10818
J. Phys. Chem. 1993,97, 10818-10823
Modification of Solvent Rotational Dynamics by the Addition of Small Molecules or Polymers Daniel J. Gisser and M. D. Ediger’ Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 Received: April 19, 1993; In Final Form: June 23, 1993” W e address the general problem of how the addition of a solute to a solvent affects the rotational dynamics of the solvent. New experimental results for two types of systems are presented. In the first set of experiments, the solute is a macromolecule (polystyrene, polyisoprene, or polybutadiene) and the solvent is toluene. In the second set of experiments, a mixture of two small molecules (1-methylcyclohexene and 1-chloronaphthalene) is studied. For this mixture the dynamics of both components are monitored across the entire composition regime. Consistent with our previous work, we find that the effect of the solute on the solvent dynamics is related to the difference in time scales between solvent and solute reorientational motion. A simple hydrodynamic model which explains this result is presented. 13Cand *HNMR relaxation measurements were used to determine rotation times.
constant for segmental motions of the polymer in dilute solution, Introduction and T ~ ~ ~is ~the~ solvent ~ ~ ( reorientation c ) time. Q is a positive We address the general issue of how one might understand the empirical constant which describes the strength of the coupling dynamics of each component in a homogeneous binary mixture. between the solvent dynamics and the local polymer dynamics. Our immediate attention is restricted to systems without strong We showed that data for three polymers (polyisoprene, polyspecific interactions between the components, Le., relatively butadiene, and polystyrene) in one solvent (Aroclor 1248) were nonpolar systems which cannot hydrogen bond. The components reasonably fit by eq 1 with Q equal to 4 mL/g, independent of might be small molecules or macromolecules. In this paper we temperature.” These data include cases where the polymer speeds present experiments on mixtures of two small molecules and up and slows down the solvent dynamics. While a coupling model mixtures of polymers with a small molecule where the polymer has been applied to some aspects of this problem,’* we believe eq concentration is low. Two other possible cases, that of polymer/ 1 is the only available prediction for the magnitude of the polymer mixtures and polymer/solvent mixtures where thesolvent modification of solvent dynamics by added polymer. (plasticizer) concentration is low, are not considered here but are of considerable technological significance. The dynamics of the Overview two components in these latter systems determine important We address three issues related to eq 1 in this paper. mechanical properties and are being studied by a number of First, does this equation describe the effect of added polymer research group^.^-^ The principles which govern the cases to solvents other than Aroclor? In some respects, Aroclor is an discussed in this paper may also be applicable to polymer blends unusual solvent. It is a mixture of chlorinated biphenyls, quite and plasticized polymers. viscous, and fairly close to its glass transition in the temperature The motivation for this work is provided by more than two range studied. In this paper we test the applicability of eq 1 with decades of research on the dynamic mechanical properties of a different solvent (toluene) but the same three polymers used dilute polymer solution^."^ While solvent properties have an in our previous study. We find that eq 1 qualitatively describes obvious effect on the dynamics of a dissolved polymer, the polymer can also substantially modify the dynamics of the ~olvent.~*~JO-I~these new results. Second, does eq 1 describe the behavior of mixtures of small Usually the polymer slows down solvent motions, but surprisingly, molecules? The physical arguments used to rationalize eq 1 are sometimes the polymer speeds up solvent motions. The modification of solvent dynamics must be understood if the dynamic also applicable to mixtures of small molecules. We have measured the rotational dynamics of 1-methylcyclohexene and 1-chloand hydrodynamic properties of polymers in solution are to be accurately extracted from viscoelastic measurements. Recent ronaphthalene in mixtures of these two liquids. As expected from our work with polymer solutions, we find that addition of a “slow” research in this area has been thoroughly reviewed by Lodge.6 solute to a “fast” solvent slows down the solvent dynamics, and Why does a particular polymer slow down or speed up the motion of a particular solvent? We16 and others6J5have argued vice versa. Equation 1 quantitatively describes the results throughout the entire concentration range with Q being the same that if local polymer dynamics in dilute solution are slower than the solvent dynamics, then solvent dynamics will slow