Unperturbed Dimensions Of Polymers Research Articles

Unperturbed dimensions of polymers revisited through the blob theory: the viscometric expansion factor

Abstract Plotting log([η]/M1/2) versus log(N/Nc) where [η] is the intrinsic viscosity of the macromolecular chain of molecular mass equal to M and N/Nc is the number of blobs of which this chain consists (N: the number of statistical segment of the chain and Nc : the number of statistical segment of one blob), we obtain the unperturbed dimensions parameter of the blob, Kθb. This graphical representation in this article is based on a modified, original equation of Han [6] based on the blob theory. The obtained value of Kθb for a given polymer, dissolved in a good solvent, is lower than the unperturbed dimensions parameter, Kθ, obtained for the same polymer in the Flory’s theta conditions. Having Kθb < Kθ we obtain for the viscometric expansion factors of a polymer, based on Kθb or Kθ, αηb > αη. With the obtained values of αηb we find αηb3/αs2αH ≈ 1, as predicted by Weill and des Cloizeauz [1], where using αη we obtain αη3/αs2αH ≈ 0.85 (αs and αH are the static and dynamical expansions factors).

Unperturbed dimensions of polymers revisited through the blob theory: the viscometric expansion factor

Unperturbed dimensions of polymers revisited through the blob theory: the viscometric expansion factor

Evaluation of unperturbed polymer dimensions from intrinsic viscosity in non‐ideal solvents

AbstractFor solutions of polystyrene (PS) samples of different relative molecular mass (molecular weight) M and intrinsic viscosities [n] have been measured at 298,15 K in pure toluene (T) and toluene/methanol (MeOH) mixtures. Upon mixing toluene (good solvent (1)) and methanol (nonsolvent (2)), a systematic decrease in the solvation power was obtained. A critical examination of the Stockmayer‐Fixman method for obtaining unperturbed dimensions from intrinsic viscosity measurements has been made. It was found that the unperturbed dimensions were not constant and different from those measured in a theta solvent (T/MeOH mixture having volume fraction of methanol (ϕMeOH) = 0,23). The derived values of unperturbed dimensions were found to increase with increasing Kuhn‐Mark‐Houwink‐Sakurada exponent a. A modified form of the Stockmayer‐Fixman equation is presented. It is suggested that the volume effect be taken into account in a complementary fashion to obtain accurate estimates of unperturbed dimensions from data in active solvents where the mean‐square end‐to‐end distance 〈r2〉 increases at these conditions more rapidly than M. Different viscosity measurements of polystyrene (PS) and poly(N‐vinyl‐2‐pyrrolidone) solutions containing non‐ideal solvents were taken from the literature and found that the newly proposed, though purely empirical equation is valid.

Calculation of the unperturbed dimensions of polymers via an equation derived from the combination of the two-parameters theory with the blob theory

A combination of two equations for the viscometric expansion factor, derived from the two-parameters theory and the blob theory, leads to an equation that permits the calculation of the unperturbed dimensions parameter K ϑ of a polymer from the values of the parameters K and a of the Mark-Houwink-Sakurada equation. The method is especially useful in the high molecular weight region in which the Stockmayer-Fixman-Burchard equation is not valid.

Solution Properties of Poly(vinylpyrrolidone) in Cosolvent Systems

For solutions of well fractionated poly(vinylpyrrolidone) (PVP) samples of different relative molar mass M, intrinsic viscosities [η] have been measured at 298.15 K in pure water and water/acetone mixtures. Upon mixing water (good solvent) and acetone (poor solvent), thermodynamically better solvents could be obtained. The cosolvancy was detected from the viscosity measurements. Several graphical procedures have been utilized for deriving the unperturbed dimensions of PVP expressed as Kθ (in the relationship [η]=KθM1/2α3, where α is the expansion factor). It was found that the unperturbed dimensions were not constant and differed from those measured in the θ-solvent (water/acetone mixture having volume fraction of acetone (φACT)=0.668) in which Kθ was found to be 74×10−3 dm3 kg−1. A solvent-dependent parameter has been utilized to correct the Kθ values derived from Stockmayer-Fixman plot, in each solvent, for the sake of achieving a constant value of Kθ via these plots. Values ranging between 73×10−3 and 75×10−3 dm3 kg−1 with a mean of 74×10−3 dm3 kg−1 were obtained by utilizing the proposed correction, thus yielding 0.666 Å g−(1/2) mol1/2 for unperturbed polymer dimensions, (〈r2〉0/M)1/2.

