1258
Langmuir 1993,9, 1258-1262
NMR Self-Diffusion Study of Poly(ethy1ene oxide)- Mock-poly(dimethylsiloxane) Diblock Copolymers in Organic Solvents and in Poly(ethy1ene oxide) Melts Z o l t h KirAly,' Terence Cosgrove, and Brian Vincent School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 lTS, U.K. Received October 16,1992. I n Final Form: February 16,1993 The self-diffusioncoefficientsof two poly(ethy1ene oxide)-block-poly(dimethylsiloxane),PEO-b-PDMS, diblock copolymers (molecularweights: 2120-b-2240 and 2120-b-5340)have been measured by the pulsed field-gradientspin-echo(PFGSE)NMFt technique. The solvents used were chloroform-d,toluene-de,and tetrahydrofuran-deat 30 O C , cyclohexane-dlzat 50 O C , dimethylformamide-d, (DMF)in the temperature range of 25-60 O C and protonated poly(ethy1eneoxide) melts of molecular weight of 222,480, and 980 in the range of 25-150 "C. The copolymers form micelles in DMF' and PEO melts and micellar break-up takes place as the temperatureis raised. The temperaturedependenceof the criticalmicelle concentration in PEO melts was determined by a turbidiometric method. The hydrodynamic radii of the micelles, calculated using the Stokes-Einstein equation, were virtually independent of solvency and had a value of about 6and 8nm for the shorterand longer chain copolymer,respectively. The correspondingaggregation numbers were calculated to be 25 and 31. silicone oil/PEO-PPO (poly(ethy1eneoxidepoly(propyIntroduction lene oxide))copolyetherand siliconeoil/poly(isobutylene)? In poly(ethy1eneoxide)-poly (dimethylsiloxane),PEOThe emulsificationefficiencyof PDMS-PEO copolymers PDMS, block copolymersthe two blocks are incompatible. for siliconeoil-in-wateremulsionswas found to be superior They can therefore be expected to adsorb at the interface to that for mineral oil-in-water emulsions? between PEO and PDMS melts and to form micelles in The applications of NMR methods to the study of the bulk polymers. Studies on the PDMS-PEO-PDMS micellar solutionshave been recently reviewed.1° Fouriercopolymers, using dilatometry, differential scanning caltransform pulsed-field-gradient spin-echo (PFGSE) nuorimetry (DSC),and small angleX-ray scattering (SAXS), clear magnetic resonance spectroscopyl1J2has proved to have revealed lamellar or hexagonal cylindricalstructures be a very powerful method for the study of micellar according to composition.' Gas chromatographic data solutions. Micellar aize, shape, and structure, and also have enabled calculations of the PEO/PDMS interaction intermicellar interactions, have been determined by such parameter ( x ) and its dependence on temperature and studies.13-16 composition to be made.' In this paper the micellar behavior and the self-diffusion Ternary phase diagrams of PEO-PDMS block copolcoefficientsl' of two PEO-b-PDMS diblock copolymersin ymers with water and cyclohexanehave been determined, various solvents and in low molecular weight PEO melts as have temperature/compositionphase diagramsof binary are presented and discussed, based on PFGSE NMR mixtures of the copolymers with water and cyclohexane experiments. In a subsequent paper we will be reporting (using DSC).2 Microphase separation of the copolymers on the preparation of PEO + PDMS emulsionsstabilized has been detected as a function of cyclohexane and water by PEO-b-PDMScopolymers. Polymer blends are of great concentration,respectively.2 Neutron-and lightmattering industrial interest for creatingnovel materials18anda PEOdata (Zimmplots) have indicated that, in dilute solutions, b-PDMS copolymer is a potential compatibilizer or the PEO-PDMS copolymerscan form micelles, depending emulsifier for a PEO + PDMS polymeric blend. The on solvency condition^.