861
Macromolecules 1989,22, 861-865 509; Proc. R. SOC. London, A 1975, 343,427. (9) See, e.g. Flory, P. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1971; Chapter 12. (10) Semenov, A. N. Sou. Phys. JETP 1985, 61, 733 (Zh. Eksp. Teor. Fiz. 1985, 88, 1242). (11) Of course, fluctuations will smear the 'time zone" boundaries
-
over a distance of order R, P/', which is the characteristic scale of fluctuation corrections to the classical limit. Nonetheless, in the limit of large molecular weight at fmed coverage, the time zones are sharply defined, insofar as R, is small compared to the brush height. (12) Several situations may be envisioned, depending on the mobility of the chain attachment points along the grafting surface. If the chain attachment points are free to move, we expect complete in-plane phase separation of sufficiently incompatible chains in a brush. If the chain ends are irreversibly atta-
ched to the surface, some sort of microphase separation may take place, with a length scale related to the brush height. These phase separations are not to be confused with the segragation by molecular weight of the free-chain ends in the direction normal to the grafting surface, which is a quite general phenomenon, as discussed above. (13) dz/dU u-l/' in eq 17 gives n = const, which may be anticipated because the integral is then a homogeneous function of U. Similarly, we may guess that shifting the square root singularity with dz/dU (V - V,)-1/2e(V- VI) may produce n(V) = const X e(V - Vl), which is exactly what happens. (14) There is always a regime of very small compressions, for which the few long chains affected are too dilute to be stretched. Here our classical limit breaks down, and the energies and densities resemble those of dilute grafted chains. (15) Milner, S. T.; Witten, T. A., to be submitted for publication.
-
-
Chemical Composition Distribution of a Graft Copolymer Prepared from Macromonomer: Fractionation in Demixing Solventst Jaroslav Stejskal,* Dagmar StrakovQ,and Pave1 Kratochvil Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia
Steven D. Smith and James E. McGrath Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061. Received March 28, 1988 ABSTRACT A graft copolymer prepared by radical copolymerization of poly(dimethylsil0xane) macromonomer with methyl methacrylate has been characterized by light scattering and osmometry. The number- and weight-average molecular weights of the whole copolymer, its backbone, and the graft part were determined. Copolymer macromolecules contain five grafts on an average. The copolymer was fractionated in a demixing solvent pair dimethyl sulfoxidetetrachloroethylene. Fractions differing up to 24 wt 70in methyl methacrylate unit content were obtained. The advantages of this novel method of fractionation are discussed. The integral distribution of chemical composition evaluated from the fractionation data agrees well with the theoretical prediction.
Introduction Synthesis of graft copolymers by statistical copolymerization of ordinary low molecular weight monomers with macromonomers has recently became an attractive field of research.' So far, not much attention has been paid to the characterization of chemical heterogeneity of these copolymers, even though the model calculations predict?3 similarly to block copolymers>6relatively broad chemical composition distributions (CCD). One of the reasons may be the limited efficiency of the present fractionation methods. Especially in the classical precipitation fractionation, the formation of polymolecular micelles6 may create serious problems.' It should be realized that, in addition to distribution of molecular weights, CCD also may affect the properties of copolymers. It is the aim of this study to contribute to the methodology of graft copolymer characterization and to confront the theoretically predicted CCD with experimental results. Poly(methy1 methacrylate) (PMMA) grafted with poly(dimethylsiloxane) (PDMS), PMMA-g-PDMS,8,9was selected for this purpose. A separation method based on the distribution of a copolymer between the phases of de+ We are happy to dedicate this paper to Professor 0. Wichterle, the founder of Czechoslovak polymer science, on the occasion of his 75th birthday.
mixing solvents'*12 was used to fractionate the graft copolymer according to chemical composition.
