Force-temperature curve

Fig. 85.—Force-temperature curves at constant length obtained by Anthony, Gaston, and Guth for natural rubber vulcanized with sulfur for elongations from 3 percent to 38 percent (at 20°C), as indicated.

Fig. 86.—The force of retraction / and its components dE/8L)t,p (curve A) and T(dS/dL)T,p (curve B), as obtained from force-temperature curves at fixed length such as are shown in Fig. 85, plotted against the percent elongation at 20°C. (Anthony, Caston, and Guth.i )...

Fig. 17 Typical lateral force-temperature curves for the PMMA brush (Mn = 45400, Mw/Mn <1.2, a = 0.8 chains nm ) and an equivalent spin-coated film at the scanning rate of 10" nms . Reproduced with permission from [148] (Copyright 2003 The Society of Polymer Science, Japan)...

Fig. 4.16 (a) Typical lateral force/temperature curves at a given scanning rate. Curves for PS with Mn = 4,900 or Mn = 140,000 at a scanning rate of 1 pm s-1 are displayed. The bulk Tg values measured by DSC are 348 and 376 K, respectively, (b) Master curves of the scanning rate/lateral force relationship for PS films drawn from each curve in panel a. Reference temperatures of 267 and 333 K have been used for PS with Mn = 4,900 and for PS with Mn = 140,000, respectively, (c) Semi-logarithmic plots of aT versus the reciprocal absolute temperature (T-1) for PS films with Mn = 4900 or Mn = 140,000. (Reprinted with permission from John Wiley Sons, Inc. [33], Copyright 2004. John Wiley Sons, Inc.)... 

Fig. 2. A force-temperature curve for kangaroo tail tendon immersed in 0.9% saline. The tendon is mounted in the apparatus of Fig. 1. The arrow pointing down indicates a glass transition, and that pointing up indicates the shrinkage temperature Tg.

Figure 6 shows the master curves for the PS films with M of 4.9k and 140k drawn by horizontal and vertical shifts of each curve shown in Fig. 5 at the reference temperatures of 267 and 333 K, respectively [26]. The master curves obtained from the dependence of lateral force on the scanning rate were very similar to the lateral force-temperature curves, as shown in Fig. 3. Hence, it seems plausible as a general concept that the scanning rate dependence of the lateral force exhibits a peak in a glass-rubber transition. Also, it is clear that the time-temperature superposition principle, which is characteristic of bulk viscoelastic materials [35], can be applied to the surface relaxation process as well. Assuming that Uj has a functional form of Arrhenius type [36, 37], the apparent activation energy for the aa-relaxati(Mi process, A//, is given by ...

Our third and final example is the use of SAW to model the micromanipulation of polymer molecules, particularly DNA, attached to a surface. In this situation, optical tweezers [77,78] are used to pull the adsorbed biological molecule from the surface. This force is applied perpendicular to the adsorbing surface and will favour desorption. It is reasonable to expect some sort of a phase transition. At low levels of the force, the polymer remains adsorbed, but at higher levels it will be desorbed. There will be a temperature dependent force /c(T) between these two states. The shape of the force-temperature curve is of considerable interest, and can be considered a phase boundary in the T — f plane. This can be modelled by a SAW, tethered to a wall, with a fugacity associated with nearest-neighbour bonds, subject to a force perpendicular to the wall, as shown in the figure below. 

Fig. 3.9. Force-temperature curve based on eqn (3.67). The slope (dfldT)i also equals the entropy change per unit extension (dSIdlh. Intercept on the vertical axis is equal to the energy change per unit extension (dUldlh-...

In addition to the use of cyclohexane, dimethylformamide (DMF) was used as a good solvent. So as to pick up the thiol-modified terminal, gold-coated cantilevers were used. The nominal values of their spring constant ki were 30 or 110 pN nm . A typical force-extension curve measured in cyclohexane is shown in Figure 21.4. The solvent temperature was kept at about 35°C, which corresponded to its temperature for PS chains. Thus, a chain should behave as an ideal chain. The slope at the lowest extension limit (dashed line in Figure 21.4) was 1.20 X lO" N m . ... 

