Acentric order parameter

The effective electro-optic coefficient, r, of a material is related to chromophore number density, N, chromophore molecular first hyperpolarizability, P, and acentric order parameter, , by... 

Avogadro s number, p is material density, and MW is chromophore molecular weight. In the absence of chromophore-chromophore interactions (the independent particle or gas model), the chromophore acentric order parameter arising from electric field poling can be expressed as... 

Figure 2. Variation of acentric order parameter with average separation distance between chromophores is shown for the chromophores (and electrostatic interactions) of Table n.

A comparison of theory and experiment establishes that it does not make sense to derivatize chromophores such as the disperse (DR) and DANS other than to improve their solubility. The attenuation of electro-optic activity is not a problem for these systems. We can gain only for those systems where optical nonlinearity is seriously attenuated and where we are in the steep region of the acentric order parameter attenuation as a function of variation of chromophore minor axes dimensions. For such cases, a change of minor axes dimensions by 1 or 2 angstroms can lead to factors of 2 and 3 increase in maximum realizable electro-optic coefficient. 

By chromophore-polymer composite materials, we refer to chromophores physically incorporated (dissolved) into commercially available polymer materials such as amorphous polycarbonate (APC) [58] finm Aldrich Chemicals. Chromophore and polymer are dissolved in a suitable spin-casting solvent, such as cyclopentanone. Spin-cast thin films are heated to near the glass transition temperature of the composite material (which will vary with chromophore concentration due to the plasticizing effect of the chromophore). Acentric chromophore order is induced by electric field poling. If one assumes that the presence of the polymer host does not stericaUy hinder the reorientation of the chromophores under the influence of the poling field, the order parameter can be readily calculated. We have already noted that if chromo-phore-chromophore intermolecular electrostatic interactions are neglected then (cos d) = fiF/5kT and the order parameter will be independent of chromophore concentration (or number density, N). Intermolecular electrostatic interactions can be treated at several levels of sophistication. 

At each stage of the refinement of a new set of parameters, the hat matrix diagonal elements were calculated in order to detect the influential observations following the criterium of Velleman and Welsh [8,9]. The inspection of the residues of such reflections revealed those which are aberrant but progressively, these aberrations disappeared when the pseudo-atoms model was used (introduction of multipoler coefficients). This fact confirms that the determination of the phases in acentric structures is improved by sophisticated models like the multipole density model. 

The carbon di oxi de/lemon oil P-x behavior shown in Figures 4, 5, and 6 is typical of binary carbon dioxide hydrocarbon systems, such as those containing heptane (Im and Kurata, VO, decane (Kulkarni et al., 1 2), or benzene (Gupta et al., 1 3). Our lemon oil samples contained in excess of 64 mole % limonene so we modeled our data as a reduced binary of limonene and carbon dioxide. The Peng-Robinson (6) equation was used, with critical temperatures, critical pressures, and acentric factors obtained from Daubert and Danner (J 4), and Reid et al. (J 5). For carbon dioxide, u> - 0.225 for limonene, u - 0.327, Tc = 656.4 K, Pc = 2.75 MPa. It was necessary to vary the interaction parameter with temperature in order to correlate the data satisfactorily. The values of d 1 2 are 0.1135 at 303 K, 0.1129 at 308 K, and 0.1013 at 313 K. Comparisons of calculated and experimental results are given in Figures 4, 5, and 6. 

Once this function is determined, it could be applied to any substance, provided its critical constants Pc, T, and V are known. One way of applying this principle is to choose a reference substance for which accurate PVT data are available. The properties of other substances are then related to it, based on the assumption of comparable reduced properties. This straightforward application of the principle is valid for components having similar chemical structure. In order to broaden its applicability to disparate substances, additional characterizing parameters have been introduced, such as shape factors, the acentric factor, and the critical compressibility factor. Another difficulty that must be overcome before the principle of corresponding states can successfully be applied to real fluids is the handling of mixtures. The problem concerns the definitions of Pq P(> and Vc for a mixture. It is evident that mixing rules of some sort need to be formulated. One method that is commonly used follows the Kay s rules (Kay, 1936), which define mixture pseudocritical constants in terms of constituent component critical constants ... 

Analysis of high-pressure PVT data or of generalized charts by Equation 22 reveals that b is about 1/10, usually a little less. Unfortunately, it is very difficult to detect from such data trends of o with either temperature or molecular complexity. I liquid-phase isotherms were infinitely steep, then one would expect b to increase with Tr and to decrease with molecular complexity (as reflected, e.g., by decreasing values of Zc, or by increasing values of the acentric factor o>). However, real liquids are compressible, and, moreover, the apparent dependence of on Tr and, say, a> is known to be influenced strongly by the method and by the data base used for determination of numerical values of the equation-of-state parameters. The best one can say is that for practically any application b is of the order 1/10, and that its temperature dependence is usually less important than that of . 

The parameter is a general function of the acentric factor ca, while k is a parameter to be found by regression. The evaluation of accuracy showed an error in correlating the vapour pressure under 1%, typically between 0.2 and 0.3%. The accuracy of PRSV is by an order of magnitude better as PR EOS and the same as Antoine equation. SRK2 and PRSV are of comparable accuracy. 

If the departure from equation (35) is not too large, it can be treated as a perturbation. The effect of non-central interactions on the second virial coefficient is second order and it is very difficult to distinguish between any of the non-central interactions on the basis of the behaviour of In essence, it is possible to fit the properties of many pure substances to equations based on simple corresponding states and additional terms whose magnitude is proportional to a perturbation parameter that is a measure of the deviation from central forces. One such perturbation parameter is Pitzer s acentric factor. 74,76 another is Rowlinson s In a homologous series the number of carbon atoms in the chain constitutes yet another measure of the perturbation. It can be shown that there is a simple relation between the different factors. ... 

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