Experimental Section Graft Copolymer. The poly(dimethylsilox) macromonomer was prepareds by anionic polymerization of hexamethylcyclotrisiloxane (Petrarch Inc.) in cyclohexane with n-butyllithium as initiator and tetrahydrofuran as promoter. Termination of living anions with (3-(methacryloxy)propyl)dimethylchlorosilane (Petrarch Inc.) resulted in formation of a macromonomer, which was then precipitated into methanol and dried in vacuo. The number-average molecular weight, determined by vapor-pressure osmometry, was M * d = 10000. Free radical copolymerization of macromonomer with methyl methacrylate (MMA)%ewas carried out at 60 "C in toluene with azobisisobutyronitrile as initiator. The isolated PMMA-g-PDMS copolymer was extracted with n-hexane to remove the residual macromonomer and then dried in vacuo. The average content of PMMA found by NMR was 59.7 wt %. Solvents. Methyl ethyl ketone, tetralin (both from Fluka AG, Switzerland), toluene, dioxane, dimethyl sulfoxide (DMSO), tetrachloroethylene (TCE), and methanol (Lachema, Czechoslovakia) applied in the characterization and/or treatment of the graft copolymer were used as supplied by the manufacturer; only TCE was distilled on a laboratory column. Differential Refractometry. Refractive index increments of PMMA and PDMS ( M , = 7000) were determined with a Brice-Phoenix BP-2000-V differential refractometer a t 25 "C for a wavelength of 546 nm. The refractive index increments, dnldc,
0024-9297/89/2222-0861$01.50/00 1989 American Chemical Society
Macromolecules, Vol. 22, No. 2, 1989
862 Stejskal et al. 4[
T.
to a bath thermostated to 25 "C. Three coexisting phases were formed at this step. The lower and upper phase were separately removed (Figure 1)with a syringe, and after evaporation of most of the solvent, the present polymer was precipitated into excess of methanol. Collected fractions were dried. Fuchsine is easily and completely removed by washing with methanol, and its presence during the fractionation does not hamper the subsequent characterization of fractions. To the original middle phase, containing most of the copolymer, was added another portion of pure solvent phases, and the system was again homogenized at 60 "C. A new phase equilibrium was established at 26 "C (Figure l),and the whole procedure was repeated at gradually increasing temperature of phase decomposition (Figure 1). At higher temperature (above 31 "C at the particular conditions), only two coexisting phases form. The removed phase containing a copolymer fraction was always replaced by a pure solvent phase of the corresponding type. If the volume of some phase in equilibrium was too large, pure DMSO or TCE was added to increase the volume of the conjugated phase, followed by homogenization at elevated temperature. The system was left to equilibrate for 12-24 h at the desired temperature to ensure complete demixing of phases. A shorter time may be sufficient due to the large difference in phase densities. For a rough check, several droplets of each coexisting phase were always dropped into methanol, and from the amount of the precipitate, it was estimated which phase contained the bulk of the copolymer and should therefore be fractionated further. Altogether, 14 fractions were collected. The recovery of the copolymer after fractionation was 99.3 wt %.
~~
'C
35 L6 I
I
2 PHAKS
I
Q "; Q
30
25
I
3
PHASES
-/ 1
Figure 1. Fractionation scheme. Fractions located in the lower, TCE-rich phase (L), upper, DMSO-rich phase (U),and middle phase (M) were either collected (circled) or further fractionated. Above 31 "C, the system decomposes into two phases; below this temperature three liquid phases coexist. Fraction M2 was combined with fraction U2.
of the copolymer in various solvents were calculated according to the additivity rule: (dn/dc)c
(dn/dc)Af
+ (dn/dc)B(l - f )
(1)
where A, B, and C refer to PMMA, PDMS, and the copolymer, respectively. f is the average copolymer composition expressed by the weight fraction of PMMA in the copolymer. For copolymer fractions, the differential refractometry was used to determine (dn/dc)c and to calculate their chemical composition, f , from eq 1. Methyl ethyl ketone was used as solvent for this purpose. Light Scattering. Intensities of light scattered by copolymer solutions were measured with a Sofica 42.000 (France) using a vertically polarized primary beam of wavelength 546 nm. Solutions were fiitered through a sintered-glassfilter G5 (VEB Jenaer Glaswerke, GDR) prior to measurement. Molecular weights were evaluated from the light-sacttering data by the Zimm method. Osmometry. The number-average molecular weight of the whole copolymer was determined in toluene solution with a Wescan Model 230 membrane osmometer. Phase Diagram. The mixtures of DMSO and TCE with a