Anthony, Caston, and Guth applied similar corrections to their measurements in order to express the force as a function of the temperature at various constant elongations. The results are shown in Figs. 87 and 88. The force-temperature plots are linear within experimental error. Their intercepts at 0°K are near zero, except at the higher elongations. These intercepts, which according to Eq. (22) must represent (dE/dL)T,Vi are plotted in the lowest curve of Fig. 88. It is doubtful... 

Fig. 90.—The force of retraction at 25°C and its internal energy component for gum-vulcanized GR-S synthetic rubber. Upper curve, total force / middle curve, dE/dL)T,p from the intercepts of force-temperature plots at constant length lower curve, dE/dL)T.v from the intercepts of stress-temperature plots at constant elongation. (Roth and Wood. )...

The triple point of a substance is reached when the vapor pressure of the solid phase is equal to that of the liquid phase. If both solid and liquid are subjected to external pressure (which may be caused by capillary forces), their curves of vapor pressure versus temperature lie above those for uncompressed phases and intersect at a temperature different from the triple point. The melting point Tm observed at atmospheric pressure, as a rule, is very near to the triple point. Thus the freezing temperature Tmr of a drop of radius r should be different from Tm. 

In her initial investigation, Lundquist studied the monolayer behavior of racemic and optically active forms of both tetracosan-2-ol and its acetate derivative on 0.0 lA aqueous HCl over a considerable range of temperature (77). In each case, it was possible to demonstrate chiral discrimination between pure enantiomers versus the racemic substance. Furthermore, the extent of enantiomer discrimination was significantly temperature dependent, being enhanced at lower temperatures and frequently disappearing at higher ones. Under favorable conditions of temperature, however, the appearance of the force-area curves could be very sensitive to the optical purity... 

The force-area curves for racemic and (5)-(+)-2-tetracosanyl acetate recorded with a barrier speed of 5 cm/min are shown in Figures 17 and 18, respectively. Again, both enantiomers showed identical monolayer behavior. The film balance behavior of the racemic acetate was indistinguishable from that of the pure enantiomers at temperatures above about 27°C however, below this temperature the force-area curves differed markedly even at low surface pressures, which indicates that racemic compound formation occurs at relatively large areas per molecule. 

The force-area curves for racemic and (5 )-(+>2-tetracosanyl acetate were shown in Figures 17 and 18, respectively, while those of methyl esters of racemic and (5 )-(+)-2-methylhexacosanoic acid are found in Figs. 21 and 22, respectively. All these curves were obtained under identical experimental conditions at thevarious temperatures indicated in the figures. Simple inspection shows that the force-area curves of the two racemic samples are very similar, as are those for both optically pure samples. Lundquist suggested that this is merely a result of the very similar shapes and molecular structures of these chiral surfactants. Apart from the chain length, the only structural difference is limited to a reversal of the positions of the carbonyl group and ester oxygen. 

Figure H2.1.1 A force/deformation curve illustrating specimen fracture of a banana (2.5 cm length, 3.0 cm diameter, 5 mm/min deformation rate), Cheddar cheese (2.0 x 2.0 x 2.0 cm, 10 mm/min deformation rate), and a seedless grape (2.2 cm length, 1.7 cm diameter, 2 mm/min deformation rate) under uniaxial compression at room temperature.

Figure H2.2.1 Force/deformation curves illustrating three puncture probe tests (50 mm/min deformation rate) of an apple specimen and a cone penetrometer test (10 mm/min deformation rate) of Cheddar cheese, all at room temperature.

Figure H2.2.3 A force/deformation curve illustrating a compression-extrusion test (10 mm/min deformation rate) for canned green peas using a Kramer shear cell (multiblade) at room temperature.

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