pubs.acs.org/Langmuir © 2010 American Chemical Society
Dynamic Viscoelasticity and Concentration Dependence of Micelle-Gel Transition of Styrene and N-tert-Butylacrylamide Diblock Copolymer Solutions Nitin Sharma† and Rajeswari M. Kasi*,†,‡ †
Polymer Program, Institute of Materials Science and ‡Chemistry Department, University of Connecticut, 97 North Eagleville Road, Storrs, Connecticut 06269 Received July 16, 2009. Revised Manuscript Received April 3, 2010
We present dynamic viscoelastic studies of styrene and N-tert-butylacrylamide block copolymers (S278NtBAM517 and S93NtBAM252) in 1-octanol as a function of copolymer concentration at 15, 25, and 35 C. Dilute solutions of these diblock copolymers in 1-octanol, a selective solvent for N-tert-butylacrylamide units, yield spherical micelles as evidenced by transmission electron microscopy (TEM). Dynamic light scattering (DLS) is used to determine hydrodynamic radius of the micelles as a function of temperature (15, 25, and 35 C). Dilute solutions of these block copolymers behave as viscoelastic fluids in the low frequency range. At higher concentrations, these copolymer solutions form glass-clear gels. Rheological measurements show that these block copolymer solutions exhibit power-law behavior at the gel point (G0 (ω) ∼ G00 (ω) ∼ ωn). In this paper, we discuss the formation and properties of critical gel states of SmNtBAMn in 1-octanol based on (1) concentration dependence of micelle-gel transition, (2) determination of critical state by rheology, and (3) temperature dependence of critical gel concentration and material parameters.
Introduction Self-assembled block copolymer (BCP) solutions, including micelles and gels, have gained considerable importance due to their numerous applications such as responsive materials,1,2 adhesives,3 rheology modifiers,4,5 drug delivery vehicles,6 and microfluidic devices.2,7 Block copolymers undergo liquid-solid transition (LST) in solvents selective to one block.8-12 The phenomenon of LST can be defined as a transition from a liquid-like to a solid-like behavior. These polymer solutions attain a state near LST known as gel point which provides characteristics of both, viscous liquid and hookean solid. Polymers at gel point are known as “critical gel”. Critical gels relax at infinite time and in a broad distribution of shorter modes which are selfsimilar.13-15 The transition from a fluid to a viscoelastic solid or gel can be through different mechanisms: (1) chemical gelation, defined as a three-dimensional network formed through permanent *Corresponding author. Fax: 8604864745. Telephone: 8604864713. E-mail:
[email protected]. (1) Suzuki, H. J. Intell. Mater. Syst. Struct. 2006, 17, 1091–1097. (2) Ahn, S.-k.; Kasi, R. M.; Kim, S.-C.; Sharma, N.; Zhou, Y. Soft Matter 2008, 4, 1151–1157. (3) Creton, C. MRS Bull. 2003, 28, 434–439. (4) Berret, J.-F.; Calvet, D.; Collet, A.; Viguier, M. Curr. Opin. Colloid Interface Sci. 2003, 8, 296–306. (5) Annable, T.; Buscall, R.; Ettelaie, R. Colloids Surf. 1996, 112, 97–117. (6) Marin, A.; Sun, H.; Husseini, G. A.; Pitt, W. G.; Christensen, D. A.; Rapoport, N. Y. J. Controlled Release 2002, 84, 39–47. (7) Sudarsan, A. P.; Wang, J.; Ugaz, V. M. Anal. Chem. 2005, 77, 5167–5173. (8) Hamley, I. W. Philos. Trans. R. Soc. London, Ser. A: Math., Phys. Eng. Sci. 2001, 359, 1017–1044. (9) Castelletto, V.; Caillet, C.; Hamley, I. W.; Yang, Z. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2002, 65, 050601/1–050601/4. (10) Castelletto, V.; Hamley, I. W.; Yuan, X. F.; Kelarakis, A.; Booth, C. Soft Matter 2005, 1, 138–145. (11) Derici, L.; Ledger, S.; Mai, S.-M.; Booth, C.; Hamley, I. W.; Pedersen, J. S. Phys. Chem. Chem. Phys. 1999, 1, 2773–2785. (12) Kapnistos, M.; Vlassopoulos, D.; Fytas, G.; Mortensen, K.; Fleischer, G.; Roovers, J. Phys. Rev. Lett. 2000, 85, 4072-4075. (13) Vilgis, T. A.; Winter, H. H. Colloid Polym. Sci. 1988, 266, 494–500. (14) Winter, H. H.; Chambon, F. J. Rheol. (N.Y.) 1986, 30, 367–382. (15) Chambon, F.; Winter, H. H. J. Rheol. (N.Y.) 1987, 31, 683–697.
