in section 'Historical approaches to elasticity theory'.Davidhanson471 (talk) 03:14, 18 December 2019 (UTC)  

   This treatment suffers the difficulty of disagreeing with observation, namely that force (at constant temperature) =(Const)x r cannot change sign, as r, the end-to-end distance cannot be <0, while in practice rubbers are often strained in (linear) compression as well as in extension--e.g., tire treads, shoe soles, shock mounts.  The difficulty is not in the model but in the arithmetic.
   
  The treatment is based on an expression for the probability that the chain ends are r units apart as a function of r.  Apart from notation this expression is the same as Eq. 3.9 in Ref. 4 (Treloar, "The Physics of Rubber Elasticity")(where it I given as P(r), not P(r,n), as n is a constant).  Differentiation shows the expression to have a maximum (most probable value) at r = √(2nb2/3)--see Ref 4, Eq. 3.10 and Fig. 3.5(b).   As entropy S≃lnP, S likewise would have a maximum at the same value of r; and as force F≃-dS/dr, F will accordingly be positive or negative as r is greater than (extension) or less than (compression) its most probable value, as is observed in practice (Ref. 4, Fig. 5.6).

  In the wiki article, when ln(P(r,n)dr) is substituted for S, only the exponential factor is carried over; the quadratic factor, which would constitute a 2ln(r) term is dropped.  Inclusion of the entire expression would lead to the appropriate maximum in S and a F(r) function similar to Ref. 4, Fig. 5.6, in agreement with experiment.

  Although ref. 4, Fig. 3.5(b) shows the maximum of P, and hence S, and hence +&- F as in Fig. 5.6,  it comes up with (Eq. 3.22) essentially the same force expression as the wiki article and which likewise cannot change sign.  This seems to result from substituting an expression for the rectangular-coordinate volume element, dτ(=dxdydz) for the spherical-coordinate volume element (cf. Fig. 3.6) and regarding it as a constant; this drops the 2ln(r) term from the entropy expression (Eqs. 3.18 and 3.19), just as the wiki article did.
  Ref. 4 observe that its "result (3.19) shows the entropy to have its maximum value when the two ends of the chain are coincident (r=0)...".  Eq. 3.9 shows P(0) = 0, which would have the probability of the maximum entropy conformation to be zero.  This unlikely event, as well as the disagreement with observation, can be avoided by keeping track of the terms.

Debosley (talk) 21:10, 29 May 2014 (UTC)

Serious problems with this page:

I applaud the effort of D Hanson in updating this page with modern modeling. The problems I see are

1) lack of balance ... apparently Hanson's work is the only work that is not merely historical. References are to him, or before 1950. Really? Nobody else at all?

2) No distinction between general truths of rubber elasticity and the details found by Hanson for polyisoprene; e.g. no discussion of the ideal rubber

3) A serious error in that dealing with polyisoprene (?cis 1-4 ? it is not clear) the word 'crystal' never appears. It is generally agreed that the turn upwards in the stress-strain curve for this material at high strain and room temperature is caused by strain induced crystallization (SIC). In this article (and Hanson's papers) it is said to be caused by elastic deformation of the chain. This would happen in materials that do not crystallize but they generally fail before getting into this regime. It is commonplace that molecular modeling does not capture crystallization in temperature regimes where it is experimentally seen; the space and time limitations of even modern computers do not include the nucleation events. But this does not mean it does not happen. I do not understand why the author does not restrict his model to the regions of strain or temperature where crystals do not form.

4) The falling slope of the stress-strain curve at lower strains is associated with details of molecular motion. But at least some of it is simply due to using engineering stress when the sample is reducing in cross-section. Identifying deviations from neo-Hookean would be more relevant.

5) A special region 1a is described in molecular terms and vaguely indicated in fig 1 as below 100% strain. The references show it to be a specially stiff region at up to 5% strain. Is there any experimental evidence for this to exist? It seems a simple experiment to do. (~~i just wanted to say i originally wanted crossbows , slingshots and rubber bands under elasticity but rubber elasticity works, second i promise to have good faith just poor skilled at coding grammar and a external link is to a Wikipedia article as a alternative only because there was a error at the time with linking to a wiki page ~~ — Preceding unsigned comment added by Timpatalpostma (talk • contribs) 18:15, 31 December 2020 (UTC) but i --Timpatalpostma (talk) 19:30, 31 December 2020 (UTC)will settle with rubber bands and slingshots for me for elasticity category and leave the rest for someone else --Timpatalpostma (talk) 19:30, 31 December 2020 (UTC)

