Elasticity measurements

At least two different techniques are available to compress an emulsion at a given osmotic pressure H. One technique consists of introducing the emulsion into a semipermeable dialysis bag and to immerse it into a large reservoir filled with a stressing polymer solution. This latter sets the osmotic pressure H. The permeability of the dialysis membrane is such that only solvent molecules from the continuous phase and surfactant are exchanged across the membrane until the osmotic pressure in the emulsion becomes equal to that of the reservoir. The dialysis bag is then removed and the droplet volume fraction at equilibrium is measured. 

Another technique consists of submitting the emulsion to centrifugation and determining the droplet volume fraction / at the top (bottom) of the cream (sediment). The centrifugation typically takes several hours until the equilibrium volume fraction is achieved. After equilibration, if the droplets occupy a distance much less than that of the centrifuge lever arm, the spatial gradient in the acceleration can be neglected, and the osmotic pressure can be determined (see Fig. 4.1)  

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The dashed line in Fig. 3.2 corresponds to a linear regression calculation yielding Me = 8 kg/mol for the average molecular mass between entanglements if no chemical crosslinks are present (MR - oo). This result agrees reasonably with values for various thermoplastics as determined from elasticity measurements on melts [30, 31, 32], Examples are given in Table 3.2. 

Elasticity measurements can serve as a measure of the degree of interconnection in gels. Covalently cross-linked networks can be distinguished from physically cross-linked networks by the use of a technique termed mechanical spectroscopy [333]. Compression of gels has also been used to assess the physical structure [28,168,303]. 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

MCA distinguishes between local and global (systemic) properties of a reaction network. Local properties are characterized by sensitivity coefficients, denoted as elasticities, of a reaction rate v,(S,p) toward a perturbation in substrate concentrations (e-elasticities) or kinetic parameters ( -elasticities). The elasticities measure the local response of a reaction in isolation and are defined as the partial derivatives at a reference state S°... 

Other experiments performed by Bergeron [34] on air foams stabilized with ionic surfactants reveal that the so-called Gibbs or dilatational elasticity e may play an important role in the coalescence process. The Gibbs elasticity measures the variation of surface tension yi t associated to the variation of the surfactant surface concentration F ... 

The work that follows pertains primarily to actin networks. Many proteins within a cell are known to associate with actin. Among these are molecules which can initiate or terminate polymerization, intercalate with and cut chains, crosslink or bundle filaments, or induce network contraction (i.e., myosin) (A,11,12). The central concern of this paper is an exploration of the way that such molecular species interact to form complex networks. Ultimately we wish to elucidate the biophysical linkages between molecular properties and cellular function (like locomotion and shape differentiation) in which cytoskeletal structures are essential attributes. Here, however, we examine the iri vitro formation of cytoplasmic gels, with an emphasis on delineating quantitative assays for network constituents. Specific attention is given to gel volume assays, determinations of gelation times, and elasticity measurements. 

Elasticity measurements already have been used to detect the presence of crosslinking proteins in cytoplasmic extracts(24). If preformed actin chains are employed, assessment of the rheological state of a network directly provides information about the parameters of crosslinking. Moreover, chain growth can bg studied, although indirectly, through the effects of Cq, Uq, on the concentration of crosslinking sites Sy. 

We again consider a network crosslinked by actin binding protein. The number of crosslinks that are formed. A, is given by Equation 10, and a plot of G vs (the total amount of added ABP) is shown, schematically, in Figure 3. Both the slope and the intercept provide information about the kinetic parameters of network formation. Elasticity determinations clearly can be used to assess the amount of crosslinking protein in an assembly if all other conditions are kept constant, G varies linearly with consequently, after appropriate calibration (in principle with only two data points), elasticity measurements could be used for quantitative assessment of the efficacy of biochemical purification procedures. Parenthetically, we note that if conditions can be arranged such that K S 1, gives a direct measure of the number of nuclei iIq. 

Overpressure gauges with elastic measuring element for general use Requirements ... 

The kinetic theory of rubber elasticity is so well known and exhaustively discussed (17, 27, 256-257, 267) that the remarks here will be confined to questions which relate only to its application in determining the concentration of elastically effective strands. In principle, both network swelling properties and elasticity measurements can provide information on network characteristics. However, swelling measurements require the evaluation of an additional parameter, the polymer-solvent interaction coefficient. They also involve examining the network in two states, one of which differs from its as-formed state. This raises some theoretical difficulties which will be discussed later. Questions on local non-uniformity in swelling (17) also complicate the interpretation. The results described here will therefore concern elasticity measurements alone. 

The difference between v calculated from Eq. (11-70) and v from elasticity measurements (Chapter III) can serve as an estimate of cyclization. Because of the very approximate validity of Eq. (11-70) and difficulties in interpretation of the data using network elasticity theories such estimates are of minor theoretical value. 

A particular polyester network may be considered as a model of degraded ideal polyester based on a prepolymer having an infinite molar mass with a number of chain scissions equal to Ave = b/2. Thus, polyester samples differing by the initial prepolymer molar mass can be used to calibrate rubber-elasticity measurements. 

This approach can be illustrated by unsaturated polyesters based on an almost equimolar combination of maleate and phthalate of propylene glycol, crosslinked by styrene (45 wt%) (Mortaigne el al., 1992). Six samples differing by the prepolymer molar mass were analyzed. The chain-ends concentration, b, was determined by volumetric analysis of alcohols and acids in the initial reactive mixture. Then, the system was cured, elastic measurements were made in the rubbery state at Tg + 30° C, and the shear modulus G was plotted against chain-ends concentration (Fig. 14.7). The following relationship was obtained ... 

Dimova, Rumiana, Motion of Particles Attached to Giant Vesicles Falling Ball Viscosimetry and Elasticity Measurements on Lipid Membranes, 6, 221. 

Figure 15.8 2H NMR spectra obtained in a randomly crosslinked, deuterated PB network. Precursor chain molecular weight 115700 g.mol"1, 1.2% crosslink agent, the average molecular weight between junctions is 27400 g.mol 1 (as determined by swelling experiments) or 11600 g.mol"1 (elastic measurements). The smooth curves are fits with a most probable distribution of chain lengths with number average molecular weight Mc = 11600 and with non-Gaussian chain statistics...

Figyre 3.16 Mooney-Rivlin plots [Eq. (3.38)] showing the effect of the temperature on stress-strain isotherms for model PDMS networks (15,16). The filled circles represent the reversibility of the elastic measurements, and the vertical lines locate the fracture points. (From Ref. 15.)... 

Detailed study of ME properties demonstrated that in the case of ME synthesis in the magnetic field, significant anisotropy of ME elasticity was observed. Elasticity measured for an ME sample... 

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