Temperature dependence of unperturbed dimensions for isotactic poly(2-hydroxyethyl methacrylate)

The unperturbed dimensions of isotactic poly(2-hydroxyethyl methacrylate) (PHEMA) were evaluated from intrinsic viscosity measurements in water, ethanol, 1-propanol, 2-propanol, and 2-butanol under θ conditions over the temperature range of 3.7–32.1°C. The smallest value of unperturbed dimensions (K_θ) and the largest negative temperature dependence of unperturbed dimensions and the polymer–solvent interaction parameter (B) were obtained in aqueous θ solvent relative to the corresponding organic θ solvents. These results were interpreted by the hydrophobic interaction between the hydrophobic groups of isotactic PHEMA and water solvent. The temperature coefficient of the unperturbed dimensions, d ln〈r〉/dT, obtained in this study has a negative value of ?1.44 × 10^?3 deg^?1 under chemically similar θ solvents such as ethanol, 1-propanol, 2-propanol, and 2-butanol where specific solvent effects are eliminated or minimized. In order to obtain the thermodynamic parameters for mixing between isotactic PHEMA and solvents, the plots of the polymer–solvent interaction parameter versus reciprocal absolute temperature (1/T) were carried out. Both the entropy of dilution and enthalpy of dilution show the negative values for water, methanol, and t-butanol, whereas the positive ones for ethanol, 1-propanol, 2-propanol, and 2-butanol. This result indicates that the solution of isotactic PHEMA behave as exothermal systems in the former class of solvents and endothermal ones in the latter class of solvents.     

Numerical estimation of unperturbed dimensions of regioirregular poly(3-ethylthiophene)s

The unperturbed chain dimensions of poly(3-ethylthiophene)s have been calculated using the full-relaxation optimization of conformational energies and the chain statistical mechanics with a rotational isomeric state model of two states. The computation indicates that the conjugated polymer with side groups is more flexible than without, and that the orientation of the ethyl group and the regioirregular sequences perturb the chain conformation to a certain extent. Specially, the calculated chain conformations under θ-conditions are more rigid than those observed in good solvent. This supports experiments showing that the chain dimensions of conjugated polymers are very sensitive to variations of intermolecular interactions.     

Estimation of unperturbed dimensions of poly(cyclohexyl) methacrylate from light scattering,osmometry and viscosity data

Dilute solution properties of poly(cyclohexyl) methacrylate were determined at various temperatures in a theta solvent by light scattering. osmometry and viscometry. The values of the unperturbed dimensions (< s²₌>/M), solvent-polymer interaction parameters and conformational parameter σ have been computed by applying the theories of Burchard-Stockmayer--Fixman, Kurata-Stockmayer, Fixman and Kurata-Stockmayer-Roig.     

Dilute solution properties of poly(styrene acrylonitrile) alternating copolymer

Kuhn-Mark-Houwink-Sakurada relations were obtained in methyl ethyl ketone N,N-di-methylformamide and dichlorethane at 30 for (styrene acrylonitrile) alternating copolymer. The values of the unperturbed dimensions. [K₀ or (r_o^?2/M)^1/2] and conformational parameter σ have been determined, using several graphical and semiempirical methods, and the results were compared with the direct determinations in a θ solvent. The best values for K_θ were obtained using the methods of Stockmayer-Fixman and Inagaki-Suzuki-Kurata. By comparing the values of σ for polystyrene, polyacrylonitrile, random and alternating (styrene-acrylonitrile) copolymers, it is to be concluded that the short-range interactions do not markedly influence the chain dimensions in solutions for random and alternating (styrene-acrylonitrile) copolymers.     

On connection between conformational and thermodynamic properties of poly-2,4-dimethylstyrene in various solvents

The unperturbed chain dimensions K_θ of polydimethylstyrene (PDMS) in 12 solvents were determined by the Stockmayer-Fixman procedure. It was found that the value of K_θ decreased monotonously with increasing solvent power (i.e. with increasing the exponent a in the relation $\text{[η] = K}{}_{\mathrm{\eta }}\text{M}{}^{\mathrm{a}}$) The unperturbed chain dimensions in θ-solvent were obtained by extrapolation of log K_θ to $\text{a =}\text{1}\text{2}$. They are equal to 0·064. Analysis of data obtained both in aromatic and non-aromatic solvents showed that the decrease of the unperturbed chain dimensions was proportional to the product (βN_s): K_θ^1,3 = K_{θ.a = 1 2}^{1 3} (1 – 2·5 × 10²¹βN_s) (β is the excluded volume of the chain units and N_s is the mean number of the absorbed solvent molecules). The values of N_s were determined by light scattering in the series of mixed solvents. In the non-aromatic solvents, the unperturbed chain dimensions decrease with increase of the density of the molecular packing. It is suggested that interaction of neighbouring bulky side groups of the polymer chain is decreased by the solvent and this replaces the potential energy minimum of the chain in the direction of more folded conformations.     