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covalent bonds13,16 and (2) physical gelation, defined by the growth of physically connected aggregates. In physical gels, the junctions may be hydrogen bonds, crystalline regions, ionic clusters and phase-separated microdomains depending on the nature of gelling system.13,16,17 More importantly, unlike chemical gels, physical gels are thermo-reversible as they can be melted and reformed without significant polymer degradation.18 We are interested in self-assembly of BCPs of styrene (S) and N-tert-butylacrylamide (NtBAM) in 1-octanol due to intrinsic properties of copolymers comprising styrene and N-tert-butylacrylamide that are widely used in adhesives applications.3 This investigation not only requires an understanding of micelles and gel phases but also of the critical state which is formed during the transition. In our previous publication, we have discussed the synthesis and characterization of BCPs comprising styrene (S) and N-tert-butylacrylamide (NtBAM) and investigated the rheological properties of micelles and gels of one copolymer, S278NtBAM517, in 1-octanol which is a selective solvent for NtBAM block.19 In this paper, we discuss our efforts in investigating the formation and properties of critical states of SmNtBAMn in 1-octanol. The general reasons for emphasizing this study are that by knowing the gel point we can include or obviate the chances of gel formation. This study offers a unique opportunity to take gel-point as a reference state and develop materials of different properties as well as processing conditions.16,20 In this paper, we will describe studies performed on copolymer solutions with similar solution morphologies based on (1) concentration dependence of micelle-gel transition, (2) determination of critical state by rheology, and (3) effect of temperature on the rheological properties and material parameters. (16) 104. (17) (18) (19) (20)
Schwittay, C.; Mours, M.; Winter, H. H. Faraday Discuss 1995, 101, 93– Hess, W.; Vilgis, T. A.; Winter, H. H. Macromolecules 1988, 21, 2536–2542. Guenet, J.-M. J. Rheol. 2000, 44, 947–960. Sharma, N.; Kasi, R. M. Soft Matter 2009, 5, 1483–1488. Winter, H. H.; Mours, M. Adv. Polym. Sci. 1997, 134, 165–234.
Published on Web 04/13/2010
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Sharma and Kasi
Article Table 1. Characteristics of Polystyrene-b-poly(N-tert-butylacrylamide), SmNtBAMna
entries
polymer
wt % (NtBAM block) (NMR)
Mn (g mol-1) (GPC)
MW/Mn (GPC)
71.00 1.29 56 218b S278NtBAM517 S93NtBAM252 80.59 1.19 27 157b b a Key: S, styrene block; NtBAM, N-tert-butylacrylamide block. Total Mn of the SmNtBAMn diblock copolymer as determined by GPC.
