Free coil

The strain-free coil of pure platinum used in the resistance thermometer must meet one of the following specifications 1 (302.9146 K) > 1.11807 or 1 (234.3156 K) < 0.844235. If the resistance thermometer is to be used over the entire range 13.8033 to 1234.93 K, it must also meet the requirement that 1 (1234.93 K) > 4.2844. Temperatures 790 are calculated from the equation... 

In the intermediate stages of the expulsion, the chain comprises a segment which is embedded in the layer to a depth of a g x g L, and an expelled segment. The configuration of the expelled chain segment is similar to that of a free coil of comparable size. The excess free energy of the partly expelled chain is thus primarily due to the embedded segment ... 

Vfe will first compare the dimensions of the adsorbed with those of the free P-1 molecules. In Figures 6, we plot, ag the amounts adsorbed in mg/g, further the areas per adsorbed molecule, and the cross sectional areas. For a conoparison we entered our Ar-values for P-1 and the diameters of the free coils in Figure 6b. We then calculated and compared the volumes enconpassed and the ratios of the corresponding segmental densities of the P-1 gelatin molecules, v en free, or adsorbed. Figure 7. The cross sections and hydrodynamic volumes of the counterpart free molecules were approximated with the help of Fox and Flory s (21) equation for random coils ... 

The curves for the two cross sections, for Ar and for the free diameters (our Figures 6) are seen to intersect at low and high pH. However, these TOints of equal Ar and 2R, and of equal area/molecule and do not coincide in their pH-values, i.e. the molecules do not become adsorbed in the state of their free conformations. Figure 7 shows the courses of the volumes of free vs. adsorbed coils, and of the ratios of the densities of the free coils and in the interphase. The curves for the volumes are very far apart and will become equal only at very lew or high pH s, that is, for very small amounts of adsorption. 

FIGURE 3.19 The same as in Figure 3.18, for q), = 10 . In this case there is an attractive region at plate separations around the R, the free coil radius, and there is a maximum in the adsorbed amount 20. Reprinted from Scheutjens and Fleer (1982) with permission from Elsevier. 

Total number of coils Number of free coils 9 ... 

Chari et al. (1994) reported the effect of SDS on both local polymer chain motions and long range dimensions of the polymer coil. They showed that when a PEO coil is saturated with SDS micelles, it is more swollen compared to free coils when it is in a good solvent. They also revealed that these swollen chains are not fully stretched. Their results showed that the polymer coil at saturation is more like a swollen cage rather than a necklace. 

Another method of reducing sedimentation is to employ the principle of depletion flocculation (described in Chapter 7). The addition of free (non-adsorbing) polymer can induce weak flocculation of the suspension, when the concentration or volume fraction of the free polymer ( p) exceeds a critical value denoted by p. Asakura and Oosawa reported the first quantitative analysis of the phenomenon [96]. They showed that when two particles approach to a separation that is smaller than the diameter of the free coil, polymer molecules are excluded from the interstices between the particles, leading to the formation a polymer-free zone (depletion zone). Figure 14.16 shows this for the situation below and above. ... 

Figure 6.10. Sketch of force response of free random coil and adsorbed chain in dependence on the coil strain related to the maximum elongation, 100% 0.81 Nh. Whilst free coil exhibits Gaussian response under given low strain approximately up to 20%, adsorbed loops and bridges, represented by A = 10 and 100, are highly Langevineau with incremental stiffness considerably increased. Strain induced perturbation of interphase accompanied by desorption of trains causes significant local stress and strain relief and, consequently, a lower stiffness...

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