Polystyrene+cyclohexane

Under 0 conditions for the polystyrene-cyclohexane system, intrinsic... 

First, the sample was examined by GPC, for which four columns of styragel of 106,10s, 104 and 103 A nominal pore size were used. The total number of theoretical plates as determined by acetone at a flow rate of 1 ml/min was ca. 26,000. The eluent was tetrahydrofuran. The chromatogram is shown in Figure 9, which indicates two peaks at ca. 21 and 24 counts. The former may be assigned to the tetra-chain, star-draped component, and the latter to the precursor. However, no complete separation of the two peaks was observed. For another comparison, velocity ultra-centrifugation was performed for the sample at 59,780 rpm using a 6-solvent for polystyrene, cyclohexane. The operation temperature was established at 35 °C, the 6-temperature, to minimize the concentration dependence of sedimentation velocity and other effects. A sedimentation pattern taken by UV-absorption is shown in Figure 10. It is seen that the separation of S-A sample into the two components was quite difficult even at a very low polymer concentration, 0.077 g/dl. 

These manipulations may appear to add little except for needless complication to an interpretation of the second virial coefficient for random coils. Recall, however, that Equation (81) allows the variation of solvent goodness caused by temperature changes to be described quantitatively. Thus the interaction parameter x is used to describe how B changes when a polymer is dissolved in different solvents. By contrast, 9 is used to describe the variation in B when a given polymer-solvent system is examined at different temperatures. This has been done for the polystyrene-cyclohexane system at three different temperatures the results are discussed in Example 3.4. 

EXAMPLE 3.4 Theta Temperature of A Polymer Solution from Second Virial Coefficient Data. Values of the second virial coefficient along with some pertinent volumes are tabulated below for the polystyrene-cyclohexane system at three temperatures. 

Eq. (5a) with v(T) = 1 and Eo(T) = 0 i.e. r0(T) = rv is identical with Eq. (2a), obtained previously by Casper and Schulz and proposed for the mathematical description of the PDC-calibration curves. It was shown above that this is not possible even in the vicinity of the theta point, if a large range of P is considered. Independently, the same result was obtained by Wolf and Breitenbach 10) from static separation experiments on the system polystyrene/cyclohexane (PS/CHX). In their notation... 

Fig. 22a and b. Dependence of the measured elution volume V = VD (in cm3, Fig. a), and of the standard deviation ctd (in cm3), skewness yD, and kurtosis 5D (Fig. b) on the weight-average of the polymerization degree Pw of very narrowly distributed polystyrene samples (BW-middle fractions of the anionic polystyrene standards), injected into the PDC-column 3) at 28 °C where the resolution of the column can be neglected in the Pw-range as indicated (polystyrene/cyclohexane, theta temperature 34 °C)... 

In order to apply the above procedure to determine the conditions of phase separation, we have chosen the system of polyisobutene-stabilized silica particles with polystyrene as the free polymer dissolved in cyclohexane. The system temperature is chosen to be the 8 temperature for the polystyrene-cyclohexane system (34.5°C), corresponding to the experimental conditions of deHek and Vrij (1). The pertinent parameters required for the calculation of the contribution of the adsorbed layers to the total interaction potential are a = 48 nm, u, =0.18 nm3, 5 = 5 nm, Xi = 0.47(32), X2 = 0.10(32), v = 0.10, and up = 2.36 nm3. It can be seen from Fig. 2 that these forces are repulsive, with very large positive values for the potential energy at small distances of separation and falling off to zero at separation distances of the order of 25, where 6 is the thickness of the adsorbed layer. At the distance of separation 5, the expressions for the interpenetration domain and the interpenetration plus compression domain give the same value for the free energy, indicating a continuous transition from one domain to the other. 

