Dipole moment mean square

Mean-square end-to-end distance Mean-square radius of gyration Mean-square dipole moment Mean-square optical anisotropy Optical configuration parameter... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

In table I we present the molar Kerr constants and mean square dipole moments of three fluorinated polymers, poly (trifluoroethylene) (PFjE), polylvinylidene fluoride) (PVF2) and poly(fluoromethylene) (PFM), dissolved in p-dioxane. The results show the sensitivity of mK to the degree and type of fluorination varying over an order of magnitude and also changing sign. Calculations of mK and for comparison are in progress (5). 

The linear response of a medium to a weak applied electric field is characterized by the dielectric constant <0. From this experiment we deduce the molar polarization mP which is related to the mean square dipole moment by... 

Tables 1, 2, and 3 present a set of five alcohols. In Table 1, it should be noted that while MM3(96) calculates the magnitude of the dipole moment to be essentially the same for the entire set of molecules, MM3(2000) is superior in reproducing the experimental dipole moments. This is demonstrated by comparing the root mean squared deviation of 0.0878 Debye in MM3 to the 0.0524 Debye deviation in MM3(2000). (All of the experimental values except where notes are stark effect measurements determined from microwave spectra.)...

It is known that ab initio methods are not accurate in reproducing or predicting molecular dipole moments. For example, a typical basis set minimization with no additional keywords was carried out, and the results show that the computed magnitude of the dipole moment is not particularly accurate when compared with experimental values. For alcohols, MP2 has a root mean squared deviation of 0.146 Debye, while HF had a deviation of 0.0734 Debye when measured against the experimental values. 

The differences between ab initio and molecular mechanics generated dipole moments were discussed. The MM3(2000) force field is better able to reproduce experimental dipole moments for a set of forty-four molecules with a root mean squared deviation (rmsd) of 0.145 Debye compared with Hartree-Fock (rmsd 0.236 Debye), M0ller-Plesset 2 (rmsd 0.263 Debye) or MM3(96) force field (rmsd 0.164 Debye). The orientation of the dipole moment shows that all methods give comparable angle measurements with only small differences for the most part. This consistency within methods is important information and encouraging since the direction of the dipole moment cannot be measured experimentally. 

According to the Kirkwood theory of polar dielectrics, simple relations (23) between molecular dipole moment vectors and the mean-square total dipole moment of water clusters can be used to compute the static dielectric constant of water. As the normalized mean-square total dipole moment increases towards unity, theory predicts decreases in the static dielectric constant. Since MD results indicate that the mean-square total dipole moment of interfacial water is greater than that for bulk water (48), the static dielectric... 

If electron clouds of cations and anions are deformable in an electric field and thus have polarizabilities of a+ and a, the value of the dipole moment induced in the cations by the presence of anions (p +) and induced in the anions by the presence of cations (p+ ) are, respectively, proportional to a+/P and a /r. The electric field acting on the cations is proportional to -a+]l L + /r, where 71I+ is the mean square dipole moment of the cations. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

Polypeptides are electrically polar, carrying permanent dipoles at the planar CO-NH groups of the backbone chain and generally at some atomic groups of the side-chains. Because of the vector nature of dipoles, we must speak of the mean-square dipole moment, averaged over all possible conformations of the backbone chain and all accessible orientations of the side-chains when the dipolar nature of a polypeptide in solution is considered. The of a polypeptide thus may depend on what conformation the molecule assumes in a given solvent. 

It can be shown that the < 2> of an interrupted helical polypeptide is expressed by Eq. (C-3) for random-coil unit. Precisely, this replacement is permissible if we neglect excluded-volume effects. Nagai (107) has shown theoretically that these effects on < 2> are virtually absent in randomly coiled macromolecules, even when they are appreciable on the molecular dimensions. It is our belief that Nagai s conclusion may apply to interrupted helical polypeptides as well. 

The secondary dispersions reported so far have been very weak. It is therefore interesting to examine the theoretical strength of this relaxation, (A e)ch, in comparison with that of the rotational relaxation, (A e)rot. For a sufficiently long polypeptide chain, the mean-square dipole moment is expressed as3... 

Today generator matrices F are known for many properties,10 among them the population of different conformers, the relative stability of macromolecular diastereoisomers, the mean-square end-to-end distance, the radius of gyration, the molecular dipole moment, the molecular optical anisotropy (and, with it, the stress-optical coefficient, the Kerr effect, depolarized light scattering, and the... 