as the no matter which molecule is considered the “solvent”. polymer concentration increases. On the other hand, if the Finally, we present a simple derivation of eq 1 for mixtures of polymer dynamics are faster than the solvent dynamics, then two small molecules. This derivation, together with the expersolvent motions will speed up as more polymer is added. The iments on the methylcyclohexene/chloronaphthalene system, greater the difference between the solute and solvent dynamics, supports the physical arguments used to rationalize the application the greater the expected effect of solute concentration on solvent of eq 1 to polymer/solvent systems. dynamics. Experimental Section We proposed the following empirical equation to test the above ideas quantitatively:I6 Materials. All polymers were purchased from Polysciences and had M , / M n d 1.07. Atactic polystyrene (PS) had M, = 50 000. Polyisoprene (PI, M, = 25 700) was 72% 1,4-cis, 18% 1,4-trans, and 10%3 , 4 4 1 ~ 1 .Polybutadiene (PB, M, = 24 000) was 40% cis, 52% trans, and 8% vinyl. Toluene-& (Aldrich and Here c is the solute (polymer) concentration, ~ ~ ~ l , ,is~ a~ time (o) Cambridge Isotope Laboratories), 1-chloronaphthalene (Kodak, Abstract published in Advance ACS Abstracts, September 15, 1993. CN), and 1-methylcyclohexene (MC, Fluka) were used as @
0022-3654/93/2097-108 18%04.00/0 0 1993 American Chemical Society
Solvent Rotational Dynamics received. The as-received "1-chloronaphthalene" contained 9% of the 2-chloronaphthalene isomer, notwithstanding the manufacturer's claim of 99% purity.lg Polymer solutions were prepared by weight and concentrations calculated assuming volume additivity with densities (g/mL) of 0.94 for toluene-&, 1.04 for PS, 0.91 3 for PI, and 0.895 for PB. CN and M C solutions were degassed through freezepumpthaw cycles. Other experimental procedures were similar to those described in ref 20. Toluene Rotation in Polymer Solutions. Toluene rotation times in dilute polymer/toluene-d8 solutions have been determined by 2H N M R TI measurements20 at Larmor frequencies of w~/27r = 55.3 and 15.4 MHz. Sample temperatures were 298.0 f 0.5 and 213 f 1 K. Most room temperature measurements were made at 15.4 MHz; all measurements a t 213 K were made at 55.3 MHz. T I was reproducible within 4% a t 298 K and 8% at 21 3 K. Our measurements for neat toluene-& are in excellent agreement with literature values.21-25 One of our sets of measurements (PS/toluene-& T = 298 K) reproduces and is in excellent agreement with previous Comparison with literature values indicates that the observed T I values are independent of Larmor frequency. The four peaks in the 2HN M R spectrum of toluene-& are at 6 = 7.14 ppm (meta), 7.06 ppm (para), 7.02 ppm (ortho), and 2.09 ppm (methyl). This assignment of the aromatic peaks is confirmed by the peak intensities, 2H TIS, and 1H-2Hcoupling patterns of the residual IH N M R spectrum of toluene-&. This assignment has not always been made correctly.26 In all 55.3MHz measurements, Tl(meta)/Tl(ortho) = 0.99 f 0.02 and Tl(meta)/Tl(para) = 1.25 f0.05. Resolutionat 15.4MHzwas not always adequate to make these comparisons. TI(methy1) is -5Tl(meta) and was not measured carefully. We analyze T I (meta) only. Rotational reorientation times of toluene-& are calculated from
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10819
-10.51 '
' ' I
"
'
I
'
' I
"
'
' -11.5
F
0.02
0.06
C-
I
"
'
1
i
0.10
[g/mIl
Figure 1. Rotationalcorrelation time of toluene-& as a function of polymer concentrationand temperature. The three polymers are polystyrene (o), polyisoprene ( 0 ) and , polybutadiene (0). The slopes of the best fit lines are included in Table I. Data in the top (bottom) half of this figure were collected at T = 213 K (298 K). TABLE I: Modification of Solvent Dynamics in Polymer/ Toluene-& Solutionss 298 K 213 K
a In v c Q (mL/g) a In v c Q (mL/g) PB 0.7 0.5 3.4 1.8 PI 0.8 0.6 3.7 2.0 PS 2.2 0.9 7.6 1.9 Uncertainties: T = 298 K: a In t/ac, k0.4;Q,f0.3. T = 213 K: a In {/lac, k0.8;Q,k0.5. The 13C N M R spectrum of M C has seven peaks.34 We use averages of the T I Sfor the four methylenes to calculate 7MC. Generally, three of the methylene Tls agree within experimental uncertainty(flO%). The fourth, intheposition para tothemethyl group, has T I about 20% shorter. The full NOE (2.98 0.05) is obtained for each methylene carbon. Rotational correlation times are calculated for C N and M C from T I and NOE data. First, the dipole-dipole contribution is determined from the experimental T I and NOE data,
*
