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Synthesis and Aggregation Behavior of Thermally Responsive Star Polymers Robert H. Lambeth,† Subramanian Ramakrishnan,‡ Ryan Mueller,§ John P. Poziemski,† George S. Miguel,† Larry J. Markoski,† Charles F. Zukoski,*,§ and Jeffrey S. Moore*,† Department of Chemistry and The Beckman Institute for AdVanced Science and Technology, The UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Department of Chemical and Biomedical Engineering, Florida A&MsFlorida State UniVersity, Tallahassee, Florida 32310, and Department of Chemical and Biomolecular Engineering, The UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ReceiVed January 17, 2006. In Final Form: May 1, 2006 To mimic the three-dimensional (3-D) globular architecture resulting from the precise positioning of hydrophobic/ hydrophilic domains (blocks) of naturally occurring proteins, water-soluble linear and star homopolymers of N,N′dimethylacrylamide (DMA) were synthesized with prescribed molecular weights via reversible addition-fragmentation chain transfer (RAFT) polymerization and subsequently used as macro chain transfer agents for block copolymerization with N-isopropylacrylamide (NIPAM). For the star block copolymers, the interior block consisted of NIPAM while the exterior block was DMA. Since polyNIPAM thermally switches from hydrophilic to hydrophobic, the 3-D solution conformations of the polymers were studied as a function of temperature using differential scanning calorimetry (DSC), static light scattering (SLS), and dynamic light scattering (DLS). The polymers were observed to form monodisperse aggregates in an aqueous pH 4 buffer solution when heated above the lower critical solution temperature (LCST) of polyNIPAM. The temperature at which the polymers aggregated and the size of the aggregates were dependent on the NIPAM block length and the core architecture. A simple model based on an optimal area per headgroup was used to analyze our experimental findings and was useful for predicting the final size and molecular weight of the aggregates formed.
1. Introduction The self-assembly of nanometer-, micrometer-, and millimetersize building blocks is expected to give rise to a new generation of materials with unique structures and physical properties.1-3 These types of materials are expected to be useful in a wide range of applications that will require the self-assembly process to mimic the precision and reliability of biological systems.4 To better understand the assembly process, computer simulation has been employed to aid in predicting the types of structures that could form from the self-assembly of nanoparticles bearing discrete, attractive interaction sites.4 The simulations show that when the complementary attractive sites, or “patches”, are placed at precise locations on particle surfaces, the overall structure of the assembly can be controlled. At present, these structures remain largely hypothetical because the synthesis of well-defined surfacestructured nanoparticles with controllable interparticle interactions remains an elusive goal. To address this problem, we are currently working toward developing a synthetic method to readily prepare “patchy” nanoparticles of well-defined size, shape, and surface functionality. The closest analogy to patchy particles is proteins where straight chain polymers fold into globular shapes. One of the major driving * To whom correspondence should be addressed. Phone: (217) 2444024. Fax: (217) 244-8068. E-mail:
[email protected] (J.S.M.). Phone: (217) 333-0034. Fax: (217) 333-5052. E-mail:
[email protected] (C.F.Z.). † Department of Chemistry and The Beckman Institute for Advanced Science and Technology, The University of Illinois at Urbana-Champaign. ‡ Florida A&MsFlorida State University. § Department of Chemical and Biomolecular Engineering, The University of Illinois at Urbana-Champaign. (1) Glotzer, S. C. Science 2004, 306, 419. (2) Glotzer, S. C.; Solomon, M. J.; Kotov, N. A. AIChE J. 2004, 50, 2978. (3) Whitesides, G. M.; Grzybowski, B. Science 2002, 295, 2418. (4) Zhang, Z.; Glotzer, S. C. Nano Lett. 2004, 4, 1407.
forces controlling this folding is the relative solvation of different monomers.5,6 The desire to prepare polymers with properties that mimic the nanostructure and function of those in biology has led to the development of a number of approaches.7-12 One approach that is particularly well-suited for preparing unimolecular nanoparticles of well-defined structure and surface functionality is based on the tethering of individual amphiphillic block copolymers to a central core.13,14 With this type of architecture, the formation of dense unimolecular core-shell nanoparticles is anticipated when the interior blocks become insoluble and collapse. If the collapsed form of the polymer remains stable, it will mimic the core-shell structure of a globular protein. “Patchiness” or instructions for guided self-assembly of the collapsed nanoparticle can be coded into the chemistry of the exterior blocks, thus giving one the opportunity to achieve a variety of useful structures. In addition to stable collapsed nanoparticles, the collapsed polymers may further aggregate into well-defined supramolecular assemblies depending on the relative block composition and architecture. A schematic of the possible conformations is shown in Figure 1. Our current goal is to better understand how varying the polymer architecture and relative (5) Fisher, H. F. Proc. Natl. Acad. Sci. 1964, 51, 1285. (6) Gates, R. E.; Fisher, H. F. Proc. Natl. Acad. Sci. 1971, 68, 2928. (7) Cunliffe, D.; Pennadam, S.; Alexander, C. Eur. Polym. J. 2004, 40, 5. (8) Zhang, Q.; Remsem, E. E.; