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Static and Dynamic Properties of Polystyrene in Good Solvents: Ethylbenzene and Tetrahydrofuran K. Venkataswamy and A. M. Jamieson* Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106
R. G. Petschek Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106. Received January 25, 1985 ABSTRACT We report static and dynamic light scattering studies of polystyrenesof narrow molecular weight distribution in ethylbenzene (EtPh) and tetrahydrofuran (THF) as solvents. These experiments generate , second osmotic virial coefficient,A2,z-average values for z-average radius of gyration, ( R g ) zweight-average translational diffusion coefficients, (Dt)z,and hence the diffusion virial coefficients, kD, and the z-average of the inverse frictional radius, (R;l)z. The results show that while for a specific molecular weight the (Rg)z values in THF are similar to our experimental values in ethylbenzene and to literature values in benzene or toluene, the A2 values, as well as hydrodynamic radii, are substantially larger for THF. We find that values of “universal ratios” of static and dynamic quantities in ethylbenzene are in good agreement with predictions of renormalization group theory appropriate to the nondraining good-solvent limit, while those for THF are not. We present a more stringent test of universality by plotting the static light scattering data directly in a “scaling”form. Identical polystyrene samples in THF and ethylbenzene are clearly different when analyzed in this way, although they do conform to an empirical universal description for solvents of arbitr-aryquality. These analyses suggest that in THF polystyrene exists in a more flexible conformation and is closer t o the nondraining, good-solvent limit.
Background Interest in measurements of the transport properties of polymer chains in good solvents has revived recently because of new theoretical developments that have established procedures by which realistic predictions of experimental parameters can be made for such systems. On the one hand, numerical simulations of chain dynamics, usually using Monte Carlo methods previously confined to Gaussian chains,lB2can now be extended to self-avoiding walk^,^-^ thus enabling one to incorporate the excludedvolume effect. On the other hand, successful application of renormalization group (RG) techniques6 to describe features of polymer chain statistics with excluded have led recently to RG calculations of polymer hydrodynamic parameter^.^-'^ Theory predicts’~~ and experiment appears to confiil3J4 that structural radii, R , exhibit power scaling laws against molecular weight, M , of the form R
-
Mu
(1)
where v is a characteristic exponent. For Gaussian coils, v = 0.5 and, as solvent quality increases, Y rises smoothly to the asymptotic value v = 0.588. Experiment indic a t e ~ ’ ~that , ’ ~ the crossover occurs more sharply for the static radius (Rg)* than for the hydrodynamic radii. Recent RG calculations further predict specific values for certain universal ratios of static and hydrodynamic par a m e t e r ~ .These ~ are 0024-9297/86/2219-0124$01.50/0
(3)
(4)
and
where the frictional coefficient f = 6 q , R f = k T / 6 ~ q , D ~ , and Do, is the limiting translational diffusion coefficient. In eq 2-6, [q] is the intrinsic viscosity, qs is the solvent viscosity, NAis Avogadro’s number, k is the Boltzmann constant, and Tis absolute temperature. These quantities have been calculated recentlys for both the 8 and asymptotic good-solvent limit, the hydrodynamics being formulated within the Kirkwood-Riseman model with a full Oseen tensor description. Polystyrene is one of the most widely studied polymers because of the availability of polymer samples of narrow 0 1986 American Chemical Society
Macromolecules, Vol. 19, No. 1, 1986
molecular weight distribution. A substantial amount of work covering a wide range of molecular weights has already been reported in the literature for "good" solvents such as benzene,'"'' toluene,lgzo and tetrahydrofuran (THF).2@24 In this paper we report results of photon correlation spectroscopy and viscosity experiments o n polystyrene i n ethylbenzene ( E t P h ) and THF. The experimental quantities of interest are the translational diffusion coefficient, ( Dt)z,the intrinsic viscosity [TI, the z-average radius of gyration, ( R g ) zand , the second virial coefficients A2. Our static and d y n a m i c light scattering results on a wide range of molecular weights (0.1 X 106-8.5 X lo6) in ethylbenzene are the first reported for this solvent. We compare these results with the chemically similar solvents toluene and benzene. In THF, we have extended the experimental i n f ~ r m a t i o non~ ~ and A2 to higher molecular weights.
