Second Virial Coefficients and Radii of Gyration for Poly(α-methylstyrene) in Cyclohexane below the ϑ Temperature

The mean-square radius of gyration 〈S 2 〉 was determined from small-angle X-ray and light scattering measurements for 20 samples of atactic oligo-and poly(R-methylstyrene)s (a-PRMS), each with the fraction of racemic diads fr ) 0.72, in the range of weight-average molecular weight from 6.48 × 10 2 (pentamer) to 3.22 × 10 6 in cyclohexane at 30.5°C (Θ). The ratio 〈S 2 〉/xw as a function of the weightaverage degree of polymerization xw first increases steeply for xw j 20, then passes through a flat hump at xw = 40, and finally approaches its asymptotic value for xw J 1 ×10 3 . On the basis of the helical wormlike (HW) chain model the HW model parameters are λ -1 κ0 ) 3.0, λ -1 τ0 ) 0.9, λ -1 ) 46.8 Å, and ML ) 39.8 Å -1 , where κ0 and τ0 are the differential-geometrical curvature and tortion, respectively, of the characteristic helix of the HW chain taken at the minimum zero of its elastic energy, λ -1 is the stiffness parameter, and ML is the shift factor defined as the molecular weight per unit contour length of the chain. The local chain conformations of a-PRMS are discussed in detail on the basis of the above values of the model parameters and compared with those of atactic polystyrene (fr ) 0.59), atactic poly(methyl methacrylate) (a-PMMA) (fr ) 0.79), and isotactic PMMA (fr = 0.01) previously studied. It is then concluded that the a-PRMS chain tends to retain large and clearly distinguishable helical portions in dilute solution like the a-PMMA chain, as was expected from their chemical structures, although the helical nature of the former is somewhat weaker. To illustrate the situation, pictures are given of representative instantaneous contours of HW Monte Carlo chains for the above four polymers.

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“…For comparison, it also includes the previous data for a-PS with 12 The solid curve connects smoothly the present data points.…”

Section: Discussionsupporting

confidence: 61%

Mean-Square Radius of Gyration of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

2000

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“…For polystyrene ͑PS͒ in cyclohexane ͑CH͒, recent experiments indicate that the chains are not collapsed near the critical point; 36 however, for poly͑␣-methylstyrene͒ in cyclohexane, significant contraction of the chains is observed 37 for TϽ⌰. It is to be noted that the coil-to-globule transition has been observed for subtheta solutions of PS in CH at concentrations far below the critical point, 38,39 and by quenching into the twophase region.…”

Section: Analytic Thread Prism Theory For Homopolymer Fluids Witmentioning

confidence: 98%

Analytic integral equation theory for the critical properties of homopolymer fluids

Chatterjee

Schweizer

1998

The Journal of Chemical Physics

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We apply the analytic version of the polymer reference interaction site model theory to determine the critical properties of homopolymer fluids. The Gaussian thread model is used throughout, together with a Yukawa form for the attractive interaction between chain segments. Atomiclike as well as molecular closures are employed, and results are presented using both the compressibility and free-energy route approaches to the thermodynamics. Predictions derived based on different closure approximations for the chain length (N) dependence of the theta and critical temperatures, and of the critical density, are compared with the results of simulations of the liquid-vapor equilibrium in homopolymer systems, as well as with experimental results for the demixing transition in polymer solutions. The large N asymptotic scaling laws, and finite size corrections, for the critical properties depend strongly on the closure employed for treating attractive interactions, and for all cases studied significant deviations from the mean-field Flory-Huggins lattice theory are found. The importance of simultaneously including fluctuation effects associated with both the repulsive and attractive interactions is demonstrated. Model calculations are also presented for the liquid-vapor spinodal and coexistence curves.

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“…This observation is consistent with the data of Auroy et al 28 and Karim et al 29,30 for tethered chain systems at higher ⌺, and also with the contraction of free chains in dilute solution. 49,[55][56][57][58] The contraction of a tethered layer is pre- …”

Section: A Segmental Concentration Profilementioning

confidence: 99%

“…For isolated free chains R g /R g, is a function of ͉͉M 1/2 . [22][23][24]49,[55][56][57][58] For Ӷ 0, R g /R g, ␣ (͉͉M 1/2 ) Ϫ1/3 , which is termed the ''collapsed'' regime, although the chains may still be quite expanded relative to the fully collapsed, nonsolvent limit. The present data are compared to this limiting behavior in Fig.…”

Section: A Segmental Concentration Profilementioning

confidence: 99%

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Tethered chains in poor solvent conditions: An experimental study involving Langmuir diblock copolymer monolayers

Kent

Majewski

Smith

et al. 1999

The Journal of Chemical Physics

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We have employed Langmuir monolayers of highly asymmetric polydimethylsiloxanepolystyrene (PDMS-PS) diblock copolymers on dioctyl phthalate (DOP) at temperatures ranging from 22 "C to -35 "C as a model system for tethered chains in poor solvent conditions. The thicknesses of the tethered PS layers extending into the DOP subphase, measured by neutron reflection, decrease with decreasing temperature (T) over this entire range. However, the variation with T becomes weak below -20 "C. At the lowest T, the layer thicknesses are contracted 55 56 -75 % of their values at the theta condition (To = 22 "C), but are still quite swollen compared to the fully collapsed, nonsolvent limit. The contraction of the layer with decreasing T is determined as a function of surface density and molecular weight. These data are compared to universal scaling forms. The PS segments are depleted from the air surface over the entire T range, the thickness of the depletion layer increasing slightly with decreasing T. The free energy of the surface layer is probed by surface tension measurements. Negative surface pressures are observed at low coverages for both PDMS-PS and PDMS monolayers, indicating metastability toward lateral phase separation. Evidence for a transition from a dispersed phase to a condensed phase with decreasing T was observed in the reflectivity at very low PDMS-PS coverage. At high coverage where the submerged blocks are strongly interacting at 22 "C. onlv a modest decrease in'surface Dressure is observed over the s .of the relative

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Second Virial Coefficients and Radii of Gyration for Poly(α-methylstyrene) in Cyclohexane below the ϑ Temperature

Cited by 18 publications

References 22 publications

Mean-Square Radius of Gyration of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

Mean-Square Radius of Gyration of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

Analytic integral equation theory for the critical properties of homopolymer fluids

Tethered chains in poor solvent conditions: An experimental study involving Langmuir diblock copolymer monolayers

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