Unperturbed Chain Dimensions

The conformation of polymer chains in an ultra-thin film has been an attractive subject in the field of polymer physics. The chain conformation has been extensively discussed theoretically and experimentally [6-11] however, the experimental technique to study an ultra-thin film is limited because it is difficult to obtain a signal from a specimen due to the low sample volume. The conformation of polymer chains in an ultra-thin film has been examined by small angle neutron scattering (SANS), and contradictory results have been reported. With decreasing film thickness, the radius of gyration, Rg, parallel to the film plane increases when the thickness is less than the unperturbed chain dimension in the bulk state [12-14]. On the other hand, Jones et al. reported that a polystyrene chain in an ultra-thin film takes a Gaussian conformation with a similar in-plane Rg to that in the bulk state [15, 16]. 

Conformational characteristics of PTFE chains are studied in detail, based upon ab initio electronic structure calculations on perfluorobutane, perfluoropentane, and perfluorohexane. The found conformational characteristics are fully represented by a six-state RIS model. This six-state model, with no adjustment of the geometric or energy parameters as determined from the ab initio calculations, predicts the unperturbed chain dimensions, and the fraction of gauche bonds as a function of temperature, in good agreement with available experimental values. 

The unperturbed chain dimensions of near-monodisperse atactic PS are evaluated from intrinsic viscosity measurements. Negative values for the temperature coefficient of chain dimensions are found. Under conditions where specific solvent effects are eliminated or minimized, measurements yield results in excellent agreement with the theoretical predictions for atactic PS. 

Molecular mechanics techniques are employed to calculate the molecular structure and conformational energies of model compounds for polyphenylmethylsllylene and polysilastyrene. In both isotactic and syndiotactic stereochemical forms. The structural and conformational energy data provided are used to calculate, by application of the RIS theory, the unperturbed chain dimensions, given as the characteristic ratio, and its temperature coefficient. 

Ab initio calculations with full geometry optimization on diphenyl carbonate and diphenylpropane are carried out to determine the bond geometries and the conformational energies and then to compute the unperturbed chsin dimensions of the bisphenol A polycarbonate. Application of these results to the RIS model of the PC chain leads to the prediction of the unperturbed chain dimension. 

Conformational Energy and Unperturbed Chain Dimensions of Polypeptide Homopolymers ... 

In summarizing the intrinsic viscosity relations presented in this section, it must be admitted that they represent nothing more than rather small semi-empirical refinements of the Flory excluded volume theory and the Flory-Fox viscosity theory. For a large fraction of the existing body of experimental data, they offer merely a slight improvement in curve-fitting. But for polymers in good solvents it is believed that a more transcendental result has been achieved. The new equations permit more reliable assessment of unperturbed chain dimensions in such cases, and in some instances (e. g., certain cellulose derivatives see Section III B) they offer possible explanations of heretofore paradoxical solution behavior. 

In this chapter the viscosity method developed and illustrated in the previous sections is systematically applied to the existing experimental data, and the resulting values of the unperturbed chain dimensions are tabulated for polymers of various kinds. 

Table 7. Unperturbed chain dimensions calculated from K values. I. Addition polymers... 

A and B are short- and long-range interaction parameters (A is also termed the unperturbed chain dimension), < R2)o/2 is the mean-square end-to-end distance of the chain in the unperturbed state, P the binary cluster integral, and nio is the molecular weight of a segment. According to the Kurata-Fukatsu-Sotobayashi-Yamakawa theory 65), ho(z) is related to z by... 

Fig. 34. Temperature dependence of the unperturbed chain dimension A, estimated by method 2B (Eq. (32)), for a cellulose diacetate (CDA) fraction in acetone (open circles), and of the number of the solvating solvent molecules at infinite dilution si of a CDA whole polymer in acetone (black circles) 7)...

It can be deduced therefore, that the rapid decrease in the unperturbed chain dimension with increasing temperature is the dominant cause of the large negative value of d In [r ]/dT. The effect of the excluded volume is negligible. 

