Elongation ratio

FIGURE 21.12 Tapping-mode topographic image of uniaxially elongated NR vulcanizate. The elongation ratio was about 4. The scan size was 20 p,m. 

VOLUME DENSITY SURFACE DENSITY SPECIFIC SURFACE MEAN INTERCEPT LENGTH MEAN FREE DISTANCE MEAN DIAMETER MEAN CURVATURE ELONGATION RATIO DEGREE OF ORIENTATION... 

An example of tlie R8/1 table of data from a correlation analysis. Column headings are MC (mean curvature), ES (elongation ratio), MFD (mean free distance between features), MIL (mean intercept length of the features). 

Here, a is the elongation ratio of the polymer chains in any direction and (r/j1/2 is the root-mean-square, unperturbed, end-to-end distance of the polymer chains between two neighboring crosslinks (Canal and Peppas, 1989). For isotropically swollen hydrogel, the elongation ratio, a, can be related to the swollen polymer volume fraction, u2,j> using Eq. (11). 

As pointed out in part 1, ° ID oxide nanostructures do not represent only particles with high elongation ratio, but possess different spedfie eharaeteristics related to the nanostructure. For example, O2 adsorption is different from that observed for Ti02 single erystals and this has consequenees on the catalytic behaviour. In order to exploit the properties of ID oxide nanostructure, however, it is essential to orient nanotubes on substrates and to create ordered arrays. 

For rounded particles the operational sphericity, is well approximated (K2, P3) by ( 2 i) which is exact for ellipsoids. However, i/ p is not generally a good approximation to ij/. Aschenbrenner (A2) showed that a better approximation to ij/ is given by a working sphericity obtained from the flatness and elongation ratios by a result derived for a specific truncated polygonal form ... 

The stress-optical behaviour of an unswollan elastomeric network of PMTHF is measured for different elongation ratios at several temperatures. Values of 4a range from 2.4 to 2.8 in units of 10 A cm3, in the temperature range studied. Theoretical calculations carried out with the RIS model give values of 4a noticeably smaller than the experimental results however, a small increase in the backbone valence angles improves the theoretical results. Theoretical and experimental values of the temperature coefficient of 4a are in clear disagreement a qualitative explanation for this discrepancy is discussed. 

The stress-optical behaviour of an elastomeric network of PDET is measured over a wide range of elongation ratios and temperatures. Theoretical calculations are carried out with the RIS model. For Act, no reasonable modification of the conformational energies or contributions to the anisotropic part of the polarizability tensor would achieve agreement between theory and experiments. The discrepancy between theoretical and experimental results may be qualitatively explained by intermolecular interactions. Agreement between theory and experiment is only obtained assuming the unlikely value of about + 4.2 kJ mol-1 for E(on). 

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

Cartesian coordinates in the relaxed state Cartesian coordinates of deformed gel elongation ratio of isotropic gel... 

With our model free energy, we can readily examine small fluctuations around homogeneous states. First let us suppose an isotropically expanded state under zero osmotic pressure IT, + njon 4- Tlel = 0. The deformed position X is composed of the average x = (xj, x2, x3) = ax°, a being the elongation ratio, and the deviation u,... 

The c is the elongation ratio in the jc-axis as compared to the isotropically swollen state with the same volume fraction. Here, the average stress tensor fly in Eq. (4.36) is diagonal and it follows a famous relation in rubber elasticity [1],... 

As a first example, a gel is assumed to change its shape only in one direction, along which the x-axis will be taken [69], The elongation ratio ax in the perpendicular directions is now held fixed at a constant. The order parameter is the elongation ratio ay in the x-axis or... 

Equation (7.31) is a familiar form in statistical mechanics. For small displacements it is negative in sign and proportional to the square of displacement. For tensile deformation a power series expansion in the elongation ratio a, and with... 

Figure 15.6 2H NMR spectra of perdeuterated free chains (Mn = 10500 g.mol 1) diffusing in a uniaxially constrained PDMS network (Mn = 10500 g.mol"1), for different elongation ratios X. At X = 1, the free chains probe an overall isotropic system, and the doublet vanishes. The fraction of free chains is 9%...

Figure 15.7 Variation of the splitting A in an elongated PDMS model network containing a small amount (9%) of free PDMS chains, as a function of (A2-A 1), with X the elongation ratio. A pair of identical network/free chains systems are used A deuterated network chains (Mn = 10500 g.mol 1) o deuterated free chains (M = 10500 g.mol"1). S is the chain segment order parameter...

Figure 15.14 2H NMR spectra of deuterated benzene molecules diffusing in a uniaxially stretched PB network for various elongation ratios. The solvent volume fraction is 9%...

Polyamide-polyether (PA-PEG) block copolymers have been studied using deuterated water (2H20) molecules as 2H NMR probes [85, 86, 87]. Well resolved doublets are observed on 2H20 on stretching the samples at room temperature. At a given elongation ratio X, the splitting depends on the water concentration c. The linewidth is that of a liquid and becomes comparable to that in bulk water for c=0.6. This confirms that water... 

Sphericity shape factor Circularity shape factor 1 W where a0 = shape factor for equidimensional particle and thus represents part of av which is due to geometric shape only av = volume shape coefficient m = flakiness ratio, or breadth/thickness n = elongation ratio, or length/breadth Sphericity = (surface area of sphere having same volume as particle) / (surface area of actual particle) Circularity = (perimeter of particle outline)2 / 4tr(cross-sectional or projection area of particle outline)... 

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