This equation is applicable to both isotropic and anisotropic reorientation of the C-2H bond vector, as long as the extreme narrowing conditions are met and 7 is interpreted as the integral of the second-order orientation autocorrelation function for the C-2H vector.27 For toluene, the quadrupole coupling constant, QCC, is taken to be 179.9 kHz.28 The rotation of toluene in solution with PS has also been investigated by light scattering e x p e r i m e n t ~ . ~ ~At J ~ room temperature, the light scattering results show a weaker concentration dependence than that reported here for the 0-1 0%polymer range. There are some indications that this is also true at lower temperatures. Three possible reasons for these differences are (i) light scattering measures collective reorientation while the N M R experiments depend upon a single particle orientation correlation function, (ii) the dynamics of the polymer must be subtracted from the light scattering observable, and (iii) different definitions of the rotation time may be implicit in the analyses. 1-Chloronaphthaleneand 1-MethylcyclohexeneRotation. I3C N M R relaxation measurements were used to determine rotation times of C N and M C in mixtures of these two components. The I3C N M R spectrum of 1-chloronaphthalene has 10 peaks. Only the seven peaks corresponding to the protonated carbons are employed in our analysis. There is some uncertainty as to the assignment of these peaks3I-j3 We ignore this uncertainty since the TIS of these seven peaks for 1-chloronaphthalene agree within 15% of their average; the average is used to calculate 7 C N . The nuclear Overhauser effect (NOE) is 2.77 f 0.10 at each concentration. As noted above, C N is a mixturecontaining about 9% 2-chloronaphthalene. Typically, 7 for 2-chloronaphthalene is about 10% longer than 7 for 1-chloronaphthalene. Only values for 1-chloronaphthalene are used to calculate 7 C N .
-
(3) Correlation times are calculated from 7 =
1 1OnKTldd
(4)
where n = 1 for C N and n = 2 for MC. The values of K were calculated p r e v i ~ u s l y K ; ~= ~ 2.42 X lo9s - for ~ CN and K = 2.29 X lo9 s - ~for MC. The 7 in eq 4 represents the integral of the second-order orientation autocorrelation function for W-H vectors in C N or MC. All N M R experiments on C N / M C mixtures were performed at 273 K. Viscosities of the mixtures at this temperature were measured with an Ostwald viscometer. Effect of Polymer Concentration on Toluene Rotation In this section we evaluate the applicability of eq 1 to dilute solutions of polystyrene, polyisoprene, and polybutadiene in toluene. Figure 1 is a plot of the polymer concentration dependence of the toluene rotation time.36 At both temperatures, addition of any of the three polymers slows down the rotation of toluene. The effect is very small at the higher temperature, particularly when polyisoprene or polybutadiene is the solute. Table I lists values of the left side of eq 1; { is the ratio 7solvent(C)/7oolvent(0).
Gisser and Ediger
10820 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
TABLE 11: Correlation Times for Pure Toluene& and Segmental Time Constants for Three Polymers in Dilute Toluene-& Solutions (ps) ~~
298 K
213 K
2.4 92 58 880
12 890 930 1.2 x 105
-p -’
-io.+
~
toluene PB PI
PS
To calculate the right side of eq 1, we need to know the correlation times for local polymer motions for the three polymers in toluene. Although some of these have not been measured in toluene, they can all be calculated from eqs 14-16 in ref 16. These equations are accurate in all solvents we have studied. The equation for polyisoprene, for example, has been shown to apply to 10 solvents over a wide temperature range.37 We note that these same equations were used to evaluate eq 1 for these three polymers in Aroclor.I6 The viscosity of toluene is needed for these calculations; it is 2.9 CPat 213 K and 0.55CPa t 298 K.38.39 The calculated values of ~~l~~~~ are listed in Table 11, along with the measured correlation times of neat toluene.40 Three qualitative features of the results in Figure 1 are consistent with eq 1: (1) In all cases, rtoluene increases with increasing polymer concentration. Since Tpolymer > ?solvent (Table 11), solvent dynamics slow down upon addition of polymer. (2) ~~~l~~~~ is about the same in PB and PI solutions but significantly longer in PS solutions. This is predicted by eq 1 since PB and PI dynamics occur on similar time scales, and ~ p iss significantly longer than T p [ or TPB. (3) The concentration dependence of ~~~l~~~~ is stronger a t low temperature. This is expected as Tplymer/Ttoluene is larger at 213 K than at 298 K. The plot analogous to Figure 1 for Aroclor rotation has strikingly different features.41 Aroclor rotation speeds up as PI or PB is added but slows down as PS is added. Nevertheless, eq 1 qualitatively predicts the observed behavior in both the toluene and Aroclor systems. Equation 1 can be tested quantitatively by calculating values of Q for each polymer a t both temperatures. These values are listed in Table I. The uncertainties in Q are rather large due to the weak concentration dependence of Ttolucne. The results of PB, PI, and PS solutions in toluene are consistent with eq 1 if QtOlUene isallowed toincreaseas the temperaturedecreases. The possibility that Q might depend on temperature was not considered in