^ Viscosity measurements sugpreparation of a PEO-in-PDMS emulsion has been regested a rather compact conformation of the copolymers ported elsewhere very recently, although a different or even intramolecular segment ~egregation.~ emulsifier was used as the stabilizing agent.lg The adsorption properties of various polysiloxane Experimental Section polyether copolymers at a variety of interfaces has been investigatedusing interfacial tension measurements. The Materials. For a systematic study and in order to minimize end-groupeffects,the polymericmaterialsused in this work were interfaces studied included aidwater, siliconeoil/water;PG poly(ethy1ene glycol) and poly(propy1ene o ~ i d e ) / a i r ; ~ * ~chosen so as to carry fully methylated end groups at both ends
* On leave from Department of Colloid Chemistry, Attila J6zsef
University, Aradi VBrtanuk tere 1, H-6720 Szeged, Hungary. (1)Galin, M.; Mathis, A. Macromolecules 1981,14,677. (2)Haesslin, H. W.; Eicke, H. F.; Riess, G. Makromol. Chem. 1984, 185,2625. (3)Haesslin, H. W. Makromol. Chem. 1986,186,357. (4)Schwarz, E. G.; Reid, W. G. Ind. Eng. Chem. 1964,56(9),26. (5)Kanellopoulos, A. G.; Owen, M. J. J. Colloid Interface Sci. 1971, 35,120. (6)Baily, D. L.; Peterson, 1. H.; Reid, W. G. In Chemistry and Application of Surface Active Substances; Asinger, B. F., Ed.; Gordon & Breach: London, 1967;Vol. 1, p 173. (7)Kendrick, T.C.; Kingston, B. M.; Lloyd, M. C.; Owen, M. J. J. Colloid Interface Sei. 1967,24,135. (8)Owen, M. J.; Kendrick, T. C.; Kingston, B. M.; Lloyd, M. C. J. Colloid Interface Sci. 1967,24,141.
(9)Patterson, H.T.;Hu, K. H.; Grindstaff, T. H.J.Polym. Sci., Part
C 1971,34,31.
(10)Chachaty, C.Prog. NMR Spectrosc. 1987,19,183. (11)Stilbs, P. Prog. NMR Spectrosc. 1987,19,1. (12)Blum, F. D.Spectroscopy 1986,1,32. (13)Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. J. Phys. Chem. 1983,87,4548. (14)Nilsson, P. G.; WennerstrBm, H.; Lindman, B. J. Phys. Chem. 1983,87,4548. (15)Nilsson, P. G.; WennerstrGm, H.; Lindman, B. Chem. Scr. 1985, 25,67. (16)JonstrBmer, M.; SjGberg,M.; Warnheim, T. J.Phys. Chem. 1990, 94,7549. (17)Cosgrove, T.;Sutherland, J. M. Polymer 1983,24,534. (18)Paul, D.;Newman,S., Eds. Polymer Blends; AcademicPress: New York, London, 1978; Vols. 1 and 2. (19) Graebling, D.; Muller, R. Colloids Surf. 1991,55,89.
0143-7463/93/2409-1258$04.00/00 1993 American Chemical Society
Self-DiffusionStudy of PEO-b-PDMS
Langmuir, Vol. 9, No. 5, 1993 1259
Table I. Molecular Weight Characteristics of the PEO and PEO-bPDMS Polymers PEO
L
PEO-b-PDMS
M(nominal) 222 500 1000 2000-b-2000 2000-b-5000 Mll 222b 48Oa 980" 2120-b-2140e 2120-b-5340e MwIMn l.Ob 1.15" 1.29" 1.33" 1.33" a Obtained from GPC as in ref 20. Manufacturer quoted purity >99%. Determined by 'HNMR as in ref 20.
lead to temperature
/ heat shrinkable sleeving
\,-
indicator
-!
block thermostat
cellhousing
b
bakelite screw cap
_thermometer lead in PTFE insulation
temperaturePC -~
60 I
80
90
100
Figure 2. A heating-cooling cycle during the turbidiometric determination of the micellization-demicellization transition temperature in a 1w t ?6 solution of PE02000-b-PDMS2000 in PE0222. The initial sample contains a small amount of PDMS solubilizate.