1 2
Theoretical Background A complete description of dynamic properties of gels is difficult near the gel point. However, the task is greatly simplified by establishing power laws. Zero shear viscosity (η0) and equilibrium shear modulus (Ge) are expressed in power law forms in the vicinity of gel point.20 The formation of gel is described by mean field theory of Flory21 and Stockmayer22 and other percolation models such as the model of percolating clusters that follow Rouse-like dynamics.23 Near the gel point, scaling laws are: ηο ∼ε - k ð p < pc Þ ð1Þ Ge ∼εz ð p > pc Þ
ð2Þ
where ε (=|p - pc|/pc) is the relative distance of the system defined by the gelation variable p from the gel-point (pc); k and z are the exponents characterizing the system below and above the gel point. At gel point, the critical gels are characterized by self-similar relaxation modulus, expressed as the power law relaxation modulus:14,15 GðtÞ ¼ Sc t - n ðλ0 < t < ¥Þ ð3Þ λ0 is a characteristic crossover time that characterizes the crossover to a different relaxation mechanism like glass transition or entanglement behavior. As a consequence, the dynamic mechanical behavior at the gel point is given by the scaling relationship14,15,17,24 G0 ðωÞ∼G00 ðωÞ∼ωn ð0 < n < 1Þ ð4Þ or
G00 ðωÞ=G0 ðωÞ ¼ tan δ ¼ tanðnπ=2Þ
ð5Þ
where n is defined as a viscoelastic exponent whose value lies between 0 and 1. Sc is defined as gel stiffness or gel strength with dimensions of Pa-sn.25 Generally, critical gels are (1) soft when n is large (approaching 1), and Sc is small and (2) stiff when n is small (approaching 0) and Sc is large.20 Equations 4 and 5 lead to a loss tangent independent of frequency at the gel point and is most widely used to determine the gel point. Different values of n are reported depending on the model assumption: (1) n = 2/3 in the case of Rouse behavior (complete screening of hydrodynamic interactions), (2) n = 1 for Zimm behavior (hydrodynamic interactions included), and (3) n = 0.72 (using electrical network analogy).26,27 A number of physical and chemical gels show power law behavior at critical point but the exponent, n, sometimes differs from the predictions of theoretical models.14,24,28-32 (21) Flory, P. J. J. Am. Chem. Soc. 1941, 63, 3083–3090. (22) Stockmayer, W. H. J. Chem. Phys. 1943, 11, 45–55. (23) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Phys. Rev. A: Gen. Phys. 1989, 39, 1325–32. (24) Lin, Y. G.; Mallin, D. T.; Chien, J. C. W.; Winter, H. H. Macromolecules 1991, 24, 850–854. (25) Mours, M.; Winter, H. H. Macromolecules 1996, 29, 7221–7229. (26) Martin, J. E.; Adolf, D. Annu. Rev. Phys. Chem. 1991, 42, 311–339. (27) Martin, J. E.; Adolf, D.; Wilcoxon, J. P. Phys. Rev. Lett. 1988, 61, 2620– 2623. (28) Winter, H. H.; Morganelli, P.; Chambon, F. Macromolecules 1988, 21, 532–535. (29) Valles, E. M.; Carella, J. M.; Winter, H. H.; Baumgaertel, M. Rheol. Acta 1990, 29, 535–542. (30) Michon, C.; Cuvelier, G.; Launay, B. Rheol. Acta 1993, 32, 94–103.
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Experimental Section Synthesis of Diblock Copolymer. The diblock copolymers, S278NtBAM517 and S93NtBAM252, are synthesized using reversible addition-fragmentation chain transfer (RAFT). The synthesis and characterization methods are reported in our previous publication.19 The molecular characteristics of the copolymers are summarized in Table 1. Preparation of Micelles and Gels. The BCP solutions are prepared by dissolving the preweighed block copolymer in 1-octanol in sealed flasks and maintained at 125 ( 5 C. Once the solutions are clear they are allowed to cool to room temperature. In this study the concentration is expressed in wt %. The solutions are stored for a week at room temperature prior to rheological experiments. Newly prepared samples are used for each experiment. Transmission Electron Microscopy (TEM). TEM is performed on a Phillips 300 electron microscope operating at an acceleration voltage of 80 kV. A drop of approximately 0.010.08 wt % copolymer solution in 1-octanol is placed on a copper grid coated with carbon film. The solvent is allowed to evaporate at room temperature and atmospheric pressure over 2 days and the sample is stained with ruthenium tetroxide and imaged using TEM. We assume that there is no significant change in morphology upon removal of solvent or during the drying process, especially in the absence of annealing processes. Light Scattering. The glassware used in light scattering are washed with condensing acetone vapor prior to use. Known concentrations of block copolymers in 1-octanol are prepared and solutions are filtered through Millipore Millex filters (0.45 μm pore size) directly into the cleaned scattering cell. Dynamic light scattering measurements (DLS) are performed on a Brookhaven BI-200SM