Light scattering study on polystyrene in cyclohexane below the θ point

ABSTRACT:The osmotic compressibility up to high concentrations as well as the second virial coefficient were measured for low molecular weight polystyrenes dissolved in a poor solvent cyclohexane at 35, 25, and 15 C, by sedimentation equilibrium. The results of the osmotic compressibility over wide concentration ranges were favorably compared with a recently developed thermodynamic perturbation theory based on the spherocylinder model bearing a square-well potential, and from the comparison, the hard-core diameter d and the depth " of the attractive square-well potential including in the theory were determined for polystyrene in cyclohexane. Compared with the previous results of d and " for the same polymer in 15 C toluene (a good solvent), it turned out that " increases and d decreases with reducing the solvent quality. [DOI 10.1295/polymj.36.747] KEY WORDS Polystyrene / Osmotic Compressibility / Second Virial Coefficient / Sedimentation Equilibrium / Thermodynamic Perturbation Theory / The distribution function theories for polymer solutions 1-3 express the polymer intermolecular interaction in terms of the potential U 12 ð1; 2Þ of mean force, where the arguments 1 and 2 represent all coordinates specifying the position, orientation, and conformation of polymer chains 1 and 2, respectively. If the polymer chain is divided into N 0 identical (spherical) segments, U 12 ð1; 2Þ may be given bywhere uðR i 1 i 2 Þ is the pair potential of mean force between segments i 1 and i 2 belonging to polymer chains 1 and 2, respectively, which is a function of the distance R i 1 i 2 of the two segments. For neutral polymers, the potential uðR i 1 i 2 Þ consists of short-ranged repulsive and long-ranged attractive interaction parts. The two-parameter theory 1-3 and also the renormalization-group theory 4-7 assume that the intermolecular excluded volume effect on the virial coefficients and the osmotic pressure can be expressed as a function of the binary cluster integral 2 defined by 2 4(k B : the Boltzmann constant; T: the absolute temperature) instead of the full function of uðRÞ. However, this assumption does not necessarily hold. Near the theta condition where 2 vanishes, the ternary cluster integral or the three-segment interaction becomes important in virial coefficients against the two-parameter theory. 8 When the polymer concentration is beyond the semidilute regime, the osmotic pressure or the osmotic compressibility cannot be described by the renormalization-group theory. Alternatively, the thermodynamic perturbation theory chooses a system of particles interacting by the hard-core potential as a reference system, and treats the long-ranged attractive interaction in a perturbative way. For example, Barker and Henderson proposed a perturbation theory for the system of spherical particles with a square-well potential. Their theory includes all perturbation terms using the Padé approximation. Recently, Koyama and Sato 10 extended the Barker-Henderson theory to the wormlike spherocylinder system. In the theory, the i...

Section: Figure 1 Shows Double Logarithmic Plots Ofmentioning

confidence: 99%

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Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

Oribe

Sato

2004

“…8 These samples ranged in molecular weight from 10 x 10 3 to 500 x I 0\ and the measurement on each was effected down to a temperature as close to the cloud point as possible. The finding is presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…8 The temperature of each measurement was maintained within 0.05°C. Use was made of a Fica 50 light scattering photometer with polarized incident light of 546.1 nm in wavelength.…”

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The Second Virial Coefficient of Monodisperse Polystyrene in Cyclohexane below the Theta Point