Fig. 1. Interaction potential between two colloidal particles as a function of the reduced centre-to-centre separation R = r/2a, where a is the radius of the particles. Curve 1, steric repulsion due to the adsorbed layer (Vs) curve 2, attraction due to the free polymer (Vd) curve 3, van dcr Waals attraction (X7.,) curve 4, sum of the contributions given by curves 1—3. System polvisobutene-stabilized silica particles and polystyrene (free polymer) in cyclohexane at 308 K. Molecular weight of the free polymer = 82,000, volume fraction of polystyrene, 0 = 0.02, a = 48 nm, thickness of the adsorbed layer 6 = 5 nm, x = 0.5 for polystyrene—cyclohexane, x, = 0.47 and xs = 0.10 for polyisobutene— cyclohexane, AjkT 4.54 and v = 0.10.

Fig. 2. Phase diagram at 340 K, showing the particle concentration p/p0 in the coexisting ordered and disordered phases as a function of the volume fraction of the free polymer for different molecular weights of the free polymer. (I), 36,000 (II), 82,000 (III), 122,000 (IV), 176,000 (V), 490,000. System polyisobutene-stabilized silica particles with polystyrene as the free polymer in cyclohexane, a = 48 nm, 6=5 lim. The lower curves represent the transition boundary from a stable disordered phase to the two-phase region, and the upper curves the two-phase region to the stable ordered phase boundary. x, = 0.47 and xs = 0.10 for polyisobutene—cyclohexane, A/kT = 4.54 and v = 0.10. The value of x for polystyrene—cyclohexane is calculated according to Eqn (16).

In a third set of experiments we compared cloud-point data of the polystyrene-cyclohexane-carbon dioxide system (9.6 wt% polystyrene, 9.6 wt% C02) to the data of de Loos (9.4 wt% polystyrene, 5.0 wt% and 9.1 wt% polystyrene, 10.0 wt% CO2) [7], This author used the identical polymer sample. The isopleths in Figure show an almost linear increase in pressure as the temperature is risen. Interpolation of the cloud-point temperature with carbon dioxide content and polystyrene content yields excellent agreement of the data. 

Figure 4 LLE polystyrene-cyclohexane-C02, literature data vs. data from this work (CO2 content as indicated)...

Krigbaum, W. R. Geymer, D. 0., "Thermodynamics of Polymer Solutions. The Polystyrene-Cyclohexane System Near the Flory Theta Temperature," J. Am. Chem. Soc., 81, 1859 (1959). 

Nakata, M. Kuwahara, N. Kaneko, M., "Coexistence Curve for Polystyrene- Cyclohexane Near the Critical Point," J. Chem. Phys., 62, 4278 (1975). 

Saeki, S. Kuwahara, N. Nakata, M. Kaneko, M., "Pressure Dependence of Upper Critical Solution Temperatures in the Polystyrene-Cyclohexane System," Polymer, 16, 445 (1975). 

For the system polystyrene/cyclohexane the following values of In as were obtained at 34°C [Krigbaum and Geymer, JACS, 81, 1859(1959)] ... 

Schroder, J.M., Wiegand, S., Aberle, L.B., Kleemeier, M., and Schroer, W. Experimental determination of singly scattered light close to the critical point in a polystyrene/Cyclohexane mixture. Phys. Chem. Chem. Phys., 1999, 1, p. 3287-92. 

Let us consider a solution of partially repulsive chains. The polystyrene-cyclohexane solutions in the vicinity of 34 °C (temperature TF) are of this type, and have been studied a great deal. We shall interpret the observations with the help of the basic parameters of the standard continuous model, which are the two-body interaction b and the three-body interaction c. In the sequel (Section 2.2), we also use the osmotic parameters g and h which are more adapted to a study of the tricritical state. 

Here, the two-body interaction b becomes attractive whereas the three-body interaction remains repulsive. In Chapter 15, Section 3.1.1, we determined how b varies with temperature, for the polystyrene-cyclohexane system. We obtained the result... 

The value of vr for the polystyrene-cyclohexane system is given by Fig. 5.15 (Chapter 5)... 

The demixtion curves were measured for various molecular masses Mw. Figure 16.2 represents a result of experiments2 made with polystyrene-cyclohexane solutions. Here the concentration is expressed with the help of the volume fraction... 

The values of Te deduced from Fig. 16.3 and the other experimental values of Tc concerning the polystyrene-cyclohexane system obey the empirical relation... 

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