Chain tension force

In latex saturation processes of preformed fiber webs, the predominant force responsible for drawing the rubber particles to fiber crossings and coagulating these particles into a coherent mass is the surface tension of the evaptxatittg water medium. Current trends are to develop latexes whose surface tension is close to water by ulibzing oligomeric emulsifiers (White, 1976) or emulsifiers polymerized into the polymer chain (Sweeney, 1958) to maximize the surface tension forces. 

When the in situ formed block or graft copolymer chains are accumulated in too large a volume at the interface, the copolymer chains are forced to elongate perpendicularly to the interface and destabilize the interface. In other words, the excess accumulation may lead to a negative interfacial tension coefficient, so that the interfacial area will tend to increase by the undulation. As an extreme case of undulation, the copolymer will escape from the interface to form micelles. Such an example was present in the PS-CCX)H/PMMA-epoxy system... 

A mechanophore (blue in Fig. 2a) is a strategically designed chemical entity which responds to mechanical force in a predictable and useful manner (Fig. 2d-f). The polymer strand here acts as an actuator to transmit macroscopic force to the target. For a fully extended polymer chain, the maximum tension force is at the middle point of the chain contour. So the mechanophore should be incorporated into the middle of the chain with its active bond along the chain contotu (Fig. 2a) [15, 29, 32]. Examples of mechanochemical reactions include homolytic scission of weak bonds (diazo [33]), electrocyclic ring-opening (benzocyclobutenes [29], spiropyrans [32, 34 5], gem-dichlorocyclopropanes [46-49], ge/n-difluorocyclo-propanes [30, 50], and epoxide [51]), cycloreversion reactions (cyclobutane derivatives [52-56], Diels-Alder adducts [57, 58], 1,3-dipolar adducts [59, 60], and 1,2-dioxetanes [61]), dative bond scission [62-64], and flex-activated reactions [34, 65, 66], as recently reviewed by Bielawski [67]. 

It is also unclear which cOTiformations can give selective midpoint scission. The coiled part is obviously more mobile and deformable than the extended part. The position of the maximum tension force thus unlikely doesn t coincide with the middle point of the chain for nonsymmetrical conformations appearing as a halfdumbbell and folded shapes. It is puzzling why the chain breaks precisely at the midpoint of the chain (red dots in Fig. 15) observed in both QSSF and FTF. 

Fig. 17 (a) Dynamic response of a driven polymer translocation upon switching the pulling force/. At time t the tension force has passed the N(f) monomer and is at distance X t) from the membrane while M i) monomers have already moved into the trans side of the separating membrane. The chain portion to the right of X(t) is moving with mean velocity v(t). (b) First and second moments of the translocation coordinate (s) and (s ), and the variance (As(t) ) = (s ) - (s) for a polymer chain with length JV = 100 and driving force / = 5.0. Reprinted with permission from [89]... 

In all equations below, we shall assume biD = b and a = ax for simplicity. Ph)rsically, the tension force is believed to arise from entropic effects. If the chain end moves in random directions, there are more possibilities for it to increase the tube length than to decrease it. This can be easily illustrated using the picture of a chain moving in an array of obstacles. However, it is difficult to derive any quantitative result from such a picture, and any such result will depend on the geometry of constraints. Thus, the indirect result (eqn [64]) is used. 

If the polymer in the latex is above its glass transition temperature, it may form a him on evaporation of the water. A simple example is the drying of a latex paint him on a wall. As the water evaporates, coalescence surface tension forces proceed from the presence of water menisci of very small radii of curvature. These menisci develop between the particles as the last traces of water are removed. The forces that these menisci generate drive the particles together. Interdiffusion of the polymer chains takes place, forming coherent hlms. 

The joint components—pins in a two-pin joint—transfer the tension forces from one row of driving link plates to the next (Figure 3-33), and they must do so while the joint is flexing and the pins are rolling on one another. The pins in silent chain are subjected almost entirely to shear and bearing (Hertz) stresses. They are not subjected to much bending because of the way that the link plates... 

The standard tooth form is designed to distribute a portion of the tension force to all of the teeth engaged with chain rollers. Figure 4-28 is a force diagram that shows how the tension force is distributed. The force bearing on each tooth may be found using the following equations ... 

FIGURE 4-38 Forces on a sprocket tooth as chain tension is applied. 

Force is transmitted in an engineering steel chain and sprocket drive through contact between the chain barrel, or roller, and the working face of the tooth. These forces are shown in Figure 4-38. The tooth face is at an angle to the pitch fine of the chain. Therefore, when chain tension, T, is applied, two forces result. One is the tooth force, Tp which is normal to the working face. The other is the roller ejection force, Tp which is parallel to the tooth face. 

Under load, roller ejection force pushes the roller center out to the pitch diameter. As the chain wears, the pitch increases and the roller moves outward on the sprocket teeth until it finds the greater pitch diameter that fits the elongated pitch of the chain. This can be seen in Figure 4-40. Most of the chain tension is absorbed by the sprocket teeth between points B and A. This is so whether the chain is new or worn. Slack strand tension is absorbed between points C and A. At point A, the unabsorbed tight strand tension and unabsorbed slack strand tension is equal. Thus point A is called the balance point. When the system is functioning properly, the working face is the only tooth snrface contacting the roller, except at the balance point... 

Take-Up and Hold-Back. An elevator chain wears and elongates, and a belt stretches during service life. A chain also elongates when handling hot materials. Therefore, a take-up adjustment is needed to maintain tension between the head and foot shafts. A manually adjusted screw take-up that moves the tail shaft or head shaft or a self-adjusting weighted take-up that maintains a constant gravity force on the tail shaft may be used. 

For a situation where large torques are involved, such as a bicycle drive, a chain linkage is superior to a belt. A person putting all his or her weight on a pedal probably would make most belt systems slip. Another advantage of a chain over a belt is that a chain is more efficient, mainly because it does not require any ambient tension. The return side of a chain drive has only enongh tension to snpport itself. Furthermore, the chain links are equipped with rollers, which can rotate as they contact the teeth, reducing the frictional forces and wear. 

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