Previous treatments of the mean-square end-to-end distance and the dipole moment of chain molecules conforming to the RIS model [Birshtein, T. M. Ptitsyn, O. B. J. Tech. Phys., USSR 1959,29, 1048 Birshtein, T. M. High Molac. Cmpds., USSR 1959, 1, 798, 1086 Ufson, S. J. Chem. Phys. 1959, 30. 964 Nagai, K. J. Chem. Phys. 1959,3/, 1169 Hoeve, C. A. J. J. Chem. Phys. 1960, 32, 8881 are restricted to chains (a) which are very long, and f>) in which identical structural units repeat with unerring regularity. Both of these restrictions are removed without approximation by the procedure presented. Numerical calculations are simultaneously simplified. 

Response of the mean square dipole moment, < J2>, to excluded volume is evaluated for several chains via Monte-Carlo methods. The chains differ in the manner in which dipolar moment vectors are attached to the local coordinate systems for the skeletal bonds. In the unperturbed state, configurational statistics are those specified by the usual RIS model for linear PE chains. Excluded volume is introduced by requiring chain atoms participating in long-range interactions to behave as hard spheres. 

A RIS model with neighbor dependence is used to calculate mean-square dipole moments and their temperature coefficients for PDMS chains over a wide range of molecular weight. Chain conformational energies required in the calculations are obtained from a previous analysis of the random-coil dimensions of PDMS chains in the limit of large x (S 116). 

Dielectric constants are determined for pure liquid dimethylsiloxane oligomers. Mean-square dipole moments, calculated from the Onsager equation, are in good agreement with predicted values based on the RIS model (S 117) with neighbor dependence and chain conformational energies obtained in an independent analysis of the random-coil dimensions of such chains. In addition, the observed temperature coefficients of are in qualitative agreement with calculated results. 

The mean-square dipole moments of POE and POMg are determined from dielectric constant measurements on dilute solutions in benzene. The values obtained are in good agreement with those predicted using the RIS models for these chains. In addition, the unperturbed dimensions of POMg are calculated as a function of molecular weight using the RIS theory. 

Samples of polyd,3-dioxocane) (-Ch OICf lsO-I and poly(1,3-dioxonane) [-Ch OICh lgO-] are prepared, and fractions of both polymers are studied in solution by means of dielectric constant measurements from 20 to 60°C. Mean-square dipole moments thus obtained are compared with theoretical results based on the RIS models of the two chains. Good agreement is obtained. 

Mean-square dipole moments of polylthiodiethylene gycol), an alternating copolymer of ethylene oxide and ethylene sulfide, are determined from dielectric constant measurements on dilute solutions of the polymer in benzene. Since the configuration-dependent properties of one of the parent homopolymers, PES, are unknown, because of its insolubility in ordinary solvents, the results are preferably compared with those of POE chains. It is found that the dipole moments of polylthiodiethylene glycol) are somewhat larger than those of POE. 

A RIS model with neighbor interactions is used to calculate mean-square unperturbed dimensions and dipole moments for vinyl chloride chains having degrees of polymerization ranging from x = 1 to 1 50 and stereochemical structures ranging from perfect syndiotacticity to perfect isotacticity. Conformational energies used in these calculations are those which have been established in the analysis based on the stereochemical equilibration of 2,4-dichloro-n-pentane by Flory and Williams (A 002). 

Dipole moments are calculated of perturbed polylvinyl chloride), polylvinyl bromide) and polylp-chlorostyrene). Recent work iMacromolecules 1984, 17, 625 1985, 18, 2236) has shown that the mean square dipole moment, , of model chains with a finite number of bonds, n, may depend on excluded volume even if 0 - 0. 

Mean-square dimensions and dipole moments of p-chlorostyrene chains are calculated as a function of their stereochemical structure, degree of polymerization, and temperature. Theoretical arguments and experimental evidence indicate that p-chlorostyrene and styrene chains differ little in conformational energy. Therefore, the present investigation employs conformational energies... 

The mean-square dipole moments of PPCS chains are calculated as a function of stereochemical composition using the RIS analysis recently published for PS. The calculations are in good agreement with the average of experimental results for atactic PPCS chains estimated to contain ca. 35% meso diads. The temperature coefficient is calculated to be negative in agreement with available experiments. 

Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

Values of the mean-square dipole moment, , of PDEI are determined as a function of temperature. The value of the dipole moment ratio is 0.697 at 303 K. Trifunctional model networks are prepared. From thermoelastic experiments performed on the networks over a temperature range 293 - 353 K, it is found that the value of the temperature coefficient of the unperturbed dimensions amounts to 1.05 0.17 K-1. The dipole moments and the temperature coefficients of both the dipole moments and the unperturbed dimensions are critically interpreted in terms of the RIS model, and are found to be in a reasonable agreement. 

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