I do not want to get into an editing war here, but I feel the current version does not serve our readers well. Clavipes (talk) 03:49, 21 September 2019 (UTC)

======================= RESPONSE ======================Davidhanson471 (talk) 16:05, 4 December 2019 (UTC) Thank you for taking the time to critique the article. With regard to problem 1 in your list that the article exhibits a ‘lack of balance…Nobody else at all?’, it depends on what you mean by ‘balance’. The original Rubber Elasticity page (before I edited it) appears unchanged in the section entitled Historical approaches…, at the end. In my opinion, this description provided the reader with a confusing and incomplete picture of elasticity and was of no use to either the scientist/ engineer or the casual reader. There were of course a number of previous polymer physics theories such as the so-called 3-chain model. These theories all had serious deficiencies. In the case of the 3-chain model and its variants, all of the network chains were assumed to be of the same length and oriented symmetrically with respect to the strain axis. These and other objections to ideal chain theories are discussed in a review article, cited as ref. 4. Interestingly, none of these elasticity models were mentioned in the original version of the Rubber Elasticity page. In my judgment, it didn’t seem appropriate to ask the reader to slog through an extensive critique of the previous unsuccessful theories when a modern successful theory was available- a theory benchmarked against experiments.

With regard to the second problem in your list having to do with ‘general truths’ and ‘ideal rubber’, I am not sure how to respond since I don’t know what is meant by these terms. The term ‘ideal’ is commonly used in reference to free polymer chains that obey Markov statistics. Chains that make up a rubber network are of course not free.

Problem 3 of your list is concerned with the omission of a discussion of strain-induced-crystallization (SIC) processes in strained rubber samples. The recent experimental papers[Toki (2002) and Tosaka (2007)] that I have read suggest that the source of the x-ray scattering remains controversial. The crystal structure is variously assigned as monoclinic, lamellar or ‘shiskabob’. Since the intensity of the x-ray scattering peaks do not correlate well with either the strain or the observed stress, I am perplexed as to why SIC continues to enjoy such widespread acceptance as the source of the elastic force. The earliest reference to SIC that I have come across is a 1942 paper by Dart in which it appears as the explanation for the upturn of the stress at high strains without any discussion. I have not run across the origin of this claim. My guess is that the x-ray scattering experiments provided a convenient escape from the failure of the 3-chain rubber model at high strain, i.e. it did not predict an upturn to the stress. However, since SIC is so well known, I would have no objection to including a discussion of it under the Experiments section of the article. At present, I just don’t know how to do that without getting into a lengthy adjudication of all the experiments. The argument supporting the assignment of the stress upturn to non-entropic bond stretching and deformation is as follows: (1) We know that a rubber sample breaks if the strain is high enough. (2) The reason it breaks is because bonds on the chain backbone or crosslink rupture. (3) State-of-the-art Quantum Chemistry simulations (Density Functional Theory with non-restricted basis sets) provide a good estimate of the bond rupture process; the chain rupture force is about 7 nN for C-C bonds and 1.5 nN for S-S bonds in sulfur crosslinks. The simulations also provide the force-extension model before bond rupture occurs. (4) When this force model is used in the network simulation code, quantitative agreement with experiment is obtained (Fig. 1) in the high strain region (including failure). There are NO FREE PARAMETERS in code for this strain region. (5) Since the regime II force model correctly predicts not only the stress upturn but also the failure point, it suggests that additional elastic forces such as SIC are unnecessary.

Problem 4 in your list claims that the simulation code is in error at lower strains because the elastic behavior is plotted as the engineering stress. Engineering stress was used simply because it is the most common convention in the literature and, presumably, the most familiar to the reader. The simulation cell is deformed by an affine coordinate transformation to impose a strain and the resulting reduction of the cross section is therefore included in the calculation of the stress.

Problem 5 is concerned with the ‘special region 1a’ depicted in Fig. 1. I’m not sure which reference your are referring to when you say that it is ‘specially stiff at up to 5% strain’. Ref. 4, Fig. 11 on page 330 shows that it extends to a strain of about 25%. This figure also shows experimental data and the theory and experiment are in very close agreement. It was difficult to show this in Fig. 1 of the article because the y axis had to be large enough to show the high failure stress.

