Gauche state

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

The columns are indexed by the three states of bond i, the rows are indexed by the three states of bond i—1, and the order of indexing is t, g+, g. The statistical weight denoted by cr, which is approximately exp (-250/T), is the first-order weight of a gauche state relative to a trans state. The second-order interaction, which arises from the pentane effect where a bond pair is g gT, is weighted by to, which is approximately exp (-1000/T). 

It is interesting to note that the mS values calculated with the gauche states of all C-C bonds at 120" (solid line) disagree with the NLDE constants measured for all the a,w dibromoalkanes except 1,3-dibromopropane. When the terminal C-C bonds are permitted to adopt g — 80", all other C-C bonds retaining gauche states at 120", the calculated NLDE constants (dashed lines) are in much better agreement with those observed for all the a, —dibromoalkanes except 1,3-dibromopropane. This behavior has a simple explanation in terms of the nonbonded steric and electrostatic interactions (21) resulting from rotation about the terminal C-C bonds. 

The sequence of low conductance values L is attributed to isomers of alkanedithiols with gauche defects. This interpretation is also supported by the experimentally observed temperature dependence of L conductance values. The alteration of gauche states appears to be an activated process [244]. 

In spite of the fact that a six-state model is a natural choice for describing the conformational distribution in PIB chains, a simpler model can be obtained by labeling all the bond conformations in the domain [60,160°] and all those in the domain [-60, - 180°I with the symbols g+ and g , respectively. This leads to a four state model formally analogous to the older ones but leaves the exact location of the gauche states undefined. 

The POM chain is discussed in terms of trans and gauche rotational stetes and is compared with PE and PDMS. Examination of distances between non-bonded atoms and groups in various conformations suggest dispersion interactions between O and CHj as being primarily responsible for preference for the gauche states coulombic interactions also favor the gauche conformation, but should be comparatively small. 

The conformational energies of the lower members of POM, 2,4-dioxapentane and 2,4,6-trioxaheptane are estimated by the empirical force field method. The gauche states of the Internal rotation around the skeletal C—0 bonds are successfully predicted to be of lower energies in both molecules. In order to calculate the unperturbed dimension and dipole moment of POM, RIS approximations are made by using the results obtained from the force field calculations on 2,4,6-trioxaheptane. Although these parameters are significantly different from those estimated earlier, they reproduce the observed values fairly well. 

In this study, the dipole moments at 298 K and the corresponding temperature coefficient of PDTC are calculated in the RIS approximation. The results are compared to the values determined by experiment. The results indicate that an extra stabilization energy of about 3.8 kj mol-1 must be added to these gauche states relative to trans state. This provides evidence of a large attractive sulfur gauche effect in the polysulfides, about equal in magnitude to that found for the analogous POM. 

The conformational energy E(op) associated with gauche states about CH2-CH2 bonds in polyethylene sulfide) (PSE) is estimated from the RIS analysis of experimental dipole moments and their temperature coefficients corresponding to the alternating copolymer of pentamethylene sulfide and ethylene sulfide (PXS) as well as to 1,2-bis(butylthio)ethane. 

Semiempirical potentials are used to compute conformational energies as function of rotations over the backbone bonds the results of these calculations indicate that skeletal C—0 bonds are always placed in trans conformation, whereas gauche states over C—C bonds have an energy of about 2 kJ mol-1 lower than their trans conformation. 

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. 

Hydroxyl-terminated POET chains are end-linked into noncrystallizable trifunctional networks using an aromatic triisocyanate. The networks thus obtained are studied with regard to their stress-strain isotherms. The analysis of the temperature coefficient of PDET in terms of the RIS model confirms the results obtained from NMR studies, according to which the gauche states... 

Dihedral angles for the gauche states are located (2tt/3 — A <(>) from the dihed atom bearing the acetate group. For these bonds, a larger value of A , 0.35,... 

Reduction of the unperturbed dimensions of the main chain is calculated when ethyl groups are attached to a polyethylene backbone. Values of most of the paramters are taken from the well-known RIS model for unperturbed polyethylene (Abe, A. Jernlgan, R. L. Flory, P, J, J, Am. Chem. Soc. 1966, 88, 631) the bond angle is 112°, gauche states are located at 60° trans 180°l. First- and second-order interactions are weighted by using o 0.43 and m 0.034 (for 300 K). An additional statistical weight, denoted by t, is required at each bond to an atom that constitutes a trifunctional branch point (Flory, P, J, Sundararajan, P. R. DeBolt, L. C. J. Am. Chem. Soc. 1974, 96, 50151. Calculations are performed with t = 0 and t = [Pg.410]

It is interesting to note that the PDMS chain and polyphosphate chain have approximately the same characteristic ratio. Isolated gauche states, of relatively high spatial extension, are more prevalent in the polyphosphate chain, but pairs of gauche states ri-rigri of the same sign are less prevalent and the two effects largely offset one another. 

Fully saturated alkyl chains are extremely flexible, with a difference in energy between a trans C-C bond and gauche+ or gauche states of only = 0.8 kT at room temperature. Therefore, the methylene chain of a typical surfactant (e.g. SDS) can exist in a large number of low energy conformations in a micellar aggregate. 

A theoretical model has been developed by Gruen (26) which helps to harmonize the apparent experimental discontinuities. The model assumes the existence of a hydrocarbon core completely devoid of headgroups, counterions, and most importantly, water. The methylene chains are men allowed to exist in a number of conformations (trans, gauche+, and gauche states for each C-C bond), and are, on average, constrained to pack at liquid hydrocarbon density. Each chain... 

Until recently, a common tendency has been to account for the behavior of polysilanes in terms of anti (often called trans) and gauche states, following the pattern familiar from hydrocarbons. From the discussion above it follows that the exact A conformation... 

If the geometry of VI and VII is very similar to bicyclo [2.2.1] heptane, and if the gauche states are more important in the C-O C-O bond than in the C-C C-O bond, it may be concluded that Vll is less stable than VI. In fact, the add-hydrolysis data112 show that VII is more reactive than VI. Hie difference of the hydrolysis rates is affected by the difference of the angles between C3-C7-C4 and C1-O7-C4 as well as the difference of Eliel s rabbit-ear" effect between O2-CV, and O2-O7. 

The gauche states are also observed in crystalline polymers, polyoxymethy-lene6,7,157-160, polyoxyethylene6,7,161,162, poly-1,3-dioxolane163, and poly-1,3-dioxe-pane164 by X-ray analysis. 

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