TCE content gradually increasing by 5 vol % were placed into sealed glass ampules. A similar set of mixtures containing 0.5 wt % of the graft copolymer was also prepared. The content of ampules was homogenized by heating at 60 "C in a constanttemperature bath. The temperature was then slowly decreased, and the temperature of the first appearance of cloudiness, indicating the formation of the second phase, was noted as a function of the mixed-solvent composition. From these data, the phase diagram was constructed. Fractionation in Demixing Solvents. Dimethyl sulfoxide (about 30 vol 70) and tetrachloroethylene were mixed together, forming two coexisting phases at 25 "C. A small amount of fuchsine was added. The upper DMSO-rich phase becomes violet, and demixing of the phases and the phase boundary is then easily visible. To 4 g of the copolymer in a cylindrical flask was added 100 mL of each stock solvent phase, and the system was heated to 60 "C until clear solution was formed. The flask was transferred
Results and Discussion Molecular Characterization of the Whole Copolymer. For a chemically heterogeneous copolymer, the light-scattering method yields an apparent molecular weight, Map,instead of the true weight-average molecular weight, M,. T h e relation bgtween quantities was formulated by Bushuk a n d Benoit:13
Map= M,
+ 2PR + QR2
(2)
where R = [(dn/dc)A- ( d n / d ~ ) ~ ] / ( d n / d c )and c (dn/dcIJ are t h e refractive index increments of the constituent homopolymers (J = A, B) a n d of t h e copolymer (J = C), respectively. Equation 2 represents a parabolic function of the variable R, t h e value of which depends mainly on t h e refractive index of t h e solvent. B y determination of at least three apparent molecular weights Mapin solvents with different refractive indices, all three parameters of eq 2, viz., M,, P, a n d Q, can be evaluated.13J4 T h e parameter of chemical heterogeneity P describes t h e interdependence of t h e chemical composition and molecular weight distributions, while t h e parameter Q is closely related t o t h e variance of t h e chemical composition distribution. Of course, t h e molecular weight of t h e whole copolymer, M,, is information of prime interest. From t h e parameters of eq 2, the weight-average molecular weights of the individual copolymer parts also can be ~ a l c u l a t e d ,i.e., ' ~ in our case, that of the backbone, MwA, and that of the graft part, MwB. These molecular weights can also be determined by light scattering directly on condition that the refractive index increment of the other copolymer part is zero, i.e., if this component does n o t contribute to the intensity of scattered light. From eq 1, i t can be shown that, for (dn/dc)B = 0, t h e parameter R = l/a, a n d
MwA= %Map
[(dn/dc)B = 01
(3)
Alternatively, for (dn/dc)A = 0, t h e relation R = -l/(l a) holds a n d
Macromolecules, Vol. 22, No. 2, 1989
Graft Copolymer Prepared from Macromonomer 863
Table I Apparent Molecular Weights, Ma,,, of the PMMA-g-PDMS Copolymer Determined in Various Solvents in Which the Homopolymers PMMA and PDMS Have Refractive Index Increments (dm/dc), and (dn/dc); (dn/dc)A,
(dn/dc)B,
0.110 0.072 0 -0.040
cm3/g 0.029
w~M,, 3.95
-0.014 -0.092 -0.130
3.30 3.50
cm3/g
sold methyl ethyl ketone dioxane toluene tetralin
5,
3.65
2.60 1.35
PMMAbackbone PDMS graft part
2.6 0.597 5.1 0.041
0.019
For the graft copolymer under study, the apparent molecular weight were determined in four solvents (Table I), and a parabola according to eq 2 was fitted to these experimental data (Figure 2). The weight-average molecular weights of the whole copolymer and of its parts read from the parabolic fit (Figure 2) are summarized in Table I1 together with the heterogeneity parameters P and Q. Unlike for the weight averages of molecular weight, a simple relation holds between the number-average molecular weights of a copolymer, M,, and its backbone and graft parts, M d and MnB, respectively?
M , = M d + MnB (5) Since these averages are also connected with the average chemical composition of a copolymer R by the relation R
I
1
I I
I
I I
I
I
;
'I-1 I-I 1-ii
21
+
'
-2
1
-1
I
0
1 1
I
'
R
2
2.9 3.5
Other Characteristics chem compn, f (wt fract of PMMA) no. of grafts, m, heterogeneity parameter P/M, heterogeneity parameter Q/Mw
I
I
Figure 2. Determination of the weight-average molecular weight, M,, of the PMMA-g-PDMS copolymer by the parabolic fit of the apparent molecular weights, Msp,according to eq 2. R = [(dn/dc)A - ( d n / d ~ ) ~ ] / ( d n / dfor c ) ~numerical ; values see Table 1. The determination of the weight-average molecular weight of the backbone and graft part, MwAand M w ~is, also indicated. e is the average chemical composition of the copolymer expressed as the weight fraction of PMMA backbone.
