Closed-chain exercises

The rehabilitation program is an important part of ACL reconstructive surgery and has mostly taken a standard form since Shelbourne s publication. The graft should be protected by closed chain exercises in the early... 

Beynnon BD, JohnsonRJ, Fleming BC, StankewichCJ, Renstrom PA, Nichols CE (1997) The strain behavior of the anterior cruciate ligament during squatting and active flexion-extension. A comparison of an open and a closed kinetic chain exercise. Am J Sports Med 25 823-829... 

At moderate to high polymer concentrations, the free polymer chains in the solution may begin to exercise an influence. One such effect is the so-called depletion flocculation caused by the exclusion of polymer chains in the region between two particles when the latter are very close to each other (i.e., at surface-to-surface distances less than or equal to approximately the radius of gyration of the polymer chains). The depletion effect is an osmotic effect and is discussed further in Section 13.6. 

Exercise 6.6. One answer for Problem 6 of Chapter 2 is c/oso-I-THF-2-PB5H4. It is a monomer from which one might construct a square joined by P-B donor-acceptor interactions. With closo-1-THF-6-PB5H4 an extended chain of clusters can be constructed, (a) Draw the chain, define the repeat unit and distance, and draw the pertinent orbitals of the repeat unit, (b) Develop qualitative band and DOS diagrams and predict whether the solid would have a band gap or not. (c) Partial reduction of the chain by adding 10 mole% Li is carried out. Assume the electron goes into a cluster-based orbital and the closed cluster structure is retained. Predict the change in the electronic properties. 

The seeming contradiction between these various experiments may be resolved if site isolation is considered to be partially a kinetic phenomenon. For slow reversible reactions, such as anhydride formation or condensation reactions, the polymer chains have sufficient time to exercise several degrees of freedom, permitting site-site interaction. For reactions that occur over shorter periods, such as the decomposition of benzynes, the probability of close contact between reactive centers is greatly reduced. Metal dimer formation was obviated simply because there was no important thermodynamic driving force. 

We have explored what happens when an individual polymer chain is stretched. This was not just an exercise. We have shown that the elasticity of a network is built up from the elasticities of all the subchains (Figure 7.2), so we can make use of what we have found. There is one tricky question though. Let s imagine a highly elastic solid body, say, a rubber ball. The macromolecules are rather closely packed in it and interact strongly with each other. So can we really treat each subchain as an ideal polymer, with no volume interactions at all ... 

The molecular models made for Exercise 4-1 reveal obvious differences between cyclopropane, cyclobutane, cyclopentane, and so forth, and the corresponding straight-chain alkanes. One notable feature of the first two members in the series is how difficult it is to close the ring without breaking the plastic tubes used to represent bonds. This problem is called ring strain. The reason for it lies in the tetrahedral carbon model. The C-C-C bond angles in, for example, cyclopropane (60°) and cyclobutane (90°) differ considerably from the tetrahedral value of 109.5°. As the ring size increases, strain diminishes. Thus, cyclohexane can be assembled without distortion or strain. 

This simple exercise demonstrates that in most well dispersed CB filled rubber compounds, average inter-aggregates distances are close to the average quadratic diameter of the polymer random coil, of the order of 50 nm for diene elastomers with molecular weight of around 400,000 g/mole. In other terms, in most rubber compounds, certain chains of elastomer are in contact with at least two aggregates, whilst others are not. 

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