Shear viscosity and mass density near the liquid-liquid critical point of polystyrene in diethyl malonate

Gruner, Karen; Habib, Sehrish; Greer, Sandra C.

doi:10.1021/ma00204a025

Cited by 13 publications

(12 citation statements)

References 14 publications

(17 reference statements)

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“…The 1 − α term has been observed in binary mixtures of small molecules 59, 60. This critical anomaly has not been observed in the solutions of linear polymers that have been studied: PS–CH,61 PS–diethylmalonate,62, 63 and poly(α‐methylstyrene)–MCH 64. There are no previous measurements of this property for a nonlinear polymer in solution.…”

Section: Previous Experimental Workmentioning

confidence: 97%

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

Alessi

Bittner

Greer

2003

J Polym Sci B Polym Phys

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We measured the cloud‐point curves of eight‐arm star polystyrene (sPS) in methylcyclohexane (MCH) for polymer samples of three total molecular masses [weight‐average molecular weight (Mw) × 10−3 = 77, 215, or 268]. We found a downward shift of 5–15 K in the critical temperature (Tc) of the star polymer solutions with respect to linear polystyrene (PS) solutions of the same Mw. The shift in Tc became smaller as Mw increased. The critical volume fraction for eight‐arm sPS in MCH was equal within experimental uncertainty (10–40%) to that of linear PS in MCH. For sPS of Mw = 77,000 in MCH, we studied the mass density (ρ) as a function of temperature (T). As for linear polymers in solution, the difference in ρ between coexisting phases (Δρ) could be described over t = (Tc − T)/Tc for 1.1 × 10−4 < t < 4.7 × 10−3 with the Ising value of the exponent β in the expression Δρ = B tβ. Both ρ(T) above Tc and the average value of ρ below Tc were linear functions of temperature; no singular corrections were observed. The measurements of the shear viscosity (η) near Tc for sPS (Mw = 74,000) in MCH indicated a strong critical anomaly in η, but the data were not precise enough for a quantitative analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 129–145, 2004

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Section: Previous Experimental Workmentioning

confidence: 97%

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

Alessi

Bittner

Greer

2003

J Polym Sci B Polym Phys

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“…Contrary to this conventional understanding, some experimental works have questioned that the dynamic critical phenomena of polymer solutions can be really categorized into the model H universality. [11][12][13][14] In fact the dynamic exponent y c obtained experimentally for polymer solutions is smaller than that in classical fluids. [11][12][13][14] Recently Tanaka et al 15) have reported experimental work of dynamic critical phenomena of polymer solutions.…”

Section: Introductionmentioning

confidence: 99%

“…[11][12][13][14] In fact the dynamic exponent y c obtained experimentally for polymer solutions is smaller than that in classical fluids. [11][12][13][14] Recently Tanaka et al 15) have reported experimental work of dynamic critical phenomena of polymer solutions. Their accurate measurements for critical anomaly of viscosity show that the dynamic exponent y c significantly decreases as the molecular weight M w increases.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Critical Phenomena of Polymer Solutions

Furukawa

2003

J. Phys. Soc. Jpn.

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Recently, a systematic experiment measuring critical anomaly of viscosity of polymer solutions has been reported by H. Tanaka and his co-workers (Phys.Rev.E, 65, 021802, (2002)). According to their experiments, the dynamic critical exponent of viscosity y_c drastically decreases with increasing the molecular weight. In this article the kinetic coefficients renormalized by the non-linear hydrodynamic interaction are calculated by the mode coupling theory. We predict that the critical divergence of viscosity should be suppressed with increasing the molecular weight. The diffusion constant and the dynamic structure factor are also calculated. The present results explicitly show that the critical dynamics of polymer solutions should be affected by an extra spatio-temporal scale intrinsic to polymer solutions, and are consistent with the experiment of Tanaka, et al.Comment: 17 pages, 2 figures, to be published in J.Phys.Soc.Jp

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“…The mixture has a viscosity of 45 CP at 0.1 K above Tc. 34 Snider estimated that wD should be near lo5 Hz for a mixture of organic liquids. We assumed the frequency to be inversely proportional to the viscosity and estimated wD to be near 25 kHz for polystyrene in diethyl malonate.…”

Section: Introductionmentioning

confidence: 99%

The dielectric constant near the liquid-liquid critical point for polystyrene in diethyl malonate

Tveekrem¹,

Greer²,

Jacobs³

1988

Macromolecules

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We have measured the dielectric constant as a function of temperature and frequency near the liquid-liquid critical point of a mixture of polystyrene (molecular weight 1.02 X lo5) in diethyl malonate at the critical composition. The range of the frequency was 20 kHz to 1 MHz. For the one-phase region above the critical point, the range of the temperature was 1.1 X lod < t < 7.9 X where t is the reduced temperature, IT-TcI/Tc, and T, is the critical temperature. The dielectric constant in the one-phase region near the critical point shows an anomalous increase of about 0.3% above the "background" behavior far from the critical point. This anomaly is consistent with the theoretical prediction of a leading critical exponent (1 -a ) , where a is 0.11. The amplitude of the dielectric constant anomaly decreases with increasing frequency, an effect not yet considered in the theory. Below the critical temperature, the dielectric constants of the coexisting phases were measured as functions of temperature and frequency. The frequency ranged from 20 kHz to 1 MHz. The temperature ranged from 1.4 X The difference between the dielectric constants of coexisting phases is consistent with a critical exponent @ of 0.325, where @ describes the vanishing of the order parameter at the critical point. The average of the dielectric constants of coexisting phases is nearly linear but shows a critical contribution that can be described by an exponent 2p. Neither above nor below the critical temperature was there any evidence of the theoretically predicted critical anomaly in the dielectric relaxation time.< t < 3.5 X IntroductionModern theories of critical phenomena are based on the idea that the origin of the anomalies in the thermodynamic and transport properties near critical points is the growth of large and long-lived fluctuations in the order parameters.lY2 We present here experiments to test these theories for the description of dielectric properties near a liquidliquid critical point in a polymer solution.One-Phase Region: Temperature Dependence. Both phenomen~logical~,~ and m i c r o s~o p i c~~~ approaches predict that the dielectric constant, e, at zero frequency in the one-phase region near a liquid-liquid critical point should have the functional form:

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Shear viscosity and mass density near the liquid-liquid critical point of polystyrene in diethyl malonate

Cited by 13 publications

References 14 publications

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

Eight‐arm star polystyrene in methylcyclohexane: Cloud‐point curves, critical lines, and coexisting densities and viscosities

Dynamic Critical Phenomena of Polymer Solutions

The dielectric constant near the liquid-liquid critical point for polystyrene in diethyl malonate

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