I
lead to electronic control unit heating element
70
magnetic stirrer
Figure 1. Cell housing and sample holder designed for automatic turbidity-temperature recording. of the polymer chains. Propylcarbamato-linked cu-methoxy-wtert-butyl[ poly(ethy1ene oxide)-block-poly(dimethylsi1oxane)1, PEO-b-PDMS, diblock copolymers were synthesized in this laboratory. The experimental details of the preparation together with the characterization of the polymers have been published previously.20 Tetraethylene glycol dimethyl ether (PE0222) was purchased from Aldrich. Polyethylene glycol 500 dimethyl ether (PE0500) and polyethylene glycol 1000 dimethyl ether (PE01000) were purchased from Fluka. The molecular weight characteristics of the polymers are listed in Table I. CDC13, toluene-d8, THF-ds (tetrahydrofuran), d12-cyclohexane-d12,DMF-& (dimethyl formamide) and D M s 0 - d ~(dimethyl sulfoxide) were all Fluorochem chemicals. Cloud Point Measurements. The temperature dependence of the critical micelle concentration (cmc) was determined by recording. The turbidity automaticturbidity (7)-temperature (7') of the mixtures a t an arbitrarily chosen wavelength of 400 nm was monitored using a Pye-Unicam SP-1800 UV-visible spectrophotometer. The cell-housing (Figurel),a purposebuilt, brass block unit was operated as an electronically controlled block thermostat. A small magnetic stirrer was placed underneath the cell-housing in order to maintain vigorous stirring during the experiment. Glass, tall-form, disposable sample vials (nominal capacity 1.75 cm3)were used as the photometer cells. A ceramic encased Platinum 100 resistance element was attached to the screw cap of the cell. The thermometer lead was connected to a digital temperature monitor (1mV/"C) suitable for the platinum resistance sensor. The output from the temperature monitor was used to drive the X axis of an X-Y recorder (Kipp & Zonen), while the output from the spectrophotometer signal drove the Y axis. In this simple arrangement the turbidity ( T in arbitrary units) as a function of temperature (7')was continuouslyrecorded at a heating-cooling rate of about 1"C/min. Each element of the electric circuit (thermometer, converter and plotter) was previously calibrated against a dc voltage calibrator. A typical 7-2' plot for a heating-cooling cycle is shown in Figure 2. The turbidity was found not to change sharply a t a particular temperature but over a certain range of temperature. We found in separate experiments that solubilized PDMS can be advantageously used as an indicator of the micellar solutionnonmicellar solution transition temperatures, even for visual observation. When pure PDMS was gradually added to a micellar solution of PEO-b-PDMS in a PEO melt, fast solubilization took place with a gradual (albeit slight) increase in the turbidity of (20) KirBly, Z.; Vincent, B. Polym. Int. 1992,28, 139.
the system. A dramatic increase in the turbidity occurred upon reaching the demicellizationtemperature. On leaving the system above this temperature, phase separation could be observed with macroscopic PDMS droplets floating on the free surface of the PEO solution. The cloudingwas found to be reversible. Tracing of micelle diffusion indirectly, by monitoring the self-diffusion of the solubilizate being incorporated in the interior of the micelles, has also been reported.21 FT PFGSE NMR Experiments. The spectrometer system was a specific configuration of several commercial and homemade units, the major parts being the electromagnet and the amplifier of a JEOL-JNM-FX100 FT NMR spectrometer, originally designed for high-resolution lH and NMR experiments. The desired (off-resonance)frequencies, around 100MHz for lH NMR measurements, were generated by a Schomandl ND lOOM frequency synthesizer (300 Hz-100 MHz). The fieldgradient pulses, in the range of 0.016-0.08 T m-l, were generated by a home-made current amplifier, based on a design by Stilbs,' calibrated for water and cyclohexane a t various "observation" times. The magnetic field was locked by an internal lock sample, DMSO-& in a sealed glass capillary; this was chosen because DMSO has a high boiling point of about 189 O C . The temperature could be adjusted to within f 0.5 "C. A home-made attenuator was used to moderate (as required) the spin-echo attenuation signals for data acquisition. The experiments, as a whole, were controlled by a SMIS computer system. The basic 9Oo-A-18O0-A Stejskal-Tanner sequence was used as follows. A 90° radio frequency (rf) pulse (typically 6.0 ps) was followed by a field-gradient (FG) pulse of strength G with a pulse length of 6 (typically 120 ms). This FG pulse was followed by a 180" rf pulse (12.0 ps) and, again a FG pulse of G was applied with a length of 6. The rf pulse interval was fixed to keep transverse relaxationtime effects constant. The FG pulse interval A and the gradient strength G were also fixed; only the duration of the gradient pulses, 6, was varied between 10 and 120 ms. This sequence was then repeated several times with a relaxation delay of about 10-20s between theexperiments. After data acquisition the spin-echo signals were Fourier-transformedinto the frequency domain and the attenuation (peak area)-field-gradient pulse length relationship, A versus 6, was analyzed. In the simplest case assuming isotropic Brownian diffusion the following, single exponential equation was used A = A, exp[-(yG6)2(A - 6 / 3 ) 0 , ]
(1)
where, as mentioned previously, G and A are constant, and y is also constant (the magnetogyric ratio of the nucleus). Hence, the self-diffusioncoefficientD,can be obtained from a nonlinear, least-squares curve-fitting procedure (A versus 6). If the same species in the sample has different diffusional states (e.g. free (21) Stilbs, P. J. Colloid Interface Sci. 1983,94,463.