instrument using vertically polarized incident light of wavelength λ = 514.5 nm supplied by a Coherent Innova 70 Series ion laser operated at 500 mW or less. The data is acquired using a BI-9000AT digital correlator fitted with the instrument. Experiment duration is 5-30 min and autocorrelation functions are measured at 7 angles (30, 50, 70, 90, 110, 130, and 150) for three different temperatures (15, 25, and 35 C). The correlation functions are analyzed by the constrained regularized CONTIN method to obtain distributions of decay rates (Γ).33 The decay rates afford distributions of apparent diffusion coefficient (Dapp = Γ/q2) and hence of the apparent hydrodynamic radius (Rh,app) via the Stokes-Einstein equation: Rh, app ¼ kT=ð6πηDapp Þ
ð6Þ
where k is the Boltzmann constant and η is the viscosity of solvent (in our system: 1-octanol) at temperature T. The values of true hydrodynamic radius (Rh) for the micelles at zero concentration are obtained by fitting the higher-concentration data points to straight lines and extrapolating to zero concentration. Rheology. The rheological properties of block copolymer solutions are analyzed using an AR-G2 rheometer (TA Instruments, minimum torque oscillation, 0.003 μN 3 m, and torque resolution, 0.1 μN 3 m) with Peltier plate-temperature control. A cone-plate geometry with a diameter, d = 40.0 mm, and cone angle (deg: min: sec) = 1 59 24, is used for more fluid-like samples with approximately 2 mL of sample added at experimental (31) Axelos, M. A. V.; Kolb, M. Phys. Rev. Lett. 1990, 64, 1457–1460. (32) Te Nijenhuis, K.; Winter, H. H. Macromolecules 1989, 22, 411–414. (33) Provencher, S. W. Makromol. Chem. 1979, 180, 201–209.
DOI: 10.1021/la100666t
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Figure 1. TEM picture of micelles from diblock copolymer (A) S278NtBAM517 and (B) S93NtBAM252. Dark phases consist of S block as it is stained with ruthenium tetroxide and light colored phase comprises NtBAM blocks. temperatures. Parallel plate geometry (20 mm diameter) is used for more solid-like samples. Only linear viscoelastic properties are measured, and the linear range is determined using stress sweep experiments. Dynamic frequency sweep experiments are performed at three different temperatures (15, 25, and 35 C) over a frequency range of 0.01 to 100 rad s-1. A solvent trap is used to prevent 1-octanol evaporation during the experiments. In each experiment 30 min conditioning time is allowed for thermal equilibration and to get rid of any shear history introduced while transferring the copolymer solutions to the appropriate geometry.
Results and Discussion Micelles. Block copolymers in which core forming block has its glass transition temperature (Tg) above room temperature forms micelles whose structures are locked. These micelles are not under thermodynamic equilibrium with the free unimers (polymer) chains. The resulting aggregated structure is known as micelle-like aggregates (mlas).34 In this study, S278NtBAM517 and S93NtBAM252, forming similar mlas morphology are selected so that we can compare the concentration dependence of the micelle-gel transition of each polymeric system in terms of the viscoelastic properties and material parameters at the critical gel states. A representative micrograph of micelles formed from very low concentrations of S278NtBAM517 and S93NtBAM252 in 1-octanol is shown in Figure 1. Both the block copolymers show spherical morphologies. The dark regions consist of polystyrene block preferentially stained by ruthenium tetroxide and the light phase is of poly(N-tert-butylacrylamide). From TEM, the polystyrene core of S278NtBAM517 is ∼30 nm and S93NtBAM252 is ∼20 nm, and this trend agrees well with the molecular weights of the polystyrene core block. Additional TEM micrographs have been included in the Supporting Information, Figures S2 (A and B). From DLS, Rh at room temperature of S278NtBAM517 and S93NtBAM252 are determined to be 47.98 and 27.06 nm, respectively, Table 2. The dilute solution behavior of S278NtBAM517 in 1-octanol is studied using DLS. Figure 2(A) shows that relaxation rates (Γ) are linearly dependent on the squared scattering vector, q2, implying a diffusional behavior. In Figure 2(B) the reciprocal of the intensity average of Rh,app is plotted against copolymer concentrations for the S278NtBAM517 copolymer solution at 15, 25, and 35 C. Plotting 1/Rh,app rather than Dapp compensates for any differences in solution temperature and solvent viscosity. Linear extrapolation of the data sets to zero concentration affords the true values of Rh. Figure 2(B) shows that (1) Rh,app increases with concentration of the block copolymer solution, while apparent diffusion coefficient (34) Zhang, L.; Eisenberg, A. J. Am. Chem. Soc. 1996, 118, 3168–3181.