ref 16. A reexamination of Figure 9 of that paper indicates that if Q A were~ allowed ~ ~to vary ~ with ~ temperature, it would also increase at lower temperatures. Q indicates the coupling strength between solvent reorientation and local polymer dynamics.I6 The values of QtOIUCnC are smaller than Q A ~ Floudas ~ ~ ~et al. ~ report . that Q for bis(2-ethylhexyl) phthalate is intermediate between these two values.30 The dynamics of small or nearly spherical molecules may be less affected by the presence of a nearby polymer chain. Other workers have suggested orientational ordering of the solvent12 and the vicinity of the solvent glass transition as important variables in determining Q.3O Mixtures of Methylcyclohexene and Chloronaphthalene System Choice. To test the applicability of eq 1 to binary mixtures of small molecules, the rotation times of both components must be measured across a wide composition range. For our purposes the two components should not be strongly interacting. We were unable to find published results from a study of this type. Published work either involved specific interactions (e.g., hydrogen measured dynamics of only one component,46 or showed only very small changes in dynamics with c~ncentration.~’Others have studied rotational dynamics of a dilute ternary probe in liquid m i x t u r e ~or~translational ~,~~ diffusion constants of both components of binary mixtures.50,51
Y
P,
-0
-1 -l .1 .1
0.0
0.2
0.4
0.6
0.8
1.0
‘C N
Figure 2. Rotational correlation times of both components of chloronaphthalene/methylcyclohexene mixtures at 273 K. See text for an explanation of the lines.
An important consideration in choosing a solvent pair for this study was that Tsolvent/~sOlutebe as different from 1 as possible. In order that the extreme narrowing conditions be achieved, it was necessary that neither liquid have rsolvcnt too long. The CN/MC pair is in some sense a chemically relevant model for the polymer/ Aroclor solutions. The slower component, CN, is a chlorinated aromatic hydrocarbon like Aroclor. MC contains the same structure as a cis-PI repeat unit: -CH2-CH-C(CH+CH2-. Although no AH,,,i, data are available for this system, we expect the dynamics of the mixtures will not be strongly influenced by thermodynamic effects given the large difference of dynamics of the pure component^.^^ Results. In this section we test the applicability of eq 1 to binary mixtures of C N and MC. Anticipating the derivation to follow, we rewrite eq 1 for small molecule mixtures using mole fraction:
As a result, Q’replaces Q. Figure 2 shows the correlation times of C N and M C as a function of solution composition. When XCN is small, solute (CN) dynamics are slower than solvent dynamics, resembling the polymer/toluene and PS/Aroclor solutions. Consistent with those experiments and eq 5 , as solute concentration increases, the solvent rotation time also increases. In the opposite concentration regime (XCN l), the solvent (CN) moves more slowly than the solute. As solute concentration increases, solvent dynamics become faster. This is predicted by eq 5 and is qualitatively similar to the behavior observed as PI or PB is added to Aroclor. Thus, themajor features of the polymer/Aroclor and polymer/toluene systems are qualitatively reproduced in this nonpolymeric system. A quantitative comparison to eq 5 begins with two observations. First, within experimental uncertainties, plots of log TCN and log TMC are linear in XCN. Thus, a In Tsolvent/aXCN is constant from XCN = 0 to l.52 Second, T C N / T M C is nearly independent of concentration and has an average value of 2.2. We assume this ratio remains constant in the limits XCN 0 and XCN 1. The correlation times for the two pure liquids are 2.6 ps (MC) and 26 ps (CN), so TCN(XCNEO) = 5.7 ps and T M C ( X C N E ~ ) = 12 ps. The two lines in Figure 2 connect the end points for each liquid a n d allow two calculations of t h e left side of eq 5 : a ln[TMC(xCN)]/axCN = 4 In[TCN(xMC)l/axMC = 1.5. The two observations above also allow calculation of the right side Of 5 : ~ ~ ~ [ T ~ ~ ( ~ ~ ~ ~ ~ ) / T =M 0.34 C ( ~and C Nlog’ o [ T ~ ~ ( X ~ ~ ~ ~ )= -0.34. / T ~ Evaluatingeq ~ ( X ~ ~5 with ~ ~ these ) ] values leads to two calculations of Q’, both of which have the result Q’ = 4.4. Thus, Q’ is the same across the entire concentrationrange no matter which molecule is considered the solvent. This result is consistent with the derivation which follows. It is difficult to compare the values of Q’for C N / M C binary mixtures to Q for the polymer solutions. Superficially, this is
-
-
-
) 1
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10821
Solvent Rotational Dynamics
0.8
F
0.6
0
Y
0.4
-
CI)
0
0.2
0.0 -2.0-
0.0
0.2
0.4
0.6
0.8
1.0
XCN
Figure 3. Viscosity of mixtures of 1-chloronaphthaleneand l-methylcyclohexene as a function of composition at 273 K. The line is eq 7, with the viscosities of the two pure components determined experimentally.