Number-Average Molecular Weights whole copolymer, 10-6M, 1.26 PMMA backbone, 10-5Md 0.75 PDMS graft part, 10-5MM, 0.51 PDMS single graft, 10-5M*d 0.10
Mw/M,,Ratios
I
4.75
Table I1 Molecular Parameters of the PMMA-g-PDMSCopolymer Weight-Average Molecular Weights
whole copolymer
I
IO-'M~
a Refractive index increment of the copolymer has been calculated according to eq 1 with f = 0.597.
whole copolymer, 10-5Mw PMMA backbone, 10-5MwA PDMS graft part, 10-6MwB
1
I
=Md/M,
(6)
determination of M , and R is sufficient to obtain all the number averages of molecular weights (Table 11). Another quantity of interest, i.e., the average number of grafts per copolymer macromolecule, m,,is evaluated from the relation m, = Md/M*,B = (1 - R)M,/M*,B
(7)
where M*,B is the number-average molecular weight of single grafts, i.e., of the PDMS macromonomer (Table 11). The ratio MwA/MnAfor the backbone (Table 11) is that which might be expected for a product of radical copolymerization carried out to medium conversions. The relatively high value of MwB/MnBfor the graft part is also understood; different copolymer macromolecules contain various numbers of grafts, and the molecular weight of the graft part in these macromolecules is therefore different, even though the individual grafts have a narrow distri-
bution of molecular weights. Fractionation in Demixing Solvents. The pair of demixing solvents used for the fractionation of block or graft copolymers should have the following properties:11J2 The miscibility of both components should be limited at or close to room temperature, and these solvents should be completely miscible at elevated temperature. The density of both solvents should differ as much as possible to ensure fast and complete separation of coexisting phases. One of the components of the demixing solvent pair should be a good solvent for one of the homopolymers and a poor solvent or precipitant for the other homopolymer; the second solvent component should have reverse properties. The solvent pair dimethyl sulfoxide-tetrachloroethylene fulfills satisfactorily these requirements for PMMA-gPDMS copolymers. The critical temperature of this solvent pair is about 56 "C. The difference in densities of components is large enough, dDmo = 1.096 g/cm3 and dTCE = 1.623 g/cm3 at 20 "C. PMMA dissolves in DMSO while its miscibility with TCE is limited, and the opposite holds for the PDMS homopolymer. If a mixture of PMMA and PDMS is introduced into the DMSO-TCE two-phase system, PMMA quantitatively enters the DMSO-rich phase and PDMS concentrates in the TCE-rich phase. Phase Separation Behavior. Several comments on phase-separation behavior might be helpful to gain a deeper insight into the fractionation process. The phase diagram for a copolymer dissolved in two solvents with a miscibility gap can generally be represented by a surface over the triangle defining the composition of a pseudoternary system (the copolymer is regarded as one component). The construction of the whole phase diagram would be experimentally very time consuming and of limited value for the present discussion. Figure 3 shows the cloud-point curve for a system containing a constant amount of the copolymer. This curve, delimiting the regions with different numbers of coexisting phases, can be regarded as a section through the phase diagram at fixed content of the polymeric component. In region I, the system forms a homogeneous copolymer
864 Stejskal et al.
Macromolecules, Vol. 22, No. 2, 1989 ..."I , .. .. ..,
I
I
: I
/ I
0.L
0.6
/
/ I
\i \i 1.0
Figure 3. Cloud-point curve of the ternary system DMSOTCE-O.5 w t % ' graft copolymer (full line and open circles). m E is the volume fraction of TCE. Regions: I, single-phasesystem;
IIa, coexistence of two phases dilute with respect to copolymer; IIb, concentrated and dilute phase; 111, three phases (the dashed boundary line is tentative). For comparison, the cloud-pointcurve for the copolymer-freesolvent pair is shown by dotted line.