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Table 2. Dynamic Light Scattering Studies of SmNtBAMn/1-Octanol at Different Temperatures block copolymer solution S278NtBAM517/1-octanol
S93NtBAM252/1-octanol
temperature, C
Rh (nm)
kd (mL/g)
Rh (nm)
kd (mL/g)
15 25 35
65.49 47.98 36.35
-593.81 -416.69 -426.39
42.44 27.06 45.52
-9.59 -47.21 -29.84
(Dapp) decreases and (2) the hydrodynamic radius of micelles decreases with increase in temperature, Table 2. The concentration dependence of apparent diffusion coefficient (Dapp or 1/Rh,app) in dilute solution can be expressed as ð7Þ Dapp ¼ Do ð1 þ kd cÞ where the expansion is truncated at the second term. Parameter kd is related to the thermodynamic second virial coefficient, A2 through the equation35 kd ¼ 2A2 Mw - kf - 2v ð8Þ where kf is the frictional coefficient and v is the partial specific volume of the micelles in solution. If the quantities Mw, kf, and v are independent of concentration, the sign of kd depends on the sign and size of A2. Figure 2B shows that kd is always negative for the copolymer solutions at all experimental temperatures indicating a substantial attractive interaction among the micelles. It results in small excluded volumes for the micelles of SmNtBAMn copolymers, which in turn gives small values of A2 and so gives negative values of kd via eq 8. DLS investigations of S93NtBAM252 in 1-octanol show that the hydrodynamic radius (Rh) of micelles decreases with increase in temperature (15, 25 C), similar to dilute solutions of S278NtBAM517 in 1-octanol, Table 2. At 35 C, we see an abrupt increase in the S93NtBAM252 micellar size which is a deviation from the trend and possibly due to intermicellar interactions leading to larger aggregates. This anomalous swelling of S93NtBAM252 micelles at 35 C is not well understood yet and requires further investigation. In the next few sections, we will correlate results obtained from DLS studies with the critical gelation concentrations obtained from rheology. Dynamic Viscoelastic Properties. Frequency sweep experiments illustrate a profound change in the rheology of S278NtBAM517 and S93NtBAM252/1-octanol solutions with change in temperature. Figure 3 represents the measurements of real and imaginary parts, G0 and G00 , respectively, of the complex modulus (G*) as a function of angular frequency (ω) for a range of (35) Vink, H. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1725–1730.
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Figure 2. (A) Plot of decay rate (Γ) versus the square of the scattering vector, q2, for c = 0.610 mg/mL at 15 C. (B) Plot of concentration dependence of reciprocal intensity-average apparent hydrodynamic radius (1/Rh,app) for S278NtBAM517 copolymer solution at 15, 25, and 35 C.
Figure 3. Plot of storage modulus (G0 ) and loss modulus (G00 ) (filled and open symbols) versus angular frequency (ω) of S278NtBAM517 / 1-octanol system shown in parts A and B and S93NtBAM252/1-octanol system shown in parts C and D for various concentrations at 15 and 25 C. In all the plots, the curves at different concentrations are shifted vertically by the factor A as indicated. A similar plot for S278NtBAM517 copolymer solution at 35 C is shown in our previous publication.19
concentrations of copolymer solutions at 15 and 25 C. A similar plot for S278NtBAM517 copolymer solution at 35 C has been published.19 The data for S93NtBAM252/1-octanol at 35 C will be discussed in the following sections. At lower concentration, micellar solutions of both copolymers behave as viscoelastic fluids in the terminal (or low) frequency range with storage modulus (G0 ) smaller than the loss modulus (G00 ) and exhibit the following scaling relationship:19,36 G0 ðωÞ∼ω2 ,
G00 ðωÞ∼ω1 ðat ω f 0Þ
ð9Þ
(36) Morrison, F. A. Understanding Rheology; Oxford University Press: New York, NY, 2001.