because Q and Q’ have different units. One could transform Q to mole fraction units based on polymer repeat units. The fundamental problem is that this would not be the correct comparison if several repeat units move together. The size of the independent moving unit is not well-known and may vary from polymer to polymer. The transformation to mole fraction does make Q’ more similar for Aroclor and toluene solutions. One would need to pick the moving unit to be about five repeat units in order for Q’for the polymer solutions to be roughly the same size as Q’for the C N / M C mixture. This estimate seems too large, a t least for PI and PB in toluene.s3 DebyeStokes-Einstein Relationship. The DebyeStokesEinstein (DSE) relation predicts molecular reorientation times based on continuum hydrodynamics: T~ = f ; . q y / k T (6) The index i = 1 or 2 identifies the two components in a binary mixture. viis the molecular volume of speciesi, k is the Boltzmann constant, and 7 is the solution viscosity. TheparameterJaccounts for the hydrodynamic boundary conditions (slip or stick) and effects of molecular shapes5* Many workers have found that the rotation of small molecules is not quantitatively described by eq 6. The data presented in the previous section for the C N / M C system are consistent with the overall picture which has emerged. Viscosities of mixtures of C N and M C at 273 K are shown in Figure 3. The line in Figure 3 is the equation (not a fit)
In q = x1In q1
0
1
2
3
7
4
5
6
7
[@I
Figure 4. Rotational correlation times of both solution components as a function of solution viscosity for chloronaphthalene/methylcyclohexene mixtures. Viscosity is varied by changing the solution composition. The
lines are best fits which have been constrainedto pass through the origin. If the DebyeStokes-Einstein relation worked for this system,the points would fall on the lines. We begin with the DSE relationship (eq 6 ) . For ease of notation, we choose component 1 to be the solvent and use T? to indicate the rotation time of either component as a pure liquid. Equation 6 can be written in the following form after dividing both sides by no:
This expression can be combined with eq 7 to yield the left side of eq 5:
(9) The ratio of times which appears on the right side of eq 5 can be rewritten using the DSE relation to give
-
(Recall TZ(O) is the rotation time of component 2 when xz 0; thus 4 0 ) # r2O.) Equations 9 and 10 can becombined to provide an expression for Q’:
+ x2 In t2
(7) The end points ql and q 2 are experimental values: TMC = 0.79 CP and ~ C N= 5.9 cP. Equation 7 has been used often for the viscosity of mixtures, although other forms have also been su~cessful.5~~55 Clearly, eq 7 provides an excellent rule for C N / M C mixtures. Figure 4 is a plot of each molecule’s rotation time versus solution viscosity. The two lines are best fits which have been constrained to pass through the origin. If the DSE relation worked, the data would fall on the two lines. As expected, the DSE relation is only obeyed approximately for these mixtures. The deviations at low viscosities can be accounted for by the introduction of a nonzero intercept into the DSE relati0n.4~~~’j-~~ If the data are fit to the form 7 = a bq, the following parameters are obtained: a C N = 2.4 PS, b C N = 3.9 pS/CP, UMC = 1.3 pS, and b M c = 1.7 pS/CP.