Unperturbed dimensions of polystyrene in mixed solvents at high temperature

At 371.5 K, which is the θ-temperature for polystyrene (PS) in 3-methyl cyclohexanol (MC), intrinsic viscosities [η] have been measured for PS samples of different relative molar mass M in mixtures of MC with a thermodynamically good solvent 1,2,3,4-tetrahydronaphthalene over the whole range of solvent composition. Eleven graphical procedures have been utilised and assessed in deriving the unperturbed polymer dimensions expressed as K_θ (in the relation $\text{[η] = K}{}_{\mathrm{\theta }}\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^3$ where α is the expansion factor). For those procedures concluded to be the most reliable, there was no influence of binary solvent composition: the value of K_θ = 78 (±1) × 10^?3 dm³ kg^?1 was the same as that obtained directly under θ-conditions.     

Solution properties of polyoxymethylene

Light scattering and viscosity have been measured at 25°C. for dilute solutions of six unfractionated polyoxymethylene samples in the mixed solvent hexafluoroacetone–water (mole ratio 1/1.7) slightly buffered with triethylamine. Dialysis equilibrium through porous Vycor glass thimbles indicates that the polymer is strongly solvated by the hydrate (CF₃)₂C(OH)₂, and this must be taken into account in evaluating weight-average molecular weights from the light-scattering data. Over the molecular weight range 23,000–185,000, the intrinsic viscosities (in deciliter per gram) follow the relation The corresponding unperturbed dimensions are σ = 2.3 ± 0.2 or r₀²/nl² = 10.5 ± 1.5.     

Random-coil dimensions of poly(methylphenylsiloxane) and their dependence on stereochemical structure

Rotational isomeric state theory was used to study the unperturbed dimensions 〈r²〉₀ of poly(methylphenylsiloxane) (PMPS) chains [Si(CH₃)(C₆H₅)? O? ]_x as a function of their stereochemical structure. The required conformational energies were obtained from semi-empirical, interatomic potential energy functions and from known results on poly(dimethylsiloxane). PMPS chains were found to differ from monosubstituted and disubstituted vinyl chains primarily in the larger distance of separation between groups in conformations giving rise to “pentanetype interactions.” In PMPS, the relatively large distance of separation, 3.8 Å, makes such in teractions attractive, particularly in the case of two phenyl groups; in contrast, such interactions are strongly repulsive at the ～2.5 Å separation characterizing vinyl chains. According to the calculated results, PMPS chains are very different from vinyl chains in that increase in isotacticity should cause a significant decrease in 〈r²〉₀ and increase in d ln 〈r²〉₀/dT. Comparison of theory with experimental results in the literature suggests that PMPS polymers which have been studied in this regard must have been significantly syndiotactic in stereochemical structure.     

Synthesis and solution properties of poly(diphenyl itaconate)

Solid diphenyl itaconate monomer was obtained by esterification in the presence of diphosphorus pentoxide and polymerized in bulk with AIBN as initiator. The non-film forming polymer powder was characterized by fractionation, viscosity measurements, light scattering and other techniques. The relation [n] = 3·6 × 10^?3$\text{M}$^0·70_w, obtained for toluene at 25° was extrapolated to θ-conditions by various procedures: the σ-value of 2·60 for unperturbed dimensions indicates a less pronounced influence of phenyl compared with other C₆ hydrocarbon substitutes.     

Molecular mechanics assessment of the configurational statistics of polyoxyethylene

Previous investigators have shown that statistical mechanical averages for configuration-dependent physical properties of long unperturbed polyoxyethylene chains are sensitive to the gauche–trans energy difference for rotation about C? C bonds. Agreement between theory and experiment could be obtained only by significant adjustment of this energy away from values predicted by semiempirical conformational energy computations. The present work examines the success of MM 2 in evaluating conformational properties of long unperturbed polyoxyethylene chains. Calculations are performed which identify the rotational isomers, and their energies, for the indicated bonds in CH₃OCH₂CH₂O? CH₂? CH₂? OCH₂CH₂OCH₃. These energies are used to assign statistical weights utilized in the configuration partition function for a rotational isomeric state chain with symmetric threefold interdependent rotations. The customary generator matrix scheme is employed to evaluate the mean-square unperturbed end-to-end distance, mean-square unperturbed dipole moment, and their temperature coefficients. Contrary to computational schemes employed previously, MM 2 is found to provide an estimate of the gauche–trans energy difference for rotation about C? C which is in harmony with the known dimensions and dipole moments of the unperturbed polymer. MM 2 also provides good estimates for most of the other parameters required in the rotational isomeric state treatment. A notable exception is provided by the gauche–trans energy difference for rotation about the C? O bond. This energy difference is overestimated by MM 2.     