I am certainly open to suggestions to make the article clearer. It was a struggle to try to make it useful to the engineer/ scientist and also be somewhat accessible to the casual reader. Davidhanson471 (talk) 22:38, 2 December 2019 (UTC)

Problem with article overview

I agree; the overview is deficient. I will re-write it shortly. Davidhanson471 (talk) 17:27, 10 December 2019 (UTC)

Comment on Freely-jointed chain model section

The editor has provided a valuable expansion of this section. There are two issues that should be addressed: 1. The equations should be numbered to facilitate discussions and 2. references should be added. Also, as it stands, it is useful mostly to scientists and engineers specializing in polymer physics. The article could benefit from additional text to motivate and explain the mathematical derivation. A short paragraph at the beginning to provide a summary of the section for the casual reader would also be appropriate. Davidhanson471 —Preceding undated comment added 23:57, 10 December 2019 (UTC)

Rewrite of Lead In section

At the request of the Wikipedia editor, I have rewritten the Lead In section to provide the reader with a better description of what is included in the article.Davidhanson471 (talk) 20:53, 20 December 2019 (UTC)

Comment on Lead In section as revised 4 Feb., 2020

First of all, profanity, even abbreviated as '----ed', has no place on a Wikipedia page. The opening sentence 'Due to the flexibility of many polymers such as chained rubber, these solids are often highly elastic ' is at best misleading. Flexibility is not the source of elasticity; nylon filament is very flexible but not elastic. I have no idea what the author means by the term 'chained rubber' or 'polymeric solids joined in a network'. The revision is indeed shorter but poorly written and less informative than the previous version. Unless Wikipedia has a length limit on Lead In sections, I recommend going back to the previous version. I also suggest that further discussions about this be carried out on the Talk Page.Davidhanson471 (talk) 19:41, 4 February 2020 (UTC)

Comment on Lead In section original version restored 5 Feb., 2020

I have restored the Lead In section to its previous version. If you have suggestions for changes, please post a comment on this talk page. Davidhanson471 (talk) 16:25, 5 February 2020 (UTC)

Comment on Lead In section posted by editor C4356278 Nov., 2019 deleted

Following the suggestion by editor C4356278 posted on 11/2019, the Lead In section was re-written, consistent with wikipedia guidelines, on 12/20/2019. Since no further comments regarding the Lead In section have been posted on the Talk Page, I have deleted the C4356278 post requesting modifications. It appears to be no longer relevant and might invite another case of mischief. Of course further comments and suggestions for improvements are always welcome on this page. Davidhanson471 (talk) 19:52, 12 March 2020 (UTC)

Rewrite of Lead In section

At the request of the Wikipedia editor, I have rewritten the Lead In section, reducing its length by about 40%.Davidhanson471 (talk) 19:47, 19 October 2020 (UTC)

Please fit in elasticity applied into projectile usage where applicable

Just rubber bands and slingshots but if you want to expand it to catapults & crossbows your welcome , I know

Second I know one of the links looks like it’s from another site it’s not I am a noob and was dodging a error bug 3DPrintingTimPostma (talk) 20:03, 31 December 2020 (UTC)

This should be merged as a elasticity category

Another point to add that’s pretty not mentioned so much is I think under physics when people think of elasticity they think of rubber bands or similar rubber materials as a projectile launcher 3DPrintingTimPostma (talk) 20:10, 31 December 2020 (UTC)

Rewrite of Lead In section

I have removed the banner requesting shortening the lead In section since this was addressed 10 Oct., 2020., Davidhanson471 (talk) 22:15, 9 January 2021 (UTC)

Moved the reference to the paper by Buche et al. to the Historical Approaches section.

Since it deals with the freely jointed chain theory, it is more appropriate to place it in that section.Davidhanson471 (talk) 17:10, 25 August 2021 (UTC)

Regarding the request for a citation to back up the 'grandiose' claim about the economic importance

"Elastomers have played a key role in the development of new technologies in the 20th century and make a substantial contribution to the global economy.[citation needed]" I have searched the web for some reference that could speak to this but have not found anything yet. Since elastomers are present in so many technologies and products, e.g. automobile and truck tires and electronic devices like cell phones, I don't think that most readers would question the claim about economic importance.Davidhanson471 (talk) 17:37, 27 August 2021 (UTC)