Kir6ly et al.
1260 Langmuir, Vol. 9,No. 5, 1993 surfactant molecules and micelles), then it may be necessary to use a double-exponentialequation. It has been found, however, that the decay of the echo amplitude of a surfactant is often single-exponentialeven in a micellar solution. This suggest that there is a rapid exchange between the two states in the solution on the time scale of the measurements (typically 50-200 ms).16 On the other hand, if the critical micelle concentration (cmc) is very much lower than the concentrationsused in the experiment, the value of D, will be negligibly effected by the monomer diffusion.13 Viscosity Measurements. The viscosity of the PEO melts and thetemepraturedependence of the viscositywere determined using Ubbelhodecapillary viscometers covering the range of 1-45 cP. Ethylene glycol was used as the referenceliquid;the viscosity data were taken from the literature.22 The viscosity of the deuterated solvents was considered to be the same as the corresponding protonated solvents.
Results and Discussion The self-diffusion coefficients of the PE02000-bPDMS2000 and the PE02000-b-PDMS5000 diblock copolymers were determined under the following conditions: in CDC13, toluene-dB and in THF-ds solvents at 30 OC, in cyclohexane-dln at 50 "C and in DMF-ds in the temperature range of 25-60 "C. The following copolymer1 PEO melt binary systems were also studied PE02000b-PDMS5000in PE0222,30-120 OC; PE02000-b-PDMS2000 in PE0222, 25-75 OC; PE02000-b-PDMS2000 in PE0500,50-150 OC; PE02000-b-PDMS2000in PE01000, 75-150 "C. In each case, 5 w t 7% block copolymer solutions were used. PE02000-b-PDMS5000 was investigated in a single PEO melt only, namely PE0222, because the copolymer did not dissolve in the higher PEO homologues. Chloroform, toluene, and THF are good solvents for both the PEO and PDMS blocks. Cyclohexaneis agood solvent for PDMS but is a poor solvent for PEO at room temperature. However,at (and above) 50 "CPEO becomes soluble in cyclohexane. The block copolymers were not soluble in cyclohexane at room temperature but clear, homogeneous solutions were obtained above 50 "C, and this temperature was chosen for the measurements. DMF is a good solvent for PEO but is a poor solvent for PDMS (even at high temperature). Both copolymers were, however, soluble in DMF at room temperature. The copolymers were not soluble in water, methanol, ethanol or not even in a mixture of H20:THF = 1:l. PEO-bPDMS Diblock Copolymers in Good Solvents. A three-dimensional representation (attenuationpulse-gradient length-chemicalshift) of the PFGSE NMR experiment for PE02000-b-PDMS2000 in toluene-& (5 wt 7% solution, 30 "C) is shown in Figure 3. Two peaks are dominant along the ppm scale: the PEO backbone (-CH2CH20- at about 3.4 ppm) and the PDMS backbone (-Si(CH&O- around 0.2 ppm) signals. A further small peak can be observedjust below 1ppm which is due to the tert-butyl end group of the PDMS block. In the PFGSE NMR experiments the attenuation is not directly proportional to the number of magnetic nuclei (in contrast with the high-resolution IH NMR experiment) because of both spin-spin relaxation and diffusion. Another, very small peak at about 2 ppm may be due to some nondeuterated residue of the methyl group of the toluene solvent. Figure 3 illustrates very well that any suitable chemical moiety of the block copolymer (PEO block, PDMS block, or the tert-butyl end group) can be used to construct the exponential decay and, hence, to calculate the diffusion coefficient. In fact, in the present case the agreement in of
(22) Viswanath, D. S., Natarjan, G., Eds.Data Book on the Viscosity Liquids;Hemisphere: New York, 1989.
