4 Critical Phenomena in Multicomponent Polymer Solutions
Downloaded by RUTGERS UNIV on January 1, 2018 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0099.ch004
W. B O R C H A R D and G. R E H A G E Physikalisch-Chemisches Institut der Technischen Universität Clausthal, Germany The maximum (or minimum) precipitation temperature of a partially miscible polymer solution cannot be identified with the critical point. These macromolecular solutions must be treated as multicomponent systems. Thus, the thermodynamic properties can be described in the critical region. The critical point can be determined by measuring phase-volume ratios as a function of concentration at temperatures near the cloud point. Light scattering measurements on the system polystyrene-cyclohexane show that the maximum dissymmetry of the scattering envelope arising from the critical opalescence lies at polymer concentrations lower than the critical point. The scattered intensities exhibit a typical function by which the cloud points can be determined. Concentration fluctuations persisting over large distances near the critical point lead to anomalous behavior of the transport coefficients.
T n the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. A t the critical con centration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, 11, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity ( 15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Ornstein and Zernike (25), Debye (3) made the as sumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local 42 Platzer; Multicomponent Polymer Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
Downloaded by RUTGERS UNIV on January 1, 2018 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0099.ch004
4.
BORCHARD A N D REHAGE
43
Critical Phenomena
gradient of the fluctuation. Fixman considers the existence of an intense spectrum of long wavelength composition variations as the basis of a theory of critical viscosities that relies on macroscopic transport equa tions to describe the interaction of a velocity gradient with composition fluctuations. As far as the above-mentioned theories were applied to binary low molecular compounds, comparisons with experiments were completely conclusive. However, applying the theoretical predictions to solutions of a solvent and a polymer the maximum i n the dissymmetry ratio was at a different polymer concentration than the maximum of the relative temperature coefficient of the viscosity (8). This paper reports measurements of light scattering and viscosity of the system polystyrenecyclohexane, which has a miscibility gap with an upper critical point. Critical Opalescence of Polystyrene in Cyclohexane According to the fluctuation theory of Einstein (10), the additional amount of light scattered by a solution compared with that scattered by a pure solvent is given by the mean square of the concentration fluctua tions in small volume elements. Derivations for the scattered light of a polydisperse polymer in a solution were given by Brinkman and Hermans ( J ) and soon afterwards by Kirkwood and Goldberg (19) and by Stockmayer (33). Zimm and Doty (35) found that the weight aver age molecular weight can be obtained from light scattering measurements. Near a critical point strong scattering, called the critical opalescence, is observed. This scattering phenomenon can be described only if the influence of the concentration gradients is taken into consideration. The intensity of light scattered at an angle θ between the secondary and primary beam at large distances R from the scattering volume V has been formulated by Debye and others (6,9,24): J
e
_ 4x
2
ΚΡ(Θ)
VOL
h ~ R* λ
(D
4
le is the intensity of the scattered light at angle Θ, 1 is the intensity of the primary light beam, λ is the wavelength of light in the medium, φ is the volume fraction of the polymer, Π is the osmotic pressure. F o r u n 0
2
polarized light a is given by *
^
Q S
^.
The optical constant Κ is a function of the refractive index and the refractive index increment, and F (θ) is the particle scattering function which depends on internal interference. This function is influenced by the particle shape and is less than 1 for molecules large compared with
Platzer; Multicomponent Polymer Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
44
M U L T I C O M P O N E N T P O L Y M E R SYSTEMS
the wavelength of light. The quantity H depends on the interaction en ergies between the different molecules and the range of molecular forces. Comparing the derivation given by Debye with the well known FloryHuggins (16, 17) treatment one can conclude that H depends on con centration if the Flory-Huggins interaction parameter is a function of the polymer concentration. If the incident beam is polarized at right angles to the plane of observation, according to the formula of Debye, the reciprocal scattered intensity is proportional to λ sin (Θ/2) at the spinodial composition. W h e n scattering intensities are extrapolated to zero angle at low con centrations of not too large molecules, Einstein's formula is obtained. A n equation for the light scattered by a polydisperse system i n the critical region has not yet been derived. F r o m the above mentioned considera tions it follows that i n the case of Debye scattering, however, the scatter ing intensities extrapolated to zero angle depend in the same way on the concentration fluctuations as in Rayleigh scattering, so that the theories for polydisperse polymer solutions can be used (32).
Downloaded by RUTGERS UNIV on January 1, 2018 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0099.ch004
2
2
Experimental The light scattering measurements were performed with a Sofica photogoniometer. The temperature was controlled by a special bath, which was mounted around the index vat, in which benzene was stirred to achieve a good temperature uniformity in the measuring cell. B y means of a heated head-piece, which was kept at bath temperature, the tem perature remained constant to 0.01 °C. The solutions from a sample of anionic polystyrene (courtesy of B A S F , Ludwigshafen) and the solvent were prepared by weighing. Poly styrene is characterized by the data in Table I. [The average molecular weights were determined in the Central Laboratory of the N . V . Staatsm i j n e n / D S M (Geleen, The Netherlands).] Solutions of polystyrene and purified cyclohexane after filtration still exhibited appreciable dissymmetry of scattered intensities at high tem peratures where the influence of the critical opalescence was precluded. Therefore all solutions were freed from dust by centrifugation. After a Table I.
Properties of Polystyrene Sample Investigated M
= (4.4 ± 0.2) Χ 10 grams mole"
M
= (4.7 ± 0.2) Χ 10 grams mole"
M
=
n
w
z
5
5
6.5 Χ 10 grams mole"
= 1.07 ± 0.07 T
e
= 27.63°C
5
1
1
1
1.4 ; ^ ± i -
1.6
= 8.5 wt %
5T,», = 28.43°C Γ">2