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Both G0 (ω) and G00 (ω) increase with concentration of the copolymer in 1-octanol, and eventually an optically transparent gel is obtained, where G0 (ω) is greater than G00 (ω) and is nearly frequency independent in the terminal (or low) frequency range which is a characteristic of solid-like behavior. The gel-like behavior indicated by the evolution of quasi-equilibrium modulus that manifests as a gel plateau follows a scaling relationship given as:17,19 G0 ðωÞ ¼ Ge ðat ω f 0Þ
ð10Þ
The evolution of gel plateau is observed at different concentrations for S278NtBAM517 and S93NtBAM252 solutions suggest a DOI: 10.1021/la100666t
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Figure 4. Loss tangent, tan δ, as a function of copolymer concentration for S278NtBAM517/1-octanol system shown in parts A and B and S93NtBAM252/1-octanol system shown in parts C and D at various angular frequencies for temperatures: 15 and 25 C. The multifrequency plot for S278NtBAM517 solutions at 35 C (not shown in this figure) also converges at a common point (cg) as reported in our previous publication.19
temperature, copolymer composition, and concentration dependence of the micelle-gel transition. Determination of Gel Point. Dynamic mechanical experiments provide an accurate and a direct way of determining the gel point. Traditionally, to determine the gel point, the crossover of storage modulus G0 (ω) and loss modulus G00 (ω) has been used as an indicator. Although this method is easy and simple, Winter and co-workers have shown that crossover does not always occur at the gel point as it is frequency dependent.37 They proposed a criterion to determine the gel point exhibited by power law behavior, shown in eq 4 and 5. The frequency independence of loss tangent (tan δ) in the vicinity of gel point has been widely used for determining the gel point. At the gel point, gelation variable looses its dependency on the frequency and converges at a point which can be critical gelation concentration (cg) and critical gelation temperature (Tgel). In this work, gelation variable is copolymer concentration in 1-octanol expressed in weight percentage (wt %). In parts A and B of Figure 3, for S278NtBAM517 solutions, liquid-like behavior is observed at concentrations below 7.4 wt % and gel-like behavior is observed at 9 wt % and above. Thus, the micelle-gel transition takes place around 9 wt % for both 15 and 25 C. For S93NtBAM252 solutions in Figure 3, parts C and D, liquid-like behavior is observed at polymer concentrations below 16.7 and 20.6 wt % at 15 and 25 C, respectively and gel-like behavior is observed at 30 wt % and above. Interestingly we can observe that in Figure 3, parts C and D, at c = 25.9 wt %, the scaling of the moduli (G0 and G00 ) is almost parallel and thus the critical concentration should be around this value. (37) Winter, H. H. Polym. Eng. Sci. 1987, 27, 1698–1702.
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Figure 4 shows a multifrequency plot of tan δ vs copolymer concentrations for S278NtBAM517 and S93NtBAM252/1-octanol solutions at 15 and 25 C. In each plot the curves passes through a common point defined as critical gelation concentration, cg. The value of cg can be read directly as the abscissa of the convergence point. The viscoelastic exponent, n, was determined from gel point using eq 5. The multifrequency plot for S278NtBAM517 solutions at 35 C (not shown in Figure 4) also converges at a common point, cg, is reported in our previous publication.19 The value of critical exponent, n, for S278NtBAM517 solutions is obtained as 0.761 at 15 C which agrees with the prediction from electrical network analogy introduced by de Gennes.26,27 The value of n obtained as 0.680 and 0.677 for S278NtBAM517 solutions at 25 and 35 C respectively agrees well with percolation theory showing Rouse dynamics.19,26,27,46 The values of critical exponent, n, for S93NtBAM252/1-octanol remains in the range of 0.3-0.5. Though some of the values of exponent, n, differ from theoretical predictions, power law frequency dependence of G0 and G00 exhibited by this system clearly shows a sign of formation and growth of self-similar clusters.38 Table 3 summarizes the values of cg and n at different temperatures (15, 25, and 35 C), determined from this method (named as method “1”). It is well-known that critical gels exhibit self-similar relaxation modulus shown in eq 3 (G(t) = Sct-n). Consequently G0 and G00 , scale with frequency, ω, at the gel point as: G0 ðωÞ ¼
G00 ðωÞ ¼ Sc Γð1 - nÞ cosðnπ=2Þωn tanðnπ=2Þ
ð11Þ
(38) Cocard, S.; Tassin, J. F.; Nicolai, T. J. Rheol. (N. Y.) 2000, 44, 585–594.