Correlation between transport and equilibrium properties through the ternary interaction parameter for cosolvent and cononsolvent polymeric systems

A study of the ternary polymer systems dimethyl formamide-ethyl acetate-polystyrene, chloroform-1,4 dioxane-polystyrene and tetrahydrofuran-chloroform-polystyrene was carried out by viscosity and light scattering at 298 K. A good correlation has been found between the excess intrinsic viscosity, unperturbed polymer dimensions, second virial coefficient and the excess Gibbs free energy by using a ternary interaction parameter, dependent on molecular weight. This modification enables the conversion between transport and equilibrium properties.

Limitations of graphical procedures based on excluded-volume theories for the determination of Kθ

The [ η]- M relations of some commonly used two-parameter excluded-volume theories have been considered in regard to estimating K θ , a measure of unperturbed dimensions of polymers. Limitations of these theories have been demonstrated using [ η]- M data of two substituted acrylamide polymers, poly( N-phenyl acrylamide) (PNPA) and poly( N-( p-methyl)phenyl acrylamide) (PNPMPA), which range in their v values from flexible to semi-rigid chain character. The analysis shows that the theories fail to accommodate any such set of [ η]- M data that leads to v values larger than its prescribed limit in the corresponding theory. For the Flory-Fox-Schaefgen and Domb-Barrett theories v max came out to be 0.80; and for the Kurata-Stockmayer-Roig, Burchard-Stockmayer-Fixman and Inagaki-Ptitsyn theories it extended to unity. As a consequence of the failure of these theories, two more equations due to first-order perturbation and Bueche-James theories were invoked with a view to extending the scope of this analysis. The upper limit of v was thus extended to 1.25 and 2.00, respectively. These theories were found to be of general applicability. The values of K θ estimated by appropriate methods were 4.65 × 10 −4 and 8.5 × 10 −4 dl mol 1 2 g −3 2 for PNPA and PNPMPA, respectively.

Unperturbed dimensions of polymers in binary and ternary systems

AbstractThe unperturbed dimensions parameter KΘ is one of the most important characteristics of a polymer chain. For binary systems (polymer/solvent) and mostly for ternary systems (polymer/solvent(1)/solvent(2)) the KΘ values show large discrepancies with respect to those under thetaconditions in a single solvent. These discrepancies can be explained by considering that the interaction parameter χ (and consequently the coil dimensions or the number of intramolecular contacts between polymer segments) changes with molecular weight M. Assuming this dependency, a modified Stockmayer‐Fixman equation is proposed from which a unique value of KΘ for a given polymer, independent of M, is obtained. The use for ternary polymer systems of an interaction parameter between polymer and the solvent mixture (χ3M) which depends on M, allows to calculate a single KΘ value for a polymer in different mixtures of solvents and justifies the proportionality found between KΘ deviations and the excess Gibbs free energy between both solvents of the solvent mixture.

Prediction of second virial coefficients from intrinsic viscosities in ternary polymer systems

AbstractDeviations in the determination of the unperturbed dimensions of polymers arising in ternary polymer systems (solvent (1)/solvent (2)/polymer) can be explained by the inaccurate use of an interaction parameter independent of polymer molecular weight. On this basis, a new formalism for the calculation of the second virial coefficient from intrinsic viscosity is proposed. This formalism was tested (and compared with well established formalisms) for all ternary polymer systems with simultaneous intrinsic viscosity and second virial coefficient data in the literature.

Determination of unperturbed dimensions of polymers in binary solvent mixtures from viscosity measurements

Intrinsic viscosity measurements were carried out on poly(vinyl pyrrolidone) and poly(vinyl alcohol) in various solvents and solvent mixtures. The values ofφ, [η] andk, the latter two being the fundamental terms in the equationC/η sp =1/ηkC, were utilized for the determination of the unperturbed dimensions in solution. The values of (¯r o 2 /M w )1/2 were calculated.

Solution properties of polystyrene in cosolvent systems

At 293 K, intrinsic viscosities [η] have been measured for polystyrene samples of different relative molar mass M in mixtures of two poor solvents. These solvents were ethyl acetate and cyclohexane. Upon mixing these two poor solvents, thermodynamically better solvents could be obtained. The cosolvency was detected from the viscosity measurements. Several graphical procedures have been utilized for deriving the unperturbed dimensions of polystyrene expressed as K θ (in the relation [η]=K θM 1 2 α 1 3 , where α is the expansion factor). It was found that the unperturbed polymer dimensions were not constant and differed from those measured in the single θ-solvent ( trans-decalin) in which K θ was found to be 81 × 10 −3 dm 3 kg −1.