Etude des dimensions moleculaires des polymeres dissous dans des melanges binaires de solvants polaires et non polaires—I. Polyvinyl-2 pyridine

We have studied the molecular dimensions of poly-2-vinylpyridine in solution in binary solvent mixtures consisting of a non polar and a polar component, viz. benzene-ethanol and benzene-chloroform. We have also studied the preferential solvation of the same polymer in the above mixtures using light scattering. We have observed a conformational transition of P2VP taking place in a composition region for each solvent mixture. This transition shows as a discontinuity in the unperturbed dimensions, in the long range interactions parameter and in the parameter of preferential solvation of the polymer. We think that this transition is related to the existence of two ordered structures of the polymer chain, one stable before and the other after the transition region.     

Conformational characteristics of poly(vinylpyrrolidone). solvent-dependence of the chain dimensions

Conformational energies as function of rotational angles over two consecutive skeletal bonds for both meso and racemic diads of poly(Nvinyl-2-pyrrolidone) have been computed. The results of these calculations were used to formulate a statistical model that was then employed to calculate the unperturbed dimensions of this polymer. The conformational energies are sensitive to the Coulombic interactions, which are governed by the dielectric constant, of the solvent, and to the size of the solvent molecules. Consequently, the calculated values of the polymeric chain dimensions are strongly dependent on the nature of the solvent, as it was experimentally found before.     

Rotational isomeric-state approximation for the unperturbed dimensions of a POLA polyester

Rotational isomeric-state theory has been applied to investigate chain configurations of a polyester prepared from 4′,5-(1,1,3-trimethyl-3-phenylindan) dicarboxylic acid and 2,2-bis(4′-hydroxyphenyl) propane (POLA polyester). Independent conformations for each repeat monomer unit of the chain have been assumed in the calculations of the unperturbed dimensions. Rotations about the oxygen-phenylene-carbon (O? ?? C) bonds are considered to be free with twofold symmetric potentials. The trans and cis conformations of the carbonyl-phenylene-carbon (O?C? ?? C) and the indan-carbonyl residues are assumed to have equal probability. Two rotational states, trans and cis, are assigned to the ester C? O bonds. Calculation of the reduced unperturbed dimensions (〈r₀²〉/M)_∞ with conformations thus assigned for the bonds in the repeat unit, and comparison with experiment (0.72 ± 0.02 Ų/g) indicate that the conformation in the ester C? O bonds is predominantly trans. An equation for the conformational potential as a function of rotational angle about the ester C? O bond has been formulated using data on potential barriers for low molecular weight compounds. This equation, yielding a potential difference between the cis the trans isomers of 2.5–3.0 kcal/mole, is in good agreement with the prediction made from the calculation of the unperturbed dimensions where a cis/trans ratio of 0.01 for the ester C? O bonds was obtained.     

Configurational characteristics of trans-1,4-polychloroprene: Experimental results on the unperturbed dimensions and their temperature coefficient

Polychloroprene [CCl?CH? CH₂? CH₂? ]_x of approximately 95% trans-1,4 stereochemical structure was prepared by low-temperature emulsion polymerization. Fractions, obtained by liquid–liquid precipitations were studied in toluene solutions at 30°C by viscometry and osmometry. In addition, force–temperature measurements were carried out on networks of the polymer in the amorphous state. The results obtained on the polymer solutions indicate that the unperturbed dimensions of trans-1,4-polychloroprene are essentially the same as those of trans-1,4-polybutadiene of the same molecular weight. This observation, that substitution of a relatively large Cl atom for one of the methine H atoms in the trans-1,4-polybutadiene repeat unit has little effect on the chain dimensions, suggests that this increase in substituent size is offset by the fact that the length of a C? Cl bond is very much greater than that of a C? H bond. The results obtained on the polymer networks indicate that the unperturbed dimensions of trans-1,4-polychloroprene decrease significantly with increasing temperature, as has also been reported for both trans-1,4-polybutadiene and trans-1,4-polyisoprene.     