+
A Simple Derivation
In this section we present a simple derivation of eq 5 which is valid only for small molecules. It provides context for understanding the results on C N / M C mixtures presented in the previous section. Thisderivation is not rigorous in the sense that it employs relationships which are known to be only approximately correct.
Thus, we have obtained eq 5 with the requirement that Q’is given by eq 11. Thisderivation matches twofeaturesof the experimental results for the C N / M C system. First, eq 5 should apply throughout the entire concentration range. Second, the value of Q’is predicted to be the same no matter which molecule is chosen as the solvent. This follows from the observation that eq 11 is invariant to switching the subscripts “1” and “2”. Can anything more specific than eq 1 1 be said about the value of Q? Rather general arguments can be made that Q’ should usually be positive. Consider the ratio of logarithm terms in eq 1 1. If 72’’ > ~ ~ one 0 generally , expects that the ratio of correlation times for two pure liquids T2’/7]’ is larger than the ratio of their viscosities. This result is sufficient to make Q’ positive. The italicized statement above can be surmised from the proportionality in the DSE relationship between T and qV at constant temperature. Since we are interested only in a correlation between T and q, we can consider V to be a function of r). Generally, V increases as r) increases, so overall we expect that T increases faster than q when pure liquids are compared at a given temperature.
10822 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
Experiments on different liquids support the italicized statement from the previous paragraph. Results from two laboratories roughly follow the relationship
We know of no theoretical basis for this expression. Ten solvents shown in Figure 9 of ref 37 roughly follow this relationship at 333 KU6OData collected by Komoroski and Levy show a similar trend at 308 K.61 Together, eq 11 and 12 specify that Q’= 9.2, not the value of 4.4determinedin the previoussection. WhiletheCN/MCsystem obeys eq 7 quite accurately, it does not follow the DSE equation or eq 12 quantitatively. Since many small molecules only approximately obey the DSE relation and eq 12, we expect binary small molecule systems to show a range of Q’. Generally, we expect Q’to be positive. This is consistent with the principle that “slow molecules” should slow down “fast molecules”, and vice versa. It is not straightforward to modify the derivation just presented to treat the case of polymer/solvent mixtures. One would need a different expression from eq 6 since the rotation of small molecules in polymer solutions does not depend upon the macroscopic viscosity. Equation 6 could be written in terms of a local viscosity.20 However, in the absence of an equation analogous to eq 7 for the local viscosity, the derivation could not be completed. Concluding Remarks The addition of a second component to a solvent modifies the rotational dynamics of the solvent. Whether the second component is a polymer or another small molecule, eq 1 provides at least a qualitative framework for understanding the experimental results. The principle contained within this equation is simply that the effect of the secondcomponent upon thesolvent dynamics depends upon the relative time scales for the dynamics of the two components. We reiterate that this simple picture is unlikely to be adequate in systems with strong interactions. In particular, we found that eq 1 holds for both toluene and Aroclor16 when the second component is polybutadiene, polyisoprene, or polystyrene. Thus, it is likely that eq 1 is applicable to a widevariety of polymer/solvent systems. A slightly modified version of eq 1 (eq 5) described the results for a binary mixture of two small molecules. Reasonable assumptions lead to the derivation of eq 5 . This derivation and the experiments on small molecule mixtures support the physical arguments used to rationalize the application of eq 1 to polymer/solvent mixtures. The qualitative features of the modification of solvent dynamics do not depend upon whether the solute is a polymer or a small molecule. Our understanding of the microscopic nature of the coupling between solvent and solute dynamics is better for binary mixtures of two small molecules, however. An understanding of this coupling when the solute is a polymer remains a challenging problem. Acknowledgment. This research was supported by the National Science Foundation through the Division of Materials Research, Polymers Program (DMR-9123238). NMR experiments were performed in the Instrument Center of the Department of Chemistry, University of Wisconsin. We thank the staff for assistance. D.J.G. is grateful for fellowship support from the U.S. Department of Education. M.D.E. thanks the Alfred P. Sloan Foundation for fellowship support. We thank Marshall Fixman and Hyuk Yu for suggesting experiments on small molecule mixtures. Tim Lodge and John Schrag are acknowledged for helpful conversations. We thank D. B. Hess and W. Zhu for experimental assistance. Useful comments by the reviewers and Richard Moog are gratefully acknowledged. References and Notes ( I ) Floudas, G.; Fytas, G.; Fischer, E. W. Macromolecules 1991, 24, 1955.