Experimental Section Materials. Polystyrene standards of very narrow molecular weight distribution were purchased from Pressure Chemicals and Toya Soda (Japan). The weight-averagemolecular weights ranged from 0.1 X lo6 to 8.48 X lo6. The sample was used as purchased and was not further purified. THF (reagent grade) and E t P h (spectroscopic grade) were obtained from Aldrich Chemical Co. The physical constants of T H F a t 30 'C were refractive index n30Dc= 1.403, viscosity 7 = 0.438 cP, and with polystyrene solute (dn/dc)30.c = 0.2133 mL/g. For ethylbenzene a t 25 "C the physical constants were refractive index ~ 1 2 5 0=~ 1.495, viscosity 7 = 0.619 cP, and with polystyrene (dn/dc)z5.c = 0.106 mL/g. Since recent work has notedz6that T H F is hygroscopic and that the presence of significant amounts of water can markedly alter the thermodynamic properties of solutions of polystyrene in THF, we felt it necessary to determine the water content of our T H F solvent. Using the Karl Fischer titration assay (photovolt Aquatest JY)we , found our THF contained 0.09% H20. This level of water should have negligible impact on the solution thermodynamic^.^^ Solutions were prepared by dissolving a known quantity of the polymer in the solvent, which was filtered thoroughly prior to use. Filtrations were carried through 0.2-pm and 0.5-pm Millipore Teflon filters under the influence of gravity. This was done to avoid any shear degradation of the polymer during filtration, and our light scattering measurements corroborated this fact. Filtrations were repeated until the samples were free from dust particles, which are centers for parasitic scattering. For light scattering measurements, the samples were diluted into sealed scattering cells and further centrifuged at low speeds, 5OOO rpm for 30 min to 1h prior to experimentation. Fortunately, because of the ease of dissolution of polystyrene in THF and EtPh, it was possible to carry out a complete light scattering analysis on freshly prepared solutions, Le., within a 12-h period after dissolution. Methods. Two instruments were employed to carry out the static and dynamic light scattering experiments: a custom-built system, which has been described elsewhere,%utilizing a Coherent Radiation Model 42 Ar' laser (A = 4880 A) with a Saicor 42 digital correlator and an Ortec photon counter to measure the mean value of the intensity of the scattered light, and a Brookhaven Instrument Corp. spectrometer comprising a BI 2000 goniometer and BI 2020 correlator with Spectra Physics 15-mW He/Ne laser (A = 6328 A). The temperature of measurements was 298 K for PS in E t P h and 303 K for P S in T H F , in each case controlled to within 10.1 K. The weight-average molecular weight M,, second virial coefz obtained ficients A2, and z-average radius of gyration ( R g ) were by measuring the average intensity of the scattered light as a function of angle and concentrations. For low molecular weights, the extrapolations were carried out a t a finite angle (6' = 40'). The working equation for the excess Rayleigh's ratio RBis given bY 1 Kc - = -+ 2Azc + 3A& + ... (7) ARB MJ(6') where K is the optical constant of the system and A2 and A, are
Properties of Polystyrene in Good Solvents 125 the second and third osmotic virial coefficients, respectively. P(6'), the particle scattering function, can be expressed in terms of the solvent refractive index n and wavelength of incident light A in vacuo as
{
P'(6')= 1 +
16.rr2n2(R;), sin2 (6'/2)
3A'
1
+ ...
(8)
For low molecular weights (M, 5 0.6 X lo6), P(6') = 1 within experimental error a t accessible angles and eq 7 reduces to Kc 1 - = - 2A2c + 3A$ ... ARB Mw
+
+
The high molecular weight samples exhibited curvature in Zimm plots,27 and hence square-root plots" were employed. Taking square roots of eq 7 and substituting A3 = (1/3)A2M,, one can write (KC/AR~)~I~B_-O = (l/Mw''z)(l
+ A2M,c)
(loa)
and
In our calculation, higher order virial coefficeints (>A3) are assumed equal to 0. Az is evaluated from the slope of ( K C / A R ~ ) ' / ~ ~ against concentration, whereas (RP)1/2zwas obtained by the slope of (KC/AR~)~/'& against sin2(6'/2).Our experiments were carried out in the angular range of 30-65' at intervals of 5'. For the lowest molecular weight for which ( R g ) zis reported here (M, = 0.9 x lo6), measurements were carried out over a much wider angular range (30-145'). Measurements below 30' were not reproducible due to scattering from the cell walls. The molecular weights obtained by the extrapolation of ( K C / A R ~ ) ~ I ' to ~ +0 angle and ( K C / A R ~ ) 'to/ ~0 ~concentration were equal within the experimental error ( e l % ) , and average values are reported here. The intensity measurements were repeated and are reproducible to within a few percent. The t-average translational diffusion coefficients (Dt)zwere determined by moment analysis of the correlation function given byz6 C ( T )=
expt-rr) d r
(11)
where F = J;G(r)r d r is the mean relaxation rate. Expansion of the correlation function as a Taylor series In C(T) = - T i
P2 + -2!1 -(rip + ... f2
(12)
where the first moment, f , can be related to the z-average translational diffusion coefficient (Dt)zby
F = 2(D,),q2
(13)
where q = ( 4 ~ n / A sin ) (6'/2), A is the wavelength of the light in vacuum, n is the refractive index of the medium, and 6' is the scattering angle. The second moment, pz, is the variance in r: p2
= (
r2)- F2
(14)
A typical correlation function is shown in Figure 1. The first and second moments were determined by moment analysis described above. For molecular weights less than 1.0 X lo6, the experiments were carried out a t a single angle 6' = 40' (qR,