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Table 3. Tabulation of Material Parameters of S278NtBAM517 /1-octanol and S93NtBAM252 /1-octanol systems block copolymer solution S278NtBAM517/ 1-octanol T, C
cga (wt %)
cgb (wt %)
n
S93NtBAM252/1-octanol Sc (Pa-sn)
cga (wt %)
cgb (wt %)
n
Sc (Pa-sn)
9.17 9.32 ( 0.33 0.761 ( 0.06 0.785 25.95 24.66 ( 0.357 0.347 ( 0.02 132.88 9.65 9.65 ( 0.022 0.680 ( 0.005 1.06 26.00 25.04 ( 0.618 0.420 ( 0.08 102.53 d d d d c c c c 11.13 ( 0.160 0.677 ( 0.013 0.55 11.3 a b c d By method 1, frequency independence of loss tangent. By method 2, uses gel point equation. Critical gel states were not observed. Data reported in our previous publication.19 15 25 35
Figure 6. Plot of tan δ versus concentrations of S93NtBAM252/ 1-octanol system at various angular frequencies for 35 C. Figure 5. Plot of G0 and G00 /tan (nπ/2) versus concentrations of S93NtBAM252/1-octanol system at various angular frequencies for 15 C.
where Γ(1 - n) is the Legendre gamma function. The physical nature of the gelling system at the gel point can be described by the gel strength Sc defined in eqs 3 and 11. For chemical gels, Sc increases while n decreases with an increase in cross-link density.39 This implies that Sc is related to the physical strength of the gel network at the gel point. According to eq 11, there is a crossover of G0 and G00 /tan (nπ/2) at the gel point.40 This equation can be used to calculate Sc when n is known for S278NtBAM517 and S93NtBAM252/1-octanol solutions at different temperatures (named as method “2”). Methods 1 and 2 are related to each other and are used for determining critical gel concentration (cg) and material parameters (n and Sc). However, Method 1 affords the values of n and cg; but it would not be possible to determine Sc through it. So for Sc determination we used the value of n obtained from method 1 in method 2. Also, since the two methods are similar, the analysis should give similar values of cg, Table 3. Figure 5 shows the plot of G0 and G00 /tan(nπ/2) against S93NtBAM252/1-octanol concentrations at 15 C. In this plot G0 (ω) and G00 (ω)/tan(nπ/2) curves at different frequencies exhibit ascending functions with increasing concentration. The plots of G0 (ω) and G00 (ω)/tan(nπ/2) against copolymer concentrations for both systems at other temperatures show similar behavior (Figure S1 in the Supporting Information). Table 3 shows that gel stiffness, Sc, increases as n decreases and vice versa in accordance with eq 3. A variety of studies on chemical gels have shown similar results implying a relation between n and Sc, but it should be noted that Sc is not always a strict function of n.39,41,42
Table 3 summarizes the results obtained for S278NtBAM517 and S93NtBAM252/1-octanol systems at 15, 25, and 35 C. At the gel point, power law behavior is observed for both the systems at experimental temperatures in a narrow ω range at high ω (>0.1 rad/s) because the gel structure often changes or gets disrupted by small changes in temperature or applied stress/strain. In Figures 4 and 5, temperature dependence of critical gel concentration is investigated for the same range of frequency as this allows us to explore structures at similar length scales. In Figure 6, the power law behavior fails at 35 C for S93NtBAM252/1-octanol system. The failure of power law behavior in the case of S93NtBAM252/1-octanol at 35 C may be attributed to the thermodynamic interactions that disrupt large-scale gel structure. These interactions, in the case of diblock copolymers, can be related to the composition fluctuations and the Brownian motion of the micelles which leads to the absence of critical gel state of S93NtBAM252/1-octanol at 35 C.24,43 From Table 3, it is observed that the critical gel concentration, cg, is lower for S278NtBAM517/1-octanol compared with the S93NtBAM252/1-octanol system. We attribute this trend in cg to the higher molecular weight and higher weight fraction of the solvophobic block in S278NtBAM517 compared to S93NtBAM252. Table 3 shows that cg of both copolymers solutions increases with temperature. To understand this trend, we assume that these copolymer solutions comprise of solvent-swollen spherical micelles that act as effective hard spheres. Gelation occurs when volume fraction of these hard spheres reaches a critical value.44,45 Furthermore, dynamic light scattering (DLS) studies of these copolymers solutions show that hydrodynamic radius (Rh) of the micelles decreases with increasing temperature (15-35 C) results in decreasing the volume fraction of the micelles in solution,
(39) (40) (41) (42) 2428.
