Relaxation force

The method (27) can best be explained with reference to Figure 2. After stretching to 10, the force f is measured as a function of time. The strain is kept constant throughout the entire experiment. At a certain time, the sample is quenched to a temperature well below the glass-transition temperature, Tg, and cross-linked. Then the temperature is raised to the relaxation temperature, and the equilibrium force is determined. A direct comparison of the equilibrium force to the non-equilibrium stress-relaxation force can then be made. The experimental set-up is shown in Figure 4. 

This block thus contains the electronically relaxed force constants along the system internal coordinates. 

There is considerable activity in the area of MM calculations on small polypeptides. A preliminary amide force field based on the CFF (231,232) and a partial relaxation force field (233) has been reported. Interested readers are referred to review articles cited in ref. 232. 

Figure 7.11 Overlay of contour plots for apparent modulus of elasticity in compression ( c)> maximum tension force (Ft) and first-cycle relaxed force (Fri). The shaded area represents optimum conditions.

The punch pressure required to form a compact for tableting indices measurements is measured at the end of a long dwell time, typically 1.5 minutes, during which the punches remain in fixed positions and stress relaxation within the compact brings about a decay in the applied load. The reported pressure or CS is calculated from the relaxed force and it is dependent on the compact SF. A sample s CS at a standard SF, such as 0.85, can be interpreted to indicate the ease (i.e., the magnitude of the pressure) of forming compacts under standardized conditions. 

Another important factor for tensile testing is cyclic testing or applying force and releasing (or relaxing) force on a test specimen to evaluate its ability to endure cyclic fatigue. A typical stress vs. strain relationship is shown in Fig. 3.16 and a cyclic stress relationship in Fig. 3.17. 

The minus sign is used because both the electrophoretic and relaxation forces act in a direction opposite to that of the externally applied field. 

Since the latter arises from the distortion of the ionic cloud, one must derive a relation between the relaxation force and a quantity characterizing the distortion. It will be seen that the straightforward measure of the asymmetry of the cloud is the distance d through which the center of charge of the ion and the center of charge of the cloud are displaced. 

However, the distortion d of the cloud itself depends on a relaxation process in which the part of the cloud in front of the moving ion is being built up and the part at the back is decaying. Hence, the distortion d and the relaxation force must depend on the time taken by a cloud to relax, or decay. 

Thus, it is necessary first to calculate how long an atmosphere would take to decay, then to compute the distortion parameter d, and finally to obtain an expression for the relaxation force F. Once this force is evaluated, it can be introduced into Eq. (4.30) for the relaxation component of the drift velocity. 

Magnitude of the Relaxation Force and the Relaxation Component of the Drift Velocity... 

The relaxation force is zero when the centers of charge of the ion and its cloud coincide, and it is nonzero when they are separated. So let it be assumed in this approximate treatment that the relaxation force is proportional to d, i.e., proportional to the distance through which the ion has moved from the original center of charge of the cloud. On this basis, the relaxation force will be given by the maximum total force of the atmosphere on the central ion, i.e., z multiplied by the... 

Thus, a more rigorous expression for the relaxation force is... 

Substituting the expression (4.313) for the relaxation force in Eq. (4.301) for the relaxation component of the drift velocity, one gets... 

In the first derivation of the relaxation force Debye and Huckel did not take into account the natural Brownian movement of the ions allowance for this was made by Onsager who deduced the equation ... 

The coefficient Ki given here differs somewhat from that (K) employed on page 86 the latter is defined as the resultant frictional coefficient, based on the tacit assumption that all the forces opposing the motion of the ion in a solution of appreciable concentration are frictional in nature. An attempt is made here to divide these forces into the true frictional force due to the solvent, for which the coefficient Ki is employed, and the electrophoretic and relaxation forces due to the presence of other ions. At infinite dilution, K and Ki are, of course, identical. 

It is now possible to equate the forces acting on an ion of the ith kind when it is moving through a solution with a steady velocity w, the driving force due to the applied electrical field is eZiV, and this is opposed by the frictional force of the solvent, equal to KiUiy together with the electrophoretic and relaxation forces hence... 

The relaxation forces are added to this equation as an afterthought to describe phenomenologically the behaviour of an isolated assembly of nuclear spins in an N.M.R. experiment. Further modification allows the description of chemical exchange. 

The relaxation forces present in the system reduce the resultant moment in the x y plane as nuclei precess faster or slower than the mean Larmor frequency. This gives rise to the free induction decay. The process of dephasing of nuclear spin moments in the x y plane can be... 

Figure 11 shows diagrammatically (Muller and Bloom, 1960) the arrangement of echoes and pulses which occur in a general type of three-pulse spin-echo experiment. In this diagram a pulse of duration 0 to t0 rotates the magnetization by the angle nj2. This pulse is followed by the free induction decay with time constant T determined by both extrinsic and intrinsic relaxation forces. At a time iq (iq > 11 t0) a pulse... 

---