Mullins factor

An additional point of interest in cyclic straining was the MuUins effect. It was helpful to have a quantitative measure of how close the materials come to exhibiting an ideal Mullins response, as defined for example by Ogden et al (1999) [175, 296]. To this end we defined a Mullins factor M, such that an ideal Mullins response was characterized by M = 1 [175] ... 

Also included in Fig. 4.13 is the Mullins factor M. It is interesting to note that in 4.13(a) it increases slightly, while in 4.13(b) it decreases slightly when the SAXS intensity increases. This is evidence for the fact that the Mullins effect, although... 

Fig. 4. 13 Variation of inelasticity measures (a) and ( ), and the first cycle energy input E ( ), with degree of phase separation as expressed by the integrated SAXS peak intensity. Results shown are for PU2 and PUS (a), and PUS and PUIO (b). Also shown is the Mullins factor in each case (o). The lines have no significance except to guide the eye [175].

Again the Mullins factor appeared to be related to the hysteresis in a remarkably similar manner for all materials. With increasing maximum extension the points moved closer to the line of equation (4.5). We noted that the two materials PU7 and PUS that are outliers in Fig. 4.15 (where Smax = 3) are here moving in the same sense, but by n = 3 they have not yet reached the line. 

Conversion factors to SI units from other units are given in Table 1.2 which is based on a publication by Mullin(3). 

The exponents i and s in equations 15.13 and 15.14, referred to as the order of integration and overall crystal growth process, should not be confused with their more conventional use in chemical kinetics where they always refer to the power to which a concentration should be raised to give a factor proportional to the rate of an elementary reaction. As Mullin(3) points out, in crystallisation work, the exponent has no fundamental significance and cannot give any indication of the elemental species involved in the growth process. If i = 1 and s = 1, c, may be eliminated from equation 15.13 to give ... 

The Bueche-Mullins method has been applied in the separation of the modulus contributions of crosslinks and entanglements in several elastomers. A front factor of g = 1 was then used to determine Me. The Langley method has also been applied in a few cases, resulting in values of both g and Me. These works are summarized below results are collected in Table 7.2. 

In this relation, 2C2 provides a correction for departure of the polymeric network from ideality, which results from chain entanglements and from the restricted extensibility of the elastomer strands. For filled vulcanizates, this equation can still be applied if it can be assumed that the major function of the dispersed phase is to increase the effective strain of the rubber matrix. In other words, because of the rigidity of the filler, the strain locally applied to the matrix may be larger than the measured overall strain. Various strain amplification functions have been proposed. Mullins and Tobin33), among others, suggested the use of the volume concentration factor of the Guth equation to estimate the effective strain U in the rubber matrix ... 

It will be appreciated that in the relations considered above the rubber has been treated as a perfectly elastic material, whereas in practice there several factors that cause departure from pure elastic behaviour. Hysteresis and the Payne effect are considered in Chapter 9, set, stress relaxation and creep in Chapter 10 and the Mullins effect was covered in Chapter 5. 

Factors identified in this body of work range from the character of colleague relationships within research networks (Mullins 1976) and the structure of the research process (Knorr 1977) to broader institutional reforms in education and academic labor markets (Ben-David and Collins 1966) and the emergence of new consumer knowledge markets (Groenewegen 1987),... 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

All of these changes in ciystal habit caused by kinetic factors are drastically effected by the presence of impurities that adsorb specifically to one or another face of a growing ciystal. The first example of crystal habit modification was described in 1783 by Rome de Lisle [77], in which urine was added to a saturated solution d NaCl changing the crystal habit from cubes to octahedra. A similar discovery was made by Leblanc [78] in 1788 when alum cubes were changed to octahedra by the addition of urine. Buckley [65] studied the effect of organic impurities on the growth of inoiganic crystals from aqueous solution, and in Mullin s book [66] he discusses the industrial importance of this practice. 

Based on the assumptions above and the equation for drift, the maximum rale of entry of PBO into aquatic systems via drift is 0,018 lb PBO per acre (or 0.0084 kg ha 1) water- The results of this calculation arc used as the input rale per acre (surface area) of water and then adjusted for depth, degradation rates, and other factors (Mullins at.. 199.1. ... 

The rate and mechanisms by which crystallization occurs are determined by numerous thermodynamic, kinetic, and molecular recognition factors. (Nyvlt et al., 1985 Sohnel and Garside, 1992 Mersmann, 1995 Mullin, 2001 Myerson, 2002) These factors are summarized in Figure 1. The solvent plays a key role in crystallization as many of the factors depend directly on the solvent (Davey, 1982). Therefore, the intricate balance between thermodynamic, kinetic, and molecular recognition must be considered when designing experiments for polymorph screening, selection, and isolation. 

Mullin, M. M., Some Factors Affecting the Feeding of Marine Copepods... 

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