doi:10.1016/S0032-3861(00)00625-X 
Copyright © 2000 Elsevier Science Ltd. All rights reserved.
Dilute-solution properties of arborescent polystyrenes: further evidence for perturbed-hard-sphere behavior
A. Strioloa, b, J. M. Prausnitz
, 
, a, b, A. Bertuccoc, R. A. Keed and M. Gauthierd
a Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 94720-1462, USA
b Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
c Istituto di Impianti Chimici, Università degli Studi di Padova, Via Marzolo 9, I-35131 Padova, Italy
d Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Received 14 February 2000;
revised 11 August 2000;
accepted 15 August 2000
Available online 4 December 2000.
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Abstract
Toward improved understanding of the dilute-solution properties of arborescent polystyrenes, new measurements are reported for osmotic second virial coefficients and for intrinsic viscosities in three common organic solvents. As observed for other branched polymers, branching decreases the second virial coefficient in good solvents and lowers the theta temperature for a polymer–solvent system. For generation-zero arborescent polystyrene in methylcyclohexane, the theta temperature is 36±2°C.
A correspondence between intrinsic viscosity and second virial coefficient, valid for hard-spheres solutions, holds in good solvents; this correspondence improves with decreasing branch molecular weight.
The osmotic-pressure data are interpreted with a colloid-like thermodynamic framework using a van der Waals-type equation of state. The reference state is the hard sphere and the perturbation is given by an attraction decaying with the sixth power of the center-to-center distance between polymers. The hard-sphere diameter is obtained from intrinsic-viscosity data. Predicted and observed osmotic pressures are in good agreement.
Author Keywords: Arborescent polystyrene; Osmotic second virial coefficient; Intrinsic viscosity
Fig. 1. Intrinsic viscosity as a function of temperature for arborescent polystyrenes, different generations, in methylcyclohexane (empty symbols) and in cyclohexane (full symbols). Squares represent G0 arborescent polymer, triangles G1, diamonds G2 and circles G3.
Fig. 2. B22 for arborescent polystyrenes in toluene as a function of molecular weight. Comparison between experimental data (empty symbols) and predictions from Eq. (3) using intrinsic-viscosity data (full symbols). [η] from Gauthier et al. [7]. Triangles are for arborescent polymers obtained from a linear polystyrene core and side chains with a molecular weight of 30,000 g/mol [11]. Diamonds are for arborescent polymers obtained from a linear core and side chains of 5000 g/mol [11]. Squares represent B22 measured in this work.
Fig. 3. Osmotic pressures for generation-zero arborescent polystyrene in different solvents. Symbols are experimental data; lines are calculated from Eq. (4). Squares are for data in toluene (filled at 38.6°C, empty at 47.7°C); circles are for data in cyclohexane at 32.2°C, and diamonds are for data in methylcyclohexane (filled at 32.6°C, empty at 41.6°C).
Fig. 4. Osmotic pressures for generation-one arborescent polystyrene in different solvents. Symbols are experimental data; lines are calculated from Eq. (4). Squares are for data in toluene (filled at 38.5°C, empty at 47.8°C); circles are for data in cyclohexane (filled at 32.2°C, empty at 43.0°C).
Table 1. Polymer characterization data
Table 2. Number-average molecular weight Mn and second osmotic virial coefficient B22 from osmometry. Radii, R, from intrinsic viscosity and energetic parameter H used to fit Eq. (4) to the experimental osmotic-pressure data
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