Tong

Ohashi

Einaga

et al. 1983

Self Cite

ABSTRACT:A light scattering study was made on monodisperse polystyrene + cyclohexane solutions in the range of molecular weight from 10000 to 500000 and that of temperature from 34.5°C (8) down to a value about I oc above the cloud point. The second virial coefficient A2 was found to depend essentially on temperature only, at least in the range of molecular weight examined. This result is not in conformity with any current two-parameter theories for A2 of polymer solutions.KEY As will be noted later, Wolf and Adam's finding does not conform to the prediction of the two-parameter regime in regard to molecular weight dependence. However, it seems too early to accept this as definitive, and more experiments must be undertaken before a general conclusion, if any, may be established on A 2 of polymer solutions below e.In the course of our recent experimental evaluation of the Flory-Huggins interaction parameter, we had an opportunity of carrying out light scattering measurements to estimate A 2 on six monodisperse polystyrene samples in cyclohexane below 8. 8 These samples ranged in molecular weight from 10 x 10 3 to 500 x I 0\ and the measurement on each was effected down to a temperature as close to the cloud point as possible. The finding is presented in this paper. EXPERIMENTAL Polystyrene SamplesWe started with five standard polystyrene samples Fl, F2, F4, F20, F40 supplied by Toyo Soda Co., and one laboratory-made sample F7 (anionically polymerized by Mr. H. Watanabe of our department). These samples were subjected to precipitation and/or column fractionation to sharpen further their already sufficiently narrow molecular weight distributions. The main fractions of the respective series of fractions were chosen as the test samples. By GPC measurements, their ratios of weight-average to number-average molecular weights were found to be smaller than 1.03. Hence, in the present data analysis, any of the samples was treated as completely monodisperse in molecular weight.The molecular weight M determined by light scattering in benzene at 25°C was 10000, 21500, 43600, 181000, 498000, for the samples F1, F2, F4, combined with small angle laser light scattering gave an M of 74000 for the sample F7. Preparation of SolutionsEach polystyrene sample was dissolved in benzene and repeatedly filtered through a Millipore membrane until no light scattered by dust particles could be observed in the laser beam passing through the solution. The filtered solution was then freezedried in a vessel covered with a Millipore film. A proper amount of the dry polymer was weighed into a cylindrical light scattering cell and again thoroughly dried. The solvent cyclohexane was distilled and immediately poured into the cell in a dry bag filled with nitrogen. The cell was then sealed with a ground glass stopper. The solution was left standing overnight at a temperature between 30 and 40°C with occasional shaking. Complete dissolution of the polymer was confirmed by observing transparency of the solution, and also by the absence of unusual inten...

“…The coefficient 2 is a parameter proportional to N 1 ' 2 and is set to the inverse of the overlap concentration cpf in this study as first proposed by Einaga et al 5 (7)…”

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Coexistence Curve of a Star-Shaped Polymer Solution. Comparison with the Hybrid Theory

Numasawa

Okada

1999

In a dilute polymer solution, polymer segments are not uniformly distributed in space because they are connected with chemical bonds. Such non-uniform distribution of local polymer segment density is of essential importance to thermodynamic properties of a dilute solution, while in a concentrated solution connectivity of segments reduces its influence on thermodynamic properties and the mean-field approximation is applicable to theoretical treatment of the solution. Phase equilibrium of a binary polymer solution is a phenomenon extending over these two concentration regimes and consequently the mean-field type theory such as the Flory-Huggins theory fails in quantitative description of phase diagram of a binary polymer solution. On the other hand, theories of dilute polymer solutions such as the virial expansions deteriorate their validity with increasing polymer concentration and cannot afford to give a phase diagram. To evade this difficulty, Koningsveld et a/. 1 proposed a theory in which the Flory-Huggins theory and the dilute polymer solution theory are combined so that the Flory-Huggins free energy crosses over to the free energy given by the virial expansion as concentration is decreased. Their theory, referred as the hybrid theory, was applied to linear polymer solutions and gave a good agreement with experimental results.Recent experimental studies on phase diagrams of star-shaped polymer solutions revealed that phase diagram of a star-shaped polymer solution differs from that of the homologous linear polymer of the same molecular weight. 2 -4 Such solubility difference caused by molecular architecture cannot be explained either by the Flory-Huggins theory. However, it is expected that the hybrid theory reproduces the observed difference of phase diagrams of these polymer solutions, if the difference in free energy of dilute phase is a principal origin of the difference in phase diagram. Since explicit expressions of the second virial coefficients of starshaped polymer solutions have been given by the perturbation theories, extension of the hybrid theory to star-shaped polymer solutions is straightforward.In this note, we calculated phase diagram of a binary star-shaped polymer solution based on the hybrid theory t To whom correspondence should be addressed.