Gisser and Ediger (2) Roland, C. M.; Ngai, K. L. Macromolecules 1992,25,363. (3) Floudas, G.; Higgins, J. S.; Kremer, F. Polym. Prepr. 1992,33 (l), 130. (4) Inglefield, P. T.; Jones, A. A.; Chin, Y. H.; Zhang, C. Polym. Prepr. 1992,33 (I), 76. (5) Floudas, G.; Fytas, G. J. Non-Crysi. Solids 1991, 131-133, 579. (6) Lodge, T. P. J . Phys. Chem. 1993,97,1480. (7) Schrag, J,L.;Stokich,T. M.;Strand,D. A.;Merchak,P. A.; Landry, C. J. T.; Radtke, D. R.; Man, V. F.; Lodge, T. P.; Morris, R. L.; Hermann, K. C.; Amelar, S.;\Eastman, C. E.; Smeltzly, M. A. J . Non-Crysr. Solids 1991,131-133, 531.’ (8) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980 and references therein. (9) For a discussion of other factors which may contribute see: Bird, R. B. Rheol. Acta 1989,28, 457. Fujita, H.Macromolecules 1993,26, 643. Fixman, M. J. Chem. Phys. 1990, 92,6858. (IO) Floudas, G.; Fytas, G.; Brown, W. J. Chem. Phys. 1992,96,2164. (11) Morris, R.L.;Amelar, S.; Lodge, T. P. J . Chem. Phys. 1988,89, 6523. (12) Amelar, S.; Krahn, J. R.; Hermann, K. C.; Morris, R. L.; Lodge, T. P. Specrrochim. Acra Rev. 1991, 14,379. (13) von Meerwall, E. D.; Amelar, S.; Smeltzly, M. A.; Lodge, T. P. Macromolecules 1989,22, 295. (14) Fytas, F.; Rizos, A.; Floudas, G.; Lodge, T. P. J . Chem. Phys. 1990, 93,5096. (15) Rizos, A.; Fytas,G.; Lodge, T. P.; Ngai, K. L. J . Chem. Phys. 1991, 95, 2980. (16) Gisser, D. J.; Ediger, M. D. Macromolecules 1992,25, 1284. (17) See Figure 9 of ref 16. (18) Ngai, K. L.J . Polym. Sci.: Polym. Phys. Ed. 1991,829,867. (19) All solution concentrations are reported as mole fraction CN. This is slightly misleading, as we actually have a ternary system. The reported values of XCN are the total mole fractions of both chloronaphthalene isomers, i.e., xcN(reported) = 1 - XMC. (20) Gisser, D. J.; Johnson, B. S.; Ediger, M. D.; von Meerwall, E. D. Macromolecules 1993,26, 5 12. (21) Spiess, H.W.; Schweitzer, D.; Haeberlen, U. J . Magn. Reson. 1973, 9,444. (22) R.&sler, E.; Sillescu, H. Chem. Phys. h i t . 1984,112,94. (23) Liu, G.; Mackowiak, Y.; Jonas, J. J . Chem. Phys. 1991, 94,239. (24) Fujara, F.; Sillescu, H.; Lodge, T. P. Unpublished results. (25) naNagara, B.; O’Connor, R. D.; Blum, F. D. J . Phys. Chem. 1992, 96,6417. (26) Bovey, F. A. Nuclear Magneric Resonance Spectroscopy. 2nd ed.; Academic Press: San Diego, 1988;p 139. (27) Lyerla, J. R.; McIntyre, H. M.; Torchia, D. A. Macromolecules 1974,7, 1I. (28) Barnes, R. G.; Bloom, J. W. J . Chem. Phys. 1972,57,3082. (29) Patterson, G. D.; Lindsey, C. P.; Alms, G. R. Macromolecules 1978, 11, 1242. (30) Floudas, G.; Steffen, W.; Brown, W.; Fischer, E. W. J. Chem. Phys., in press. (31) Sadtler Siandard Carbon-I3 N M R Spectra; Sadtler Research Laboratories: Philadelphia, 1976. (32) Ernst, L. J. Magn. Reson. 1975, 20, 544. (33) Wilson, N. K.;Zehr, R. D. J . Org. Chem. 1978,43, 1768. (34) Shapiro, B. L.;Johnston, M. D. J . Magn. Reson. 1973,12, 199. (35) Gisser, D. J.; Glowinkowski,S.; Ediger, M. D. Macromolecules 1991, 24,4270. (36) In general, nonsphericalmolecules have different rotational correlation times depending upon how the observed vector is oriented in the molecular frame. (See: Bauer, D. R.; Alms, G. R.; Brauman, J. I.; Pecora, R. J . Chem. Phys. 1974,61,2255. Lui, G.; Mackowiak, M.; Li, Y.; Jonas, J. J . Chem. Phys. 1991,94,239 and references therein.) For toluene, CN, and MC, these differencesaresmall and independent