t
i
I
4.03
3.00 2.w 1.00 chemical shift / ppm
0.00
Figure 3. A graphical representation of the PFGSE NMR experiment via a 5 w t 5% solution of PE02000-b-PDMS2000 copolymer in toluene-& at 30 OC: field-gradientstrength, 0.038 T m-l; 90° radio frequency (rf) pulse length, 6.0ps; 180° rf pulse length, 12.0ps; gradient pulse separation time, 0.120s; number of samples,2048;numberof scans, 8;relaxationdelay,10s;receiver filter, 4 kHz; sweep width, 8 kHz.
the calculated diffusion coefficientswas better thanO.576. It follows from this argument that when nondeuterated PEO melt is used as the solvent, the overlap of the solvent and PEO block signal is no longer a problem: the PDMS block signal can be used to monitor the whole block copolymer diffusion. (In principle, the two PEO signals may be separated from each other making use of the different molecular weights, hence different relaxation times of the two PEO chains, but this is not straightforward). The self-diffusion Coefficients of the block copolymers, in various deuterated solvents (except for DMF-4 which will be discussed separately) are listed in Table 11. This table also contains the solvent viscosity data and the normalized diffusion coefficients of the copolymers, defined by
D , = DllqdT (2) The self-diffusion coefficient is inversely proportional to the hydrodynamically equivalent radius, RH,according to the Stokes-Einstein equation
R, = kT16q,Do
(3) This equation is applicable to spherical particles a t infinite dilution [DO= D,(c 011. Electron microscopic studies of similar block copolymer micelles have indicated them to be spherical.23 PEO-bPDMS Diblock Copolymers i n Selective Solvents. While in the caae of deuterated solvents the data acquisition was completed after a few scans, in the case of protonated solvents, such as PEO melts, a large number of scans was required in order to obtain reliable data. The self-diffusion coefficients of the block copolymers in DMF-d, and PEO melts are plotted against temperature in Figure 4. The "S-shaped" plot suggests a gradual break-up of the micelles rather than an abrupt transition. The cmc-temperature relationship, determined by turbidity measurements, is shown in Figure 5. The cmc increases with increasing temperature and the shape of
-
(23) McMahon, J.; Price, C. Eur. Polym. J. 1991,27, 761.
Langmuir, Vol. 9, No. 5,1993 1261
Self-DiffusionStudy of PEO- b-PDMS
Table 11. Self-Diffusion Coefficient and Normalized Self-Diffusion Coefficient Data for PEO-bPDMS Diblock Copolymers in Various Deuterated Solvents at Copolymer Concentrationsof 5 wt % block copolymer solvent TI"C dcP 1010 DJm2 a-1 1016DN/NK-' PE02000-b-PDMS2000 chloroform 0.51 1.47 f 0.07 2.47 f 0.12 30 0.52 1.69 f 0.02 2.89 f 0.04 30 toluene
THF
30 50 30 30 30 50
cyclohexane chloroform toluene
PE02000-b-PDMS5000
THF
cyclohexane
0.47 0.61 0.51 0.52 0.41 0.61
1.77 f 0.07 1.37 f 0.06 1.18f 0.04 1.32 f 0.06 1.38 f 0.05 1.03 f 0.02
2.75 f 0.10 2.83 f 0.12 1.98 f 0.07 2.27 f 0.10 2.14 f 0.08 1.95 f 0.04
A 2-
6
-
\!
\\ -\ \*
\
, . \ \ \ \
\
1
A
\ \
O(!
% ' Figure 4. Temperature dependence of the translational selfdiffusion coefficient of PEO-b-PDMS diblock copolymers in selective solvents at copolymer concentrations of 5 w t %: M, PE02000-b-PDMS2000 in PEOlOOO; A, PE02000-b-PDMS2000 in PE0500; *, PE02000-b-PDMS2000 in PE0222; 0,PE02000b-PDMS5000 in PE0222; 0, PE02000-b-PDMS5000 in DMFd7; 0 , PE02000-b-PDMS2000 in DMF-d,.
