Fractional polarity, theory

The wetting behavior of polymers is reviewed beginning with the thermodynamic conditions for contact angle equilibrium. The critical surface tension of polymers is discussed followed by some of the current theories of wettability, notably the theory of fractional polarity and theories of contact angle hysteresis. The nonequilibrium spontaneous and forced spreading of polymer liquids is reviewed from two points of view, the surface chemical perspective and the hydrodynamic perspective. There is a wide di.sperity between these two viewpoints that needs to be resolved inorder to establish the predictive relations that govern spreading behavior. 

Numerous assumptions have been made in developing this theory of fractional polarity, most of which lead to its being limited to systems where at least one of the components is relatively non-polar. The theory breaks down rather quickly when both phases are polar, especially if the interfacial interactions lead to molecular rearrangements. Moreover, the theory has been criticized because it ignores the possibility of induced polarity at the interface between polar and non-polar components. 

The theory of fractional polarity can be used to separate dispersion and polar interaction terms from contact angle data. Combining Young s equation (Eq. (1)) and the equation for the work of adhesion (Eq. (7)) gives. 

The equilibrium wetting behavior of simple liquids (including low MW polymers) on low polarity polymer surfaces is well documented and consistent with Gibbsian thermodynamics within specific constraints. Empirical relationships have been established between observed contact angles and polymer surface chemical composition. Predictive relationships have been established between contact angles and polymer substrate surface chemistry based on the theory of fractional polarity surface energies can be factored into dispersion and polar components. These relationships seriously break down with increasing polarity of either the liquid or solid surface. 

The theory of fractional polarity combined with Yoimg s equation provides another means of estimating the surface tension of the sohd (3). Apphcation of the harmonic mean approximation leads to the relation... 

An alternative treatment [153, 195] is based upon (18), where the work of adhesion is calculated using the theory of fractional polarity. Intermolecular energies are assumed to consist of additive nonpolar (i.e., dispersive) and polar components. Thus, the work of adhesion and the pure-component surface tensions can be separated into their dispersive (superscript d) and the polar (superscript p) components, such that ... 

Throughout this chapter it is assumed that the intensity of the polarized exciting pulse is sufficiently low that only a small fraction of the fluorophores are ever excited.(29) High light intensities are treated elsewhere/73 74) The following subsection presents some very general and basic theory that is not specifically directed toward rotational relaxation of DNA. The reader may wish to skip directly to the final result in Eq. (4.15), or even skip this subsection entirely. 

The behavior of many fillers can be roughly treated as spheres. Current theories describing the action of these spherical-acting fillers in polymers are based on the Einstein equation (8.1). Einstein showed that the viscosity of a Newtonian fluid (t/J was increased when small, rigid, noninteracting spheres were suspended in a liquid. According to the Einstein equation, the viscosity of the mixture (17) is related to the fractional volume (c) occupied by the spheres, and was independent of the size of the spheres or the polarity of the liquid. 

Chapter 8 by W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, entitled Fractional Rotational Diffusion and Anomalous Dielectric Relaxation in Dipole Systems, provides an introduction to the theory of fractional rotational Brownian motion and microscopic models for dielectric relaxation in disordered systems. The authors indicate how anomalous relaxation has its origins in anomalous diffusion and that a physical explanation of anomalous diffusion may be given via the continuous time random walk model. It is demonstrated how this model may be used to justify the fractional diffusion equation. In particular, the Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker-Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. Thus, the authors show how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended via the continuous-time random walk to yield the empirical Cole-Cole, Cole-Davidson, and Havriliak-Negami equations of anomalous dielectric relaxation from a microscopic model based on a... 

While not directly relevant to H-bonds per se, a recent work compared the H/D fractionation factors for a number of small molecules, as computed at various levels of theory . The results indicated that the relative free energy of protiated versus deuterated species is rather insensitive to choice of basis set. Best results are achieved if polarization functions are added to all atoms, and correlation is recommended, but even SCF computations with a basis set as small as 3-21G can provide quite reasonable results. 

The present theories of the effects of solvents on the rates of polar (ionic) reactions do not permit a quantitative analysis of the above cited results. Fractions of AHp and ASp, due to solvation, apparently compensate each other, because the increase in the energy needed for desolvation is just compensated by equal contributions of the entropy (a more firmly bound or larger number of molecules are desol-vated). This compensation phenomenon is well known in organic chemistry. For instance, the difference between the activation enthalpies (AAH ) of the reaction of benzyl chloride with pyridine in DMF and CH3OH is equal to -5.3 kcal mole". ... 

The inclusion or omission of the permittivity of free space, So in these equations does not affect the discussion of the integer or simple fractional numerical factors, although it does change the units in which F or are reported (see Appendix).] Optical theory then relates the 2m polarization to the observed second harmonic intensity. Assuming that F has been correctly determined in terms of the fields as defined in (7.1) it has then to be expressed in terms of the molecular parameters. 

Kauffman and coworkers118 119 tried to fit the solvatochromic shifts of l-(9-anthryl)-3-(4-/V,/V-dimcthylanilino)propanc (83), relative to the hydrocarbon homomorph with the dimethylamino group replaced by H, to the dielectric non-ideality of solvent mixtures involving hexane with ethanol, tetrahydrofuran and dichloromethane. The shifts were not linear with the mole fraction of the polar component, and Suppan s theory of dielectric enrichment was applied to the data. It was found that the dielectric enrichment that can be calculated from the relative permittivities of the components and of the mixtures is not sufficient to account for the observed solvatochromic shifts, but that preferential solvation of the probe by the polar component is superimposed on this dielectric effect. Earlier,... 

In the present section, it is demonstrated how the linear response of an assembly of noninteracting polar Brownian particles to a small external field F applied parallel and perpendicular to the bias field Fo may be calculated in the context of the fractional noninertial rotational diffusion in the same manner as normal rotational diffusion [8]. In order to carry out the calculation, it is assumed that the rotational Brownian motion of a particle may be described by a fractional noninertial Fokker-Planck (Smoluchowski) equation, in which the inertial effects are neglected. Both exact and approximate solutions of this equation are presented. We shall demonstrate that the characteristic times of the normal diffusion process, namely, the integral and effective relaxation times obtained in Refs. 8, 65, and 67, allow one to evaluate the dielectric response for anomalous diffusion. Moreover, these characteristic times yield a simple analytical equation for the complex dielectric susceptibility tensor describing the anomalous relaxation of the system. The exact solution of the problem reduces to the solution of the infinite hierarchies of differential-recurrence equations for the corresponding relaxation functions. The longitudinal and transverse components of the susceptibility tensor may be calculated exactly from the Laplace transform of these relaxation functions using linear response theory [72]. 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

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