ofconcentration. Thus, for our purposes, these molecules can be described by a single rotation time. (37) Glowinkowski,S.;Gisser, D. J.; Ediger, M. D. Macromolecules 1990, 23, 3520. (38) Inrernarional Crirical Tables;Washburn, E. W., West, C. J., Dorsey, N. E., Ring, M. D., Eds.; McGraw-Hill: New York, 1930;Vol. VII, p 211. (39) Barlow, A. J.; Lamb, J.; Matheson, A. J. Proc. R . SOC.London A 1966,292, 322. (40) It may be surprising that the segmental time constant for PB listed in Table I1 is longer than the values for PI at 298 K. This is due to the approximate na&e of eq 16 in ref 16 and to the fact that the tabulated values are segmental rather than correlation times. Direct experiments on PB and PI in toluene would likely show that T I values for PB are longer than those for PI (indicating that PB has a shorter correlation time). Given the uncertainties in evaluating the left side of eq 1, the error associated with using eq 16 can be ignored. (41) See Figure 1 of ref 6. (42) Goldammer, E. V.; Zeidler, M. D. Ber. Bunsen-Ges. Phys. Chem. 1969,73,4. (43) Wang, C. H.; Whittenburg, S. L.; Lund, P.-A.; Christensen, D. H. J . Chem. Phys. 1980,72,4228. (44) Cebe., E.; Kaltenmeier, D.; Hertz, H. G. Z . Phys. Chem. (Munich) 1984,140, 181. (45) Kovacs, H.; Kowalewski, J.; Maliniak, A. J . Phys. Chem. 1989,93, 96’) ”_. ~
(46) Matsubayashi, N.; Nakahara, M . J . Chem. Phys. 1991,94,653.
Solvent Rotational Dynamics (47) Suhm, M. A.; Miiller,K. J.; Weingiirtner,H.Z. Phys. Chem. (Munich) 1987, 155, 101. (48) Alavi, D. S.;Waldeck, D. H. J . Phys. Chem. 1991, 95, 4848. (49) Kowert, B.; Kivelson, D. J . Chem. Phys. 1976,64, 5206. (50) von Meerwall, E.; Ferguson, R. D. J. Chem. Phys. 1981, 75, 937. (51) von Meerwall, E.; Van Antwerp, R. Macromolecules 1982,15,1115. (52) Generally, a In sdV,,,/ac is not constant (with respect to c) in concentrated polymer solutions. See for example, refs 20 and 25. An apparent counterexample is the poly(methy1 methacrylate)/toluene system (ref 10). For that system, a In T,lvcnt/ac is constant from 0 to 70% polymer. (53) Adolf, D. A.; Ediger, M. D. Macromolecules 1992, 25, 1074. (54) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley & Sons: New York, 1954; p 630. (55) Doolittle, A. K. The Technology of Solvents and Plasticizers; John Wiley & Sons: New York, 1954; p 784. (56) Alms, G. R.; Bauer, D. R.; Brauman, J. I.; Pecora, R.J. Chem. Phys. 1973, 58, 5570.
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10823 (57) Artaki, I.; Jonas, J. J . Chem. Phys. 1985, 82, 3360. (58) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981,85, 2169. (59) Kivelson, D. In Rorafional Dynamics of Small and Macromolecules; Pecora, R., Dorfmuller, T., Eds.; Lecture Notes in Physics, Vol. 293; Springer-Verlag: Berlin, 1987; p 1. (60) The data in ref 37 are actually not from neat liquidsbut fromsolutions of 10% PI in 10. dents at 333 K. Modification of solvent dynamics due to the presenckgftlg% PI is a negligible effect at 333 K, even in Aroclor. The two liquids uJd in this work, CN and MC (at 273 K), fall well within the scatter of Figure 9 of ref 37. (61) Komoroski, R. A.; Levy, G. C. J. Phys. Chem. 1976,80,2410. 13C T I values were measured for a series of pure cyclic methyl ethers whose viscosities span the range 0.5-4.4 cP. TI-',which is directly proportional to T C , increases as for this series. In a similar set of experiments with pure cycloalkanones, T increased as $ . I .