I
I
I
50
loo
150
Temperature I OC
Temperature I
Figure 6. Variation of the (noncorrected) apparent hydrodynamic radius with temperature for PEO-b-PDMS copolymer (micelles)in selective solvents at copolymer concentrations of 5 w t %. Notations as in Figure 4. Table 111. Self-Diffusion Coefficient and Apparent Hydrodynamic Radius Data for PEO-BPDMS Diblock Copolymers in DMF-d, at Copolymer Concentrationsof 5 wt % PE02000-b-PDMS2000
150
PE02000-b-PDMS6000
T/"C q/cP 1011D$m2s-l RH,ap&m 1011D$m2a-l RH,app/nm 100
50
I
Ob
'
1I
" 2
'
3I
4
,
I
5
,*
copolymer concentration / wt% Figure 5. Variation of the critical micelle concentration with temperature in various PEO-b-PDMS + PEO systems: 0, PE02000-b-PDMS2000 in PE01000,A,PE02000-b-PDMS2000 in PE0500; 0 , PE02000-b-PDMS5000 in PE0222.
the curve suggests the existence of an upper critical temperature beyond which no copolymer aggregation is possible. The transition temperatures for PE02000-bPDMS5000/PE0222 and PE02000-b-PDMS2000/PEO&)O can be directly compared with the (mean)demicellization temperatures obtained from NMR measurements in Figure 4; the agreement is remarkable. The apparent hydrodynamicradii, RHapp,corresponding to the self-diffusing species, were calculated using the Stokes-Einstein equation and are plotted, as a function of temperature, in Figure 6. Again, a distinct transition region can be observed at the demicellizationtemperature. It should be noted that the apparent hydrodynamicradii were calculated from the diffusion coefficientsD, measured directly at a block copolymer concentration of 5 w t 5%. (An alternative calculation, leading to& instead Of RH,app,
20 25 30 35 40 45 50 55 60
0.84 5.00f 0.57 0.79 5.55 f 0.45 0.75 5.98 f 0.42 0.71 6.00h 0.51 0.68 6.51 f 0.61 0.65 10.09 f 1.05 0.62 13.58 f 2.05 0.60 0.58 48.30f 7.42
5.11 f 0.51 3.28 f0.68 4.98 f 0.37 3.59 f 0.57 4.95 f 0.33 3.71 f 0.42 5.30f 0.41 4.24 fO.62 5.18 i 0.45 3.55 f 0.33 5.00 f 0.34 2.81 f 0.37 10.74 f 0.71 14.33 f 1.42 0.87 f 0.16 42.77 f 6.47
7.80f 1.33 7.70 f 1.04 7.95 f 0.80 7.41 f 0 . 9 5 3.51 f 0.22 3.51 f 0.22 2.76 f 0.25 0.97 f0.13
would require DO values rather than D,, which can be obtained using the approximationD, = DO( 1- 24), where 4 is the volume fraction of the block copolymer.16 A volumetric correction of this kind can account for the reduced mobility due to micellar repulsion.) The results forRH,appare tabulated in Tables 111-V, including viscosity data for the solvents. It would seem that the size of the copolymer micelles is not seriously affected by the nature of the solvent. The close agreement in the calculated micelle sizes for the same copolymer in different solvents is remarkable since the calculations are baaed on the experimental quantities q, T,and D,, the values of which vary over a wide range. In fact, both in DMF and in the PEO melts, the PE02000-b-PDMS2000 micelles have an average diameter of 10nm and the PE02000-b-PDMS5000 micelles about 16 nm. It would seem that the demicellization temperature is primarily affected by the viscosity of the medium and that, in a given solvent, the higher molecular weight copolymers demicellize at higher temperatures. No clear indication of a micelle formation was found with the system PE02000-b-PDMS2000/PEO222 above
1262 Langmuir, Vol. 9, No. 5, 1993
Kir&ly et al.
