Bueche parameter

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

Results from the Bueche analysis give higher values for the zero snear viscosity when compared to results from the Graessley analysis, but lower values for the molecular response time. However, the Bueche parameters are linearly correlated with the Graessley parameters. The Graessley molecular response times are linearly proportional to the Bueche response times. The zero shear... 

Affected by multiple scattering are, in particular, porous materials with high electron density (e.g., graphite, carbon fibers). The multiple scattering of isotropic two-phase materials is treated by Luzatti [81] based on the Fourier transform theory. Perret and Ruland [31,82] generalize his theory and describe how to quantify the effect. For the simple structural model of Debye and Bueche [17], Ruland and Tompa [83] compute the effect of the inevitable multiple scattering on determined structural parameters of the studied material. 

Thus the relaxation spectrum resulting from the average coordinates equation11 of our model has the same form as that of Rouse, of Kargin and Slonimiskii, or of Bueche. In order to relate the parameters of the model to those of the Rouse theory, the time scale factor a must somehow be connected to the frictional coefficient for a single subchain of a Rouse molecule. To achieve this comparison, we may23 study the translational diffusion coefficients as computed for the two models. 

In this respect, another insufficiency of Lodge s treatment is more serious, viz. the lack of specification of the relaxation times, which occur in his equations. In this connection, it is hoped that the present paper can contribute to a proper valuation of the ideas of Bueche (13), Ferry (14), and Peticolas (13). These authors adapted the dilute solution theory of Rouse (16) by introducing effective parameters, viz. an effective friction factor or an effective friction coefficient. The advantage of such a treatment is evident The set of relaxation times, explicitly given for the normal modes of motion of separate molecules in dilute solution, is also used for concentrated systems after the application of some modification. Experimental evidence for the validity of this procedure can, in principle, be obtained by comparing dynamic measurements, as obtained on dilute and concentrated systems. In the present report, flow birefringence measurements are used for the same purpose. 

There has been a prevailing theory that oxidative degradation is accelerated by mechanical stress [100]. This theory is based on fracture kinetic work by Tobolsky and Eyring [101], Bueche [102, 103, 104], and Zhurkov and coworkers [105, 106, 107]. Their work resulted in an Arrhenius-type expression [108] sometimes referred to as the Zhurkov equation. This expression caused Zhurkov to claim that the first stage in the microprocess of polymer fracture is the deformation of interatomic bonds reducing the energy needed for atomic bond scission to U=U0-yo, where U0 is the activation energy for scission of an interatomic bond, y is a structure sensitive parameter and o is the stress. 

As mentioned earlier, in the limit of 1/2 0 (2 —> oo), a soft particle becomes a hard particle, we call 1/2 the softness parameter. Debye and Bueche [53], on the... 

Theories for the dependence of F on molecrdar parameters will be reviewed in section 3, but it should be pointed out that Eq. (2.6) coincides exactly with the results calculated for an isolated chain (76, 190) for F for X predict quantitatively rj, given o q/JVg and C which can be obtained respectively from dilute solution studies and from viscoelasticity measurements (46). 

Bueche suggests that this factor be applied to modify the structural factor to correct for entanglement effects. Thus, only the asymptotic form of Eq. (3.5) is utilized, the predictions at intermediate molecular weight being scarded. Equating the two asymptotic forms at the critical chain length Z (not to be confused with Z ) results in expressions for F that can be written in a form identical to Eq. (2.6) in terms of the parameter X = s )p/M) Z/v as ... 

The combined Yarusso/Debye-Bueche model provides an excellent fit to the full range of the ASAXS data, as shown in Figure 7 for the difference pattern. The fit parameters are listed in Table III. 

Table III. Yarusso/Debye-Bueche Model Fit Parameters for NiSPS 3 2...

Figure 5-6. (a) Dependence of T on p for mixtures of polymethyl methacrylate with diethyl phthalate. Comparison of experimental results with equation (5-8). Parameters found were ctjctp = 2.32, Tgd = -57 °C, Tgp = 104 °C.f [After F. N. Kelley and F. Bueche, J. Polym. Sci., 50 549 (1961)] (b) Variation of Tg for a miscible polymer blend of polycaprolactone (PCL) and poly(styrene-co-acrylonitrile) (SAN), with a description of the data using the Gordon-Taylor relationship, equation (5-27). The two points at low SAN content have a higher-than-expected Tg because of crystallization of the PCL. [After S-C. Chiu and T. G. Smith, J. Appl. Polym. Sci., 29,1797 (1984). Copyright 1984, Wiley Periodicals, Inc., a Wiley Company.]... 

Figure 35.7 Plots of ulc versus for polyvinyl acetates in benzene at 20°C. Data are from C. R. Masson and H. W. Melville, Poly. 5c/., 4, 337 (1949). Curves are drawn using Eq. (35.20) with Eg = values for (tc/c )q and were calculated from parameters given by T. G. Fox, Jr., P. J. Flory, and A. M. Bueche, JA.C.S. 73, 285 (1951). (Units for T, are m /kg.)...

In conclusion, both the Graessley and Bueche theories confirm the general experimental observation that the reduced solution viscosity, ti/Doj function of X. Therefore, solution rheological behavior can be described by two material parameters, the zero shear viscosity and polymer response time. In turn, these parameters are functions of macromolecular structure and solvent properties. 

Hence, both Equations (4) and (5) declare the gradient dependence of tj by the function of the one non-dimensional parameter gf. However, under the theoretical estimation of 1) and t as a function of N there are contradictions between the experimentally determined ratio Equation (1) and P = 3, 4. Thus, the analysis of the entrainment of the surrounding chains under the movement of some separated chain by Bueche [11] leads to the dependencies rj but t. At the Edwards and Grant [12]... 

This parameter was correlated with the characteristics of the macromolecular chain by the relationship derived by Bueche [730] and completed by Allen and Fox [731],... 

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