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Langmuir 2010, 26(10), 7418–7424
DOI: 10.1021/la100666t
7423
Article
Sharma and Kasi
Table 2. Decrease in volume fraction of the micelle will require higher copolymer concentration to transition from micelles to gels at higher temperatures. This trend is observed in the case of S278NtBAM517/1-octanol (15, 25, and 35 C) and S93NtBAM252/ 1-octanol (15, 25 C). Additional studies will be necessary to understand the anomalous behavior of S93NtBAM252/1-octanol solutions at 35 C, which is beyond the scope of this paper. We are interested in investigating the influence of composition and molecular weight of the copolymers on n and Sc. However, we need to determine specific refractive index increment (dn/dc) values for the copolymer solutions to perform static light scattering (SLS) experiments that will help us establish these relationships. Because of experimental difficulties including large fluctuations in the signals from the differential refractometer and poor reproducibility, we could not determine dn/dc of copolymer solutions and hence could not perform SLS experiments. At this stage, further experimentation is required to establish the impact of polymer composition on n and Sc. In summary, DLS data along with rheological data of SmNtBAMn/1-octanol suggests that concentration dependence of micelle-gel transition, formation of critical states, and material parameters can be tailored using composition and molecular weight of the block copolymers as well as processing conditions.
Summary In this paper, we present dilute solution properties and dynamic viscoelastic studies of S278NtBAM517 and S93NtBAM252 in 1-octanol as a function of copolymer concentration at different temperatures. TEM investigations show that both the copolymers
7424 DOI: 10.1021/la100666t
in 1-octanol form spherical micelles. DLS measurements show that hydrodynamic radii of these micelles decreases with increasing temperature. Rheological measurements show that these BCP solutions exhibit power law behavior at the gel point (G0 (ω) ∼ G00 (ω) ∼ ωn), which is a signature of transition between liquid-like and solid-like behavior at the gel point. Critical gelation concentration (cg) is determined by frequency independence of loss tangent in the vicinity of gel point and exhibit an increasing trend with temperature, while, material parameters, n and Sc, vary with temperature. Determination of n and Sc are vital as we obtain gelpoint as a reference state to develop materials of different desired properties. In summary, we can tailor the processing conditions of these block copolymer solutions to affect the occurrence of gelation, which can be modified depending on the applications. Acknowledgment. Partial financial support was provided by the University of Connecticut new faculty start up funds, University of Connecticut Research Foundation, and a NSF CAREER Award to RMK (DMR-0748398). Central instrumentation facilities in the Institute of Materials Science and Chemistry Department at University of Connecticut are acknowledged. The authors acknowledge fruitful discussions with Profs. Montgomery Shaw and Thomas Seery. Supporting Information Available: Figures showing plots of G0 (ω) and G00 (ω)/tan (nπ/2) versus concentration, TEM pictures of micelles from diblock copolymers, and plots of storage modulus G0 and loss modulus G00 against temperature. This material is available free of charge via the Internet at http://pubs.acs.org.
Langmuir 2010, 26(10), 7418–7424