Table IV. Self-Diffusion Coefficient and Apparent Hydrodynamic Radius Data for PEO-bPDMS Diblock Copolymers in PE0222 Melt at Copolymer Concentrations of5wt%
25 30 35 45 55 65 75 85 95 105 120
3.54 2.82 f 0.11 3.15 3.47 f 0.25 2.82 4.99 f 0.35 2.31 6.13 fO.61 1.93 7.48 f 0.42 1.65 9.48 f 0.41 1.43 12.29 f 0.47 1.26
2.16 f 0.08 2.03f 0.13 1.60 f 0.10 1.65f0.14 1.66 f 0.09 1.58f 0.06 1.45 f 0.05
1.12
1.01 0.87
0.82 f0.10
8.56f0.97
1.14f0.16 1.49 f 0.30 1.70 f 0.23 3.42 f 0.44 7.59 f 0.68 12.77 f 0.64 13.73 f 1.03 13.90 f 0.72
8.85f 1.08 8.34i 1.39 8.81 f 1.05 5.20f 0.59 2.74 f 0.22 1.88 f 0.09 2.00 f 0.14 2.38 f 0.11
Table V. Self-Diffusion Coefficient and Apparent Hydrodynamic Radius Data for PE02000-bPDMS2000 Diblock Copolymer in PE0500 and PEOlOOO Melts at a Copolymer Concentration of 5 wt % T/"C qlcP 1011D$m2s-l RH.aDo/nm solvent 50 75 100 110 120 125 130 140 150 75 100 125 150
12.52 6.97 4.14 3.41 2.84 2.59 2.36 2.00 1.70 20.09 11.88 7.90 5.64
0.36 f 0.09 0.68 f 0.09 1.26 f 0.07 1.52 f 0.17 2.61 f 0.36 6.49 f 0.62 10.92 f 0.67 15.65 f 0.76 15.96 f 0.92 0.24 f 0.16 0.39 f 0.16 0.60 f 0.13 0.95 k 0.12
5.28 f 1.09 5.41 f 0.65 5.24 f 0.28 5.43 f 0.54 3.89 f 0.47 1.73 f 0.15 1.20 f 0.07 0.97 f 0.04 1.14 f 0.06 5.31 f 2.14 5.90 f 1.73 6.14 f 1.09 5.69 f 0.67
PE0500
PEOlOOO
room temperature. The data obtained suggest possible micelle formation just below room temperature (Table IV). An S-shapedD versus T diagram has been published in the literature by Price et al.% They determinedthe mutual diffueioncoefficient of a polystyrene-b-polyisoprenediblock compolymer in n-decane using dynamic light scattering. The diffusion coefficient-temperature relationship was found to be S-shaped as here, and this transition was also attributed to a demicellization process as the temperature was increased.
From knowledge of this diffusion coefficientDo and the corresponding intrinsic viscosity 171 of the copolymer solution, the aggregation number Pmay be calculated asz4
where Mappis the apparent molar mass of the block copolymer (micelles),M,is the number average molecular weight of the free polymer coil, k g is the Boltzmann constant, NA is the Avogadro number, 70 is the viscosity of the solvent, while the ratio RJRDcan be taken to have a value of 1.05 for compact structures such as micelles.24 In order to obtain the necessary [73 data, viscosity measurements were performed at block copolymer concentrations of c = 1,2, 3, and 4 g/100 cm3 in DMF at 30 "C. The viscosity of the solutions were plottd as (7 - qo)/ C ~ versus O c and the intrinsic viscosity, obtained as the intercept of the straight line, was found to be 5.93 cm3 g1 for PE02000-b-PDMS2000 and 11.72 cm3 g1for PEO2OOO-b-PDMS5000. The aggregation numbers obtained were 25 and 31, respectively, for the two copolymer solutions. Similar calculations with the PEO melts were not possible due to the high viscosity of the solvents; the presence of the copolymers at low concentrationshad little effect on the viscosity of the system (not detectable by capillary viscometry). However, since the micelle sizes in DMF and PEO melts were found to be similar for a given copolymer (see Figure 61, a similar aggregation number may be expected in PEO as found in DMF. This is an important conclusion since aggregation numbers for copolymer micelles in polymer melts have not yet been reported. The present work is currently being extended to the study of PEO-b-PDMS micelles in PDMS melts.
Acknowledgment. I.C.I. Chemical & Polymer Division (Wilton, U.K.) is gratefully acknowledged for providing research funds for this project and for providing a research assistantship for Z.K.In particular, we thank Dr. Simon Gibbon and others at I.C.I. for many helpful discussions throughout the course of this work. (24) Price, C.; McAdam, J. D. G.; Lally, T. P.; Woods,D. Polymer
1974, 15, 228.
