Stiffness index

The stiffness index of hair fibers by the method of Scott and Robbins provides falling curves when plotted against weight attached to the fibers. Routine measurements are made at 0.2g total weight (0.1 g per fiber leg), and with a wire hook 0.77mm in diameter (0.19-1.28mm). For thin fibers, less than 50 pm in diameter, smaller weights (0.05 g per fiber leg) are recommended. (For additional details, see References 73 and 74.)... 

Figure 8-22. Hair fiber stiffness index and linear density [74]. Reprinted with permission of the Journal of the Society of Cosmetic Chemists.

The future market success depends decisively on the polymers performance where e.g. Cerenol is superior to PLA and starch-based polymers concerning the strength versus stiffness index (Figure 12.8). 

Kumar B, Das A, Alagirusamy R. Analysis of factors governing dynamic stiffness index of medical compression bandages. Biorheology 2012 49(5—6) 375—84. 

Let us now return to considering the cohomology classes [cr ] defined in Subsection 20.3.2, though this time we are working with integer coefficients. Clearly, these stiff index the generators of Xhe new feature appear-... 

Partsch H. The static stiffness index a simple method to assess the elastic property of compression material in vivo. Dermatol Surg 2005 31(6) 625-30. 

The stiffness of a dynamical system can be characterised via its timescales. Remember that the ratio l/IRe(A,) I is called the /-th timescale of a dynamical system (see Sect. 6.3). The most widely used stiffness index is the reciprocal of the shortest timescale of the system ... 

Tobolsky [10] observed that the slope of the relaxation curve, n, appears to be related to the relative stiffness of the polymer chain. This would indicate a qualitative interaction between the chain stiffness index Ng and n on the matrix. It became apparent after examining the literature that no quantitative assessment of this interaction has been presented, although the data available from several sources could be combined for such a purpose. 

Plot of slope of the relaxation curve, n, against stiffness index, Ng, for several polymers. Circles are polyurethanes of nearly the same cross-link density, but varying catalyst to prepolymer ratios as indicated [23]. Other polymers and associated references areO - polyisoprene [13,21], - SBR [21,22], polyisobutylene [15,21], 7- polymethyl methacrylate [15,21] and - polystyrene [15,24]. 

The modified power law may then be expressed in terms of Ng, the chain stiffness index, for purposes of examining the dependence of the design variables upon this particular molecular parameter. 

The index J can label quantum states of the same or different chemical species. Equation (A3.13.20) corresponds to a generally stiff initial value problem [42, 43]. In matrix notation one may write ... 

The mass of the beam, for given stiffness F/8, is minimised by selecting a material with the minimum value of the material index... 

However, in general these fabrication and performance advantages are common to all plastics and so a decision has to be made in regard to which plastic would be best for a particular application. Rather than compare the basic raw material costs it is better to use a cost index on the basis of the cost to achieve a certain performance. Consider again the material selection procedures illustrated in Section 1.4.1 in relation to strength and stiffness. 

One of the most common ways of expressing the effectiveness of strength or stiffness of a material is as a ratio of either of the quantities to the density, i.e., weight per unit volume. Such an index does not include the cost to achieve a certain strength or stiffness, but cost comparisons are probably not valid by themselves because many factors influence cost beyond raw material cost. 

A simplified performance index for stiffness is readily obtained from the essentials of micromechanics theory (see, for example. Chapter 3). The fundamental engineering constants for a unidirectionally reinforced lamina, ., 2, v.,2, and G.,2, are easily analyzed with simple back-of-the-envelope calculations that reveal which engineering constants are dominated by the fiber properties, which by the matrix properties, and which are not dominated by either fiber or matrix properties. Recall that the fiber-direction modulus, is fiber-dominated. Moreover, both the modulus transverse to the fibers, 2, and the shear modulus, G12. are matrix-dominated. Finally, the Poisson s ratio, v.,2, is neither fiber-dominated nor matrix-dominated. Accordingly, if for design purposes the matrix has been selected but the value of 1 is insufficient, then another more-capable fiber system is necessary. Flowever, if 2 and/or G12 are insufficient, then selection of a different fiber system will do no practical good. The actual problem is the matrix systemi The same arguments apply to variations in the relative percentages of fiber and matrix for a fixed material system. 

At very low frequencies the movement of the panel will be controlled by the stiffness, as inertia is a dynamic force and cannot come into effect until the panel has measurable velocity. Stiffness controls the performance of the panel at low frequencies until resonance occurs. As the driving frequency increases, the resonance zone is passed and we enter the mass-controlled area. The increase in the sound-reduction index with frequency is approximately linear at this point, and can be represented by Figure 42.8. 

El theory In each case displacing material from the neutral plane makes the improvement in flexural stiffness. This increases the El product that is the geometry material index that determines resistance to flexure. The El theory applies to all materials (plastics, metals, wood, etc.). It is the elementary mechanical engineering theory that demonstrates some shapes resist deformation from external loads. 

The UV and CD spectra of 117 and 121 (V) are shown in Figure 48. Considering 117, at —40°C a negative Cotton effect, coincident with the UV absorption, is evident, and at —5 °C a positive Cotton effect, coincident with the UV absorption (both of which are slightly red-shifted with respect to the —40°C profiles), is observed. It is thus apparent that 117 underwent a helix-helix transition at some temperature between —5 and —40°C. In contrast, the Cotton effects of 121(V) were positive at all temperatures, indicating that no helix-helix transition occurred. Similarly to 121, 88 did not undergo a helix-helix transition. These results are due to the different stiffness of the molecules, which is quantified by the viscosity index, a. 

Other difficulties are owing to the influence of the solvent. With stiff and bulky chains the so-called micro-form-effect becomes of importance, when the refractive index increment differs considerably from zero (7). In this case the random link approximately acts like a cylinder of length A and with a refractive index different from that of the solvent. Another effect occurs in good solvents which consist of anisotropic molecules. These molecules become oriented along the polymer chain, considerably contributing to its anisotropy [Frisman, Dadivanyan and Dyuzhev (752)]. In this way, the determination of the eigen anisotropy of weekly anisotropic polymer chains becomes rather doubtful. 

Calculations based on Stiff and Davies stability index (Ref. 11 indicated that under normal producing temperatures formation water 1s not expected to form scale. However, the high skin temperature (up to 150° C) of the crude heaters will cause severe CaCO-scaling. This expectation was confirmed by laboratory tests using synthetic formation water. The result indicates a requirement to Inject scale inhibitor upstream of the heaters. A polyphosphate scale inhibitor was found to be effective in the laboratory tests. 

POLYETHYLENE, A thermoplastic molding and extrusion material available in a wide range of flow rates (commonly referred to as melt index) and densities. Polyethylene offers useful properties, such as toughness at temperatures ranging from —76 to +93°C. stiffness, ranging from flexible to rigid, and excellent chemical resistance. The plastic can be fabricated by all thermoplastic processes. 

Other indices proposed that have tried to overcome the basic limitations of LSI include the Stiff and Davies Saturation Index, Larson and Buswell Index, Puckorius (Practical) Scale Index, Oddo-Tomson Index, and Larson-Skold Corrosivity Index, some of which are discussed briefly here. 

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