Synthesis and Characterization of the Poly-(2-Methoxycyanurate) of 1,1′-Bis-(4-Hydroxyphenyl)-cyclohexane

The poly-(2-methoxycyanurate) of l, l′-bis-(4-hydroxyphenyl)-cyclohexane (PMCBC) was synthesized by the interfacial poly-condensation technique. The polymer was fractionated by preparative gel permeation chromatography (GPC). The fractions were characterized by viscometry, osmometry, and GPC techniques. The viscosity-molecular weight relationship was established in pure solvent and in different binary solvent mixtures. The unperturbed dimensions, (〈R²〉₀/M)^1/2, and the solvent-polymer interaction parameter, B, were computed by applying the two-parameter theories of the excluded-volume effect.     

Molecular Dimension and Interaction Parameters of Polyacrylamide in Water‐N,N‐Dimethylformamide Mixtures

The intrinsic viscosities [η] of polyacrylamide (PAM) having different average molecular weights are measured in various mixtures of water (good solvent) and N, N dimethyl formamide (DMF, nonsolvent) at different temperatures. The observed results show a significant variation of cosolvency as a function of solvent composition (?_DMF). The nature of curves in [η] vs. ?_DMF plot at different temperatures indicates the existence of two antagonistic effects. The unperturbed dimensions (K_θ) of the polymer are determined by a number of methods, which agree well with each other. The temperature coefficient of unperturbed dimension (K′), molecular extension factors (α_n), characteristic ratio (C_α) and chain rigidity (σ) are evaluated and the effects of temperature, solvent composition are discussed. The volume related parameter V_E and shape factor ν were also computed, which shows the shape of polymer molecules to be more or less spherical in solution.     

Dilute solution behaviour of amylose tributyrate. Light scattering,viscosity and osmotic pressure measurements in non-ideal solvents

Amylose tributyrate has been prepared and fractionated; the dilute solution behaviour of the polymer has been studied in four solvents, ethyl acetate, methyl ethyl ketone, carbon tetrachloride and tetrahydrofuran. The Mark-Houwink relations have been established for each solvent and the exponent γ varies between 0·72 and 0·86, for different solvents. Perturbed dimensions have been measured for the polymer dissolved in two solvents and an estimate of the unperturbed dimensions has been made; the latter appear to be solvent dependent. Heterogeneity corrections were applied using data established by gel permeation chromatography measurements. Values of the effective bond length b of between 17 and 19·5 × 10^?8 cm and the Kuhn statistical segment A_m of 70 to 180 x 10^?8 cm, indicate that amylose tributyrate behaves like a moderately stiff coil in good solvents, with a chain stiffness intermediate between the vinyl and cellulosic polymers.     

Flow-dependent rejection of polystyrene from microporous membranes

Dilute solutions of polystyrene (molecular weight 1 × 10⁵?2 × 10⁷) in a mixed solvent of 90% carbon tetrachloride-10% methanol were filtered through track-etched porous mica membranes. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was measured as a function of polymer size r_s, pore radius r_o, and solvent flow rate q through each pore. Polymer size was characterized by the Stokes-Einstein radius, as determined from diffusion coefficients measured by quasielastic light scattering, and chain relaxation times τ were estimated from measured intrinsic viscosities. In the case of chains whose unperturbed radius was smaller than the pore, σ depended on the ratio r_s/r_o in the manner predicted by a hard-sphere theory, as long as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \tau < < 1 $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q, toward zero at high q. The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r_s > r_o by a single similarity variable \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} \mathord{\left/ {\vphantom {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} {(\dot \gamma \tau)^n}}} \right. \kern-\nulldelimiterspace} {(\dot \gamma \tau)^n}} \sim ({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})^{1 - 3n} q^{- n} $\end{document}; a least-squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.     

混合溶剂中高分子的尺寸

三元体系(高聚物／混合溶剂)性质不能简单地直接从相应的两种二元体系(高聚物／单一溶剂)性质来推演，混合溶剂中排除体积效应往往不是两种单一溶剂中排除体积效应的加权平均。高分子的尺寸除了与单一溶剂一高分子间的相互作用有关外。还受到两种溶剂间的相互作用、高分子的自缔合趋势的影响。在不同的θ溶刺中高分子的无扰尺寸往往不同。两种溶剂间的相互作用是重要的影响因素之一。     

Unperturbed dimensions of amylose tributyrate from viscosity data in non-ideal solvents

The unperturbed dimensions of amylose tributyrate have been estimated from viscosity measurements in non-ideal solvents. The validity of several methods of extrapolation has been assessed for this polymer. A small solvent dependence of the unperturbed dimensions has been observed and the characteristic ratio C_∞ has been found to vary between 5·6 and 6·8. One can conclude from this that the ester chain is only slightly more extended than the native amylose, assuming that the ring conformation in the backbone remains unaltered when the ester is formed.