Static expansion factor

Figure 4 shows a plot of the static expansion factor (o ) as a function of the relative temperature 0/T, where a is defined as Rg(T)/Rg(0) and r is the number of residues that may be one monomer unit or a number of repeat units. When T < 0 (water is a good solvent for PNIPAM), the data points are reasonably fitted by the line with r = 105 calculated on the basis of Flory-Huggins theory [15]. Similar results have also been observed for linear polystyrene in cyclohexane [25,49]. The theory works well in the good-solvent region wherein the interaction parameter (x) is expected to be... 

Fig. 4 Plot of static expansion factor (as) as a function of relative temperature 0/T, where a is defined as Rg(T)/Rg((9) symbols are our measured results and the lines are calculated data with three different values of r. If choosing M = 113 (molar mass of monomer NIPAM), we have r 105 for both the PNIPAM samples used [32]...

In several theories, the effects of excluded volume are combined into a static expansion factor a relating the total, experimentally measured mean square radius of gyration <5 > to the value with no long-range intramolecular forces accounted for,... 

With knowledge of obtained at very high ionic strength, can hence be computed using and from Equation 5.85, so that<5 > can be computed by Equation 5.19. The measured value<5 >is related to<5 > via the static expansion factor a, introduced earlier in Equation 5.25. 

In a series of papers [216,217], Nakata and Nakagawa have studied the coil-globule transition by static light scattering measurements on poly(methyl methacrylate) in a selective solvent. They have found that the chain expansion factor, a2 = R2/R20, plotted against the reduced temperature, r = 1 - 0/T, first decreases with decreasing r, as it should be, but then begins to increase (see, e.g., Fig. 2 presented in [217]) In the authors opinion, the increase of... 

Ap = upstream static pressure minus the downsteam or throat static pressure, Pa Pi = density at the upstream tapping, kgm gv=measured at the upstream density pi, m s gm = constant right through the airway system, kg m a = flow coefficient as given in the appropriate standard E = expansibility factor as given in the appropriate standard... 

Figure 6.6 Experimental (left column) and simulated (right column) Si-NMR spectra of a synthetic sample of jaffeite, acquired under static conditions and with spinning speeds of = 1000 and 4000 Hz. The experimental spectra were obtained with the Si H CP experiment (CP contact time of 5.0 ms and an 8 s relaxation delay) and the vertical expansion factors for the spectra are indicated relative to the = 4000 Hz spectrum. The simulations employ the parameters 5 so = -82.2 ppm, 6, = -51.2 ppm and r = 0.07, as determined from analysis of the static and MAS (v = 1000 Hz) spectra.

Figure 6.9 Left Experimental Al MAS NMR spectra (7.1 T) of the central and satellite transitions for AICI3-6H20 obtained without spinning and with spinning speeds of Vr = 12.0 kHz and 2.0 kHz. Right simulations of the full static-powder spectrum along with subspectra of the central transition (Cen), the inner (In) and outer (Out) satellite transitions and the MAS spectrum including all transitions acquired with Vr = 2.0 kHz. The vertical expansion factors are indicated at the right-hand side. The spectra were simulated with the parameters 5 so = 0.0 ppm, Cq = 0.116 MHz and tIq = 0.0, as determined from the experimental spectra.

The discharge head of a pump is the head measured at the discharge nozzle (gauge or absolute), and is composed of the same basic factors previously summarized 1. static head 2. friction losses through pipe, fittings, contractions, expansions, entrances and exits 3. terminal system pressure. 

The next step in the design procedure is to select the materials. The considerations are the physical properties, tensile and compressive strength, impact properties, temperature resistance, differential expansion environmental resistance, stiffness, and the dynamic properties. In this example, the only factor of major concern is the long-term stiffness since this is a statically loaded product with minimum heat and environmental exposure. While some degree of impact strength is desirable to take occasional abuse, it is not really subjected to any significant impacts. 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

Four frequently used conventions exist for the definition of non-linear optical polarizabilities, leading to confusion in the realm of NLO. This has been largely clarified by Willets et al. (1992) and in their nomenclature we have used the Taylor series expansion (T convention), originally introduced by Buckingham (1967), where the factorials n are explicitly written in the expansion. Here the polarizabilities of one order all extrapolate to the same value for the static limit w— 0. /3 values in the second convention, the perturbation series (B), have to be multiplied by a factor of 2 to be converted into T values. This is the convention used most in computations following the sum-over-states method (see p. 136). The third convention (B ) is used by some authors in EFISHG experiments and is converted into the T convention by multiplication by a factor of 6. The fourth phenomenological convention (X) is converted to the T convention by multiplication by a factor of 4. 

Many industrial processes require accurate environmental control. Examples include chemical reactions and processes that are affected by atmospheric conditions biochemical reactions quality, uniformity, and standardization of certain products factors such as rate of crystallization and size of crystals product moisture content or regain deliquescence, lumping, and caking of hygroscopic materials expansion and contraction of macliines and products physical, chemical, and biological cleanliness effects of static electricity odors and fumes conditions in storage and packaging quality of painted and lacquered finishes simulation of stratosphere or space conditions and productivity and comf ort of workers. Controlled atmospheric conditions are... 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

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