Temperature-concentration diagram of polymer solutions

Daoud, M.; Jannink, G.

doi:10.1051/jphys:01976003707-8097300

Cited by 293 publications

(200 citation statements)

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“…7 The dashed curve fitting Nierlich et al's data points behaves approximately as predicted by the theory of Daoud and Jannink. 3 It shows that the size of a linear flexible polymer begins to exhibit globular behavior as soon as it decreases to a value slightly less than the unperturbed one. The solid curve, however, gives a smooth decrease of molecular dimensions and displays no such cross-over as predicted by Daoud and Jannink.…”

Section: Chain Dimensionsmentioning

confidence: 99%

Excluded-Volume Effects in Dilute Polymer Solutions. X. Polystyrene in Cyclohexane below the Theta Temperature

Miyaki

Fujita

1981

Polym J

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ABSTRACT:Mean-square radii of gyration and viscosities of polystyrene samples covering a broad range of molecular weight M in cyclohexane were measured at temperatures above and below the theta temperature () in order to see how the coil of a linear flexible polymer collapses to a globule as T is lowered. The data for either the radius expansion factor or the viscosity expansion factor as a function of T and M gave a composite curve when plotted against (Tie-I)M 1 1 2 or (l-eiT)M 1 1 2 In the range of the abscissa values studied, this curve did not reach the asymptote for globular behavior. Thus, the coil-to-globule transition of a linear flexible polymer should be a very gradual process.KEY WORDS Coil-Globule Transition I Polystyrene I Cyclohexane I Radius of Gyration I Intrinsic Viscosity I Much still remains te be investigated theoretically and experimentally in regard to the chain dimensions and flow properties of a linear flexible polymer in a poor so.lvent below the theta temperature e. Long ago Stockmayer 1 suggested that a random coil might eventually collapse to a globule as the temperature Tis lowered below e. This coilglobule transition should manifest itself as a change in molecular weight dependence of (S 2 ) from the type (S 2 )a;:Mto the type (S 2 )ocM 213 , where (S 2 ) is the mean-square radius of gyration at infinite dilution and M is the molecular weight of the polymer.By extending Flory's mean-field theory to include a term associated with the ternary cluster integral {J3 and assuming that the binary cluster integral {J 2 is proportional to r and {J3 is independent of T, de Gennes 2 showed that as a coil shrinks to a globule, the dependence of (S 2 ) on M and Tasymptotically approaches the form (1) where r is a reduced temperature defined by r=(T-e)je (2)

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Section: Chain Dimensionsmentioning

confidence: 99%

Excluded-Volume Effects in Dilute Polymer Solutions. X. Polystyrene in Cyclohexane below the Theta Temperature

Miyaki

Fujita

1981

Polym J

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“…1), where T is the temperature and C the monomer concentration (g cm-3) is in fact partitioned into regions in which RG has characteristic scaling laws in these three variables (Table I) (Refs. [6,30] 1) Recent progress [8] in the theory of critical phenomena has shown that there are characteristic exponents associated with the cross-over between critical and tricritical behaviour [9].…”

mentioning

confidence: 99%

“…Experimental study of température and concentration cross-overs. -We have investigated by SmallAngle Neutron Scattering cross-overs predicted by the theory [6] in region 1 (dilute solutions) and region II (semidilute solutions) of the temperature-concentration diagram (Fig. 1).…”

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confidence: 99%

“…All measurements are performed on a small-angle scattering spectrometer of the Laboratoire Léon-Brillouin set on a cold neutron guide of the EL3 reactor at Saclay [10]. The incident 6 The pair correlation function has been derived by Edwards [5] as leading to the Fourier transform For elements with n greater than ncc, screening effects occur and the behaviour of 5;1 (q) is of a random coil type which is simply deduced from the Debye [17] form :…”

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Cross-over in polymer solutions

et al. 1978

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Résumé. 2014 La fonction de corrélation de paire P(r) pour les polymères en solution a été mesurée par diffusion de neutrons aux petits angles dans l'intervalle 3 RG ~ r ~ I où RG est le rayon de giration et l la longueur du monomère. A la température thêta cette fonction est décrite par la loi de Debye 1/r. En bon solvant (limite haute température) et à la limite de la concentration nulle, S. F. Edwards prédit que cette fonction est uniformément proportionnelle à r-4/3.Cependant le résultat expérimental montre que pour des concentrations assez élevées ou pour des températures intermédiaires la fonction P(r) présente les deux comportements. On trouve qu'ils sont séparés par des longueurs de cross-over r* qui dépendent de la température et de la concentration. Le scaling de r* est relié au scaling de la longueur de corrélation 03BE et du rayon RG dans le diagramme température-concen tration.Abstract. 2014 Using a small-angle neutron scattering experiment, we measured the pair correlation function P(r) in polymer solutions in the interval 3 RG ~ r ~ l, where RG is the radius of gyration and I the step length. At the theta temperature, this function is known to follow the characteristic Debye law P(r) ~ r-1. In good solvents (high temperature limit) and in the limit of zero polymer concentration this function is uniformly proportional to r-4/3, as predicted by S. F. Edwards.We observe however, that at higher concentrations or intermediate temperatures, P(r) exhibits both characteristic behaviours, depending on the range of r. The cross-over distances r* which separate the patterns are found to depend upon concentration and temperature. The scaling of r* is related to the scaling of the screening length 03BE and the radius RG in the temperature-concentration diagram.

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“…Daoud and Jannink (14) have summarized the behaviour of <R^>5 over the various regions of the temperature-composition phase diagram for a polymer in a good (i.e. better-than-θ) solvent; this is shown in figure 2, where τ is a relative temperature, i.e.…”

Section: <Rm = a (1)mentioning

confidence: 99%

Polymers in Disperse Systems: An Overview

Vincent

1984

ACS Symposium Series

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In this paper some of the current thinking in three closely-related areas is highlighted: polymer adsorption; the effect of polymer on the pairwise interaction between particles; and the effect of polymers on dispersion stability.It would be an impossible task to summarize in one short review the many facets of this subject. This has been more than adequately attempted in several other recent reviews of the fields of polymer adsorption (1-4) and dispersion stability in the presence of polymers (1_, 5-7).My objective, therefore, is primarily to set the scene for the papers that follow: to highlight current theoretical and experimental work, and to indicate where future research efforts might conceivably be directed.It is convenient to divide this topic into three areas, which follow on from each other in a logical sequence : i) polymers at a single interface: adsorption and depletion ii) interactions between two particles in the presence of polymer: establishment of the pair potential. iii) dispersion stability in the presence of polymer: thermodynamic and kinetic considerations. Polymers at a Single InterfaceOur understanding of polymer adsorption has followed in the wake of developments in the theory of adsorption of small molecules and that of polymer solutions. It is useful, at the outset to introduce some of the ideas that have been developed in recent years, particularly with regard to the latter topic. The characteristic feature of a macromolecule in solution is its high degree of conformational freedom. The simplest possible model for an isolated macromolecule is the random walk (or 0097-6156/84/ 0240-0003S06.00/0

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Temperature-concentration diagram of polymer solutions

Cited by 293 publications

References 5 publications

Excluded-Volume Effects in Dilute Polymer Solutions. X. Polystyrene in Cyclohexane below the Theta Temperature

Excluded-Volume Effects in Dilute Polymer Solutions. X. Polystyrene in Cyclohexane below the Theta Temperature

Cross-over in polymer solutions

Polymers in Disperse Systems: An Overview

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