Estimation of molecular weight averages from intrinsic viscosity

AbstractThe weight‐average molecular weight is estimated by an extrapolation technique based on a linear relation between the viscosity‐average molecular weight Mv and a Mark–Houwink–Sakurada constant. This method may also be used to assess the unperturbed dimensions of polymers. If the Mv data are known with high accuracy, then the straight line may be stretched to reach the number‐average molecular weight confidently. The slope of the linear plot is associated with the molecular weight distribution and as such can be utilized to compute the polydispersity index.

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 [η] = K θM 1 2 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 dm 3 kg −1 was the same as that obtained directly under θ-conditions.

Polymers in mixed solvents: linear representation of viscosity data as a function of molecular weight

In this paper the corrected Stockmayer-Fixman-Burchard equation recently proposed 13 is applied to the case of polymers dissolved in mixed solvents. A linear plot for viscosity over a very broad range of molecular weights is observed. The unperturbed dimensions of polymers obtained in mixed solvents are related to the thermodynamic properties of the solvent mixtures.

On the excluded volume theories: fifth-power type equations

Two new equations, based on the Domb—Barrett and Kurata theories of excluded volume, have been proposed to estimate unperturbed dimensions of chain molecules in solution from the viscosity—molecular weight data of polymers in good solvents. The fifth-power type equations of excluded volume theories by Domb and Barrett, Kurata, and Flory have been compared using the experimental data on several polymers. It has been found that the Domb-Barrett theory not only reliably yields the unperturbed dimensions of polymers but also adequately measures the solvent-polymer interaction parameter.

Unperturbed Polymer Chain Dimensions from Intrinsic Viscosities Determined in Good Solvents

Abstract Experimental criteria are presented to determine the region of validity of the intrinsic viscosity-molecular weight relation proposed by Stockmayer and Fixman for use in good solvents. Use of these criteria in several good solvents yields the same value for unperturbed polymer dimensions as do measurements made at “θ” conditions. Intrinsic viscosity determinations conforming to these criteria, made in two good solvents, allow the determination of weight-average molecular weights of the polymer solute.

The Relationship between the Unperturbed Dimensions of Polymers in Mixed Solvents and the Thermodynamic Properties of the Solvent Mixture

The Relationship between the Unperturbed Dimensions of Polymers in Mixed Solvents and the Thermodynamic Properties of the Solvent Mixture

Unperturbed polymer chain dimensions from intrinsic viscosities determined in good solvents

Abstract Experimental criteria are presented to determine the region of validity of the intrinsic viscosity-molecular weight relation proposed by Stockmayer and Fixman for use in good solvents. Use of these criteria in several good solvents yields the same value for unperturbed polymer dimensions as do measurements made at “θ” conditions. Intrinsic viscosity determinations conforming to these criteria, made in two good solvents, allow the determination of weight-average molecular weights of the polymer solute.

The Influence of Solvents on Unperturbed Dimensions of Polymer in Solution

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe Influence of Solvents on Unperturbed Dimensions of Polymer in SolutionAnastasios Dondos and Henri BenoitCite this: Macromolecules 1971, 4, 3, 279–283Publication Date (Print):May 1, 1971Publication History Published online1 May 2002Published inissue 1 May 1971https://doi.org/10.1021/ma60021a003RIGHTS & PERMISSIONSArticle Views138Altmetric-Citations70LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (560 KB) Get e-Alerts Get e-Alerts

Unperturbed Dimensions of Polymers in Binary Solvent Mixtures

Intrinsic viscosity measurements were carried out on polystyrene and polyvinylpyridine solutions in various solvents and solvent mixtures. The Stockmayer-Fixman extrapolation was applied to the date: it yields the unperturbed dimensions K θ of the chain. A unique value of K θ was found for a given polymer in all pure solvents, as expected; in the case of binary mixtures, the K θ value is found higher or lower than this unique value, depending upon the thermodynamic parameter x 12 characterizing the solvent mixture. According to these results, the properties of θ-solutions (as defined classically for pure solvents) should not be extended to ternary systems, since K θ does not depend solely on temperature.