Two conflicting theoretical views concerning the flexibility of polymer chains and the role of the volume effect and the draining effect on fry] are discussed in the literature polymer chains of typical flexibility such as vinyl polymer chains, and a large value of Ip] can be interpreted in terms of the excluded volume effect (view point A) polymer chains are semi- or inflexible and their large unperturbed chain dimension is mainly responsible for a large [ry] (view point B). The former has its foundation on the two parameter theory 110. Untill 1977 these inconsistencies constituted one of the most outstanding problems yet unsolved in the science of polymer solutions. 

Table 13. The unperturbed chain dimension A estimated by various methods for solutions of cellulose and its derivatives 7-119)... 

For indefmitly large M/(qML), an unperturbed polymeric chain may be regarded as Gaussian. For this chain, q is related to the unperturbed chain dimension Aw at infinite Mw by... 

Fig. 40. Plot of the unperturbed chain dimension A against the total degree of substitution for cellulose acetate (CA)-solvent systems. Solid line CA-DMAc chain line asymptotic A at the limit of the dielectric constant s = I broken line A of cellulose at the free rotational state7 asymptotic A value at the limit of s = 1 asymptotic A value at the limit of e = 1 and = 0 (j formamide ) water (j DMAc O- acetone -O THF O TCE...

Fig. 41. Dependence of the most probable unperturbed chain dimension A on the dielectric constant e of the solvent for cellulose acetate (CA)-solvent systems7). Broken line the unperturbed chain dimension of a hypothetical cellulose with free internal rotation. Open marks Am values estimated from experimental data closed marks asymptotic Am values at the limit of e = 1. Circles CA(0.49) diamond CA(1.75), triangles CA(2.46) rectangle CA(2.92)...

CD molecules are partially free draining chains and the negative temperature dependence of the limiting viscosity number fn] can be attributed to the temperature dependence of the unperturbed chain dimension A. 

The unperturbed chain dimension A is relatively large, being larger in solvents having higher dielectric constants e The flexibility of the CD molecule depends on the polarity of the solvent. 

W. J. Welsh, L. DeBolt, and J. E. Mark, Macromolecules, 19, 2978 (1986). Conformational Energies and Unperturbed Chain Dimensions of Polysilane and Poly(dimethylsilylene). 

Now in some cases a direct study of a polymer under 0 conditions is not feasible or, more frequently, not desired. The need to work under 0 conditions when determining unperturbed chain dimensions might be circumvented if one could rely on theories connecting accurately measurable quantities such as intrinsic viscosity, second virial coefficient etc. obtained in good solvents, with the chain expansion factor. 

However as Takahashi and Nagasawa also point out, the fact that part of the short range interactions which determine the unperturbed chain dimensions of polyions are electrostatic in nature, inclines one to believe that the unperturbed dimensions should be dependent on ionic strength. 

Comparison of Chain Dimensions. Knowledge of the intrinsic viscosities and molecular weights of a series of PMDA/DAPE polyamic acids allows estimation of the unperturbed chain dimensions. Comparison may then be made with the cured polyimide, with results obtained by other workers, and with calculated values. The expressions in the literature using values for [n] obtained in good solvents generally involve extrapolation of [t)]/M toM = 0, where excluded volume effects are presumed to be minimal (12-14). Although this method is not strictly valid, it is useful for comparison purposes when direct measurement of the dimensions is impractical. The data in Table I for the polyamic acid in distilled NMP and in the poorer mixed solvent NMP/dioxane yield (see Figure... 

N, indicating that the solvent quality is substantially reduced by addition of salt, as in Wallach s study. If the extrapolation to M = 0 is not sufficient to eliminate all excluded volume contribution, then the estimated unperturbed dimensions could be affected. The samples used in reference 3 were also of varying polydispersity, and the intrinsic viscosity molecular weight relation showed more uncertainty than we have observed in this study, which is also sufficient to explain the difference in estimated unperturbed chain dimensions. 

---