Interaction parameter, solid

T. F. Kemp and M. E. Smith, QuadFit—a new cross-platform computer program for simulation of NMR line shapes from solids with distributions of interaction parameters. Solid State Nucl. Magn. Reson., 2009, 35,243-252. 

FIGURE 2.29 The miscibility map for the system styrene-co-vinyl phenol (S-co-VPH) (l)-poly(methyl methacrylate) (PMMA) (2) at 40°C as given by the spinodal lines (dash-dotted lines) and the line of zero Xi2 interaction parameter (solid line) as functions of the vinyl phenol content (Fypg) of the copolymer. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

Table 1 Interactions in solid state NMR, parameters, their selective measurement, and...

Good-GLrifalco-Fowkes (GGF) equation Using ysi = ysv + yiv - 20(ysvyiv) in Young s equation leads to 1+COS0 2 Uvj Yggf obtained from a plot COS0 versus 4> is solid-liquid interaction parameter 0 = 1 if the interactions are purely dispersive. Based on Berthelot relation for attractive constants valid only when the solid-liquid interactions are dominantly dispersive. [77-82]... 

The Good-Girifalco theory [77-82] was originally formulated to make an attempt to correlate the solid-liquid interfacial tension to the solid surface energy and the liquid surface tension through an interaction parameter, basic formulation of the theory is ... 

Because the appearance of a superlattice is usually well characterized qualitatively in terms of an interaction parameter w which has nothing to do, in the usual treatments, with the melting of the parent solid solution, one does not expect to find a simple relationship between the critical temperature for disordering of the superlattice, and Ts, the solidus temperature of the corresponding solid... 

Figure 10. Adsorbed cation coverage as a function of electrode potential, assuming a cation interaction parameter / = 6.18 The solid line is the steady-state solution, whereas the broken line is the quasi-steady solution. Open circles indicate the unstable area. (From G. L. Griffin, J. Electrochettu Soc. 131, 18, 1984, Fig. 1. Reproduced by permission of The Electrochemical Society, Inc.)...

Fig. 51 Phase diagram for PS-PI diblock copolymer (Mn = 33 kg/mol, 31vol% PS) as function of temperature, T, and polymer volume fraction, cp, for solutions in dioctyl ph-thalate (DOP), di-n-butyl phthalate (DBP), diethyl phthalate (DEP) and M-tetradecane (C14). ( ) ODT (o) OOT ( ) dilute solution critical micelle temperature, cmt. Subscript 1 identifies phase as normal (PS chains reside in minor domains) subscript 2 indicates inverted phases (PS chains located in major domains). Phase boundaries are drawn as guide to eye, except for DOP in which OOT and ODT phase boundaries (solid lines) show previously determined scaling of PS-PI interaction parameter (xodt

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

Fig. 5.4. Dependence of hydrogen chemisorption energy AE (solid line) and adatom charge transfer Aq (dashed line) of 2-layer Ni film on interaction parameter 7. Reprinted from Davison et al (1988) with permission from Elsevier.

Figure 4. Distribution of the ionic compounds AX and BX over the solid phase and the aqueous phase for different values of the distribution parameter D under the assumption that AX and BX form homogeneous regular solid solutions with a negative value for the interaction parameter W.

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Figure2.17 Formal Os(lll)/Os(ll) redox potential as a function of the average fraction of oxidized osmium sites for Qai,= 1 mM (dashed lines) or 1.2 M (solid line). From the slope it is possible to predict the lateral interaction parameters in Brown and Anson model, Equation 2.8. Taken from Ref [120].

Fig. 4 a Mean-field result (solid line) for the rescaled brush free energy per polymer as a function of the inverse interaction parameter 1/F- The infinite stretching resnlt is indicated by a horizontal dotted line, the broken straight line denotes the infinite stretching result with the leading correction dne to the finite end-point distribntion entropy. b Rescaled lateral pressnre within mean-field theory (solid line) compared with the asymptotic infinite-stretching result (dotted line)... 

It is important to emphasize here that, theoretically, if a solid mixture is ideal, intracrystalline distribution is completely random (cf section 3.8.1) and, in these conditions, the intracrystalline distribution constant is always 1 and coincides with the equilibrium constant. If the mixture is nonideal, we may observe some ordering on sites, but intracrystalline distribution may still be described without site interaction parameters. We have seen in section 5.5.4, for instance, that the distribution of Fe and Mg on Ml and M3 sites of riebeckite-glaucophane amphiboles may be approached by an ideal site mixing model—i.e.. 

If the solid solution is regular, with an interaction parameter W (cf. section 3.8.4), the equilibrium distribution curve is defined by... 

As outlined in section 10.1, the presence of trace elements in crystals is attributable to several processes, the most important one being the formation of substitutional solid solutions. The ease of substitution depends on the magnitude of interactions between trace element and carrier. We have already seen (section 3.8.4) that macroscopic interaction parameter W can be related to microscopic interactions in a regular solution of the zeroth principle ... 

Empirical and semi-empiriad approaches. The problem of making dieoretical estimates for the interaction coefficients for the liquid phase has been tackled in different ways by various authors. Kaufman and Bernstein (1970) considered that the liquid state would exhibit the lowest repulsive forces of all the states of condensed matter and that a description of the interaction parameters for the liquid state would be the best basis for die prediction of interaction parameters for various solid phases. 

Koller, H., Englehardt, G., Kentgens, A. P. M., and Saur, J. (1994). NMR spectroscopy of solids Interpretation of quadrupole interaction parameters and chemical shifts. J. Phys. Chem. 98, 1544-51. 

For dilute solid solutions A(+B],B2,...) the interaction parameter formalism as outlined in Section 2.2 is adequate. 

Fig. 6.45 Two-dimensional phase diagram as a function of chain composition for a blend of two diblocks (

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