solution. Two-phase regions differ in their nature. Two phases, both dilute with respect to copolymer, coexist in region IIa, in close analogy to the demixing of copolymer-free solvent components with limited miscibility. In region IIb, a dilute phase is in equilibrium with another one, concentrated with respect to the copolymer, similarly to phase equilibria observed with polymers in single solvents or solvents consisting of completely miscible components, used, e.g., in classical precipitation fractionation. I t should be noted that the miscibility of our graft copolymer with pure TCE is limited below 25 "C. The cloud-point curves corresponding to different regions could easily be distinguished. In region IIa the decomposition into coexisting phases is fast because of the great difference in their densities. In region IIb, the difference in densities of phases is much smaller and decomposition slower by an order of magnitude. Finally, in region 111, which is only tentatively outlined (because of experimental difficulties, its boundary has not been determined) by a dashed curve in Figure 3, three phases coexist: two dilute and one concentrated with respect to the copolymer. It is worth noticing that even a relatively small concentration of the copolymer in the solvent system substantially affects the phase-separation behavior. In the case under discussion (Figure 3), the presence of 0.5 w t % for the graft copolymer investigated lowers the demixing temperature by 10-20 "C, compared to the copolymer-free solvent system. Experimental Results. The graft copolymer PMMAg-PDMS has been fractionated in the DMSO-TCE demixing solvent pair to a series of fractions (Table 111) according to the fractionation scheme given in Figure 1. As expected, fractions with a high content of PMMA were isolated from DMSO-rich phases. With a few exceptions, the content of PMMA in fractions isolated from these phases decreased as the temperature of separation increased. In the present case, the distributions of chemical composition and of molecular weight are expected to be mutually dependent, and thus fractionation according to chemical composition implies also fractionation according to molecular weight. However, no unambiguous correlation seems to exist between the chemical composition of frac-
Table I11 Results of Fractionation of the PMMA-g-PDMSCopolymer in Demixing Solvents' 1 w, Xi 10-6Mwb L-10 0.107 0.51 6.6 u-10 0.023 0.53 5.2 U-8 0.238 0.54 3.0 L-4 0.130 0.55 3.5 u-7 0.046 0.57 3.7 L-5 0.022 0.59 4.1 L-1 0.165 0.60 3.8 u-2 0.048 0.62 3.9 U-6 0.041 0.63 5.6 u-5 0.060 0.65 6.0 u-4 0.019 0.66 5.2 u-9 0.024 0.67 2.9 u-3 0.031 0.72 2.7 0.046 0.75 2.5 u-1 av 0.585 4.0 Owi is the weight fraction of the ith fraction having chemical composition xi (weight fraction of PMMA backbone) and molecular weight Me For the fractionation scheme cf. Figure 1. bBy light scattering in methyl ethyl ketone neglecting the residual chemical heterogeneity, Le., assuming Map,i= Me.
tions and their molecular weight (Table 111), probably because of complexity of the fractionation scheme employed. The weighted average of molecular weights of fractions (Table 111) is about 10% higher than the weight-average molecular weight of the whole copolymer (Table 11). This may be due to the neglect of the residual chemical heterogeneity of fractions, which were assumed to be chemically homogeneous in the light-scattering determination of molecular weight. The chemical composition of fractions has been determined by differential refractometry, since the routine elemental analysis has not yielded tolerably reproducible results. IR analysis cannot be recommended either, becaw the calibration curve constructed from measurements on homopolymer mixtures in chloroform was linear for neither carbonyl nor siloxane absorption bands. Moreover, the chemical composition of copolymers calculated from this calibration differed substantially depending on the absorption band used. Comparison with Theoretical Prediction. In our recent paper,3 a modified Stockmayer distribution of chemical composition (CCD) describing the statistical chemical heterogeneity of graft copolymers prepared from macromonomers has been derived. The concepts used in the theoretical derivation do not cover the potential drift of the monomer mixture composition during copolymerization. The conversion chemical heterogeneity is not taken into account, even though it could seriously affect the CCD.16 No compositional changes of this type have been observed during preparation of graft copolymers involved in this study. This observation is supported by the recent results of Tsukahara et al." When the comonomer was of the same chemical nature as the end group of the macromonomer, these authors found no compositional drift with conversion. Also in our case, the effect of the conversion heterogeneity seems to be negligible. The differential weight-distribution function W ( x )of chemical composition x (weight fraction of the backbone) can be written as3
Graft Copolymer Prepared from Macromonomer 865
Macromolecules, Vol. 22, No. 2, 1989 1.01
I
I -7.5
1
W(d
- 5.0
- 2.5
The differential and integral CCD functions shown in Figure 4 have been calculated for the following values of parameters: P, = 750, Pw/P, = 3.5 (Table 11), i ! = 0.585 (Table 111),and t = 102/104 = 0.01 (Table 11). The parameter k, given by eq 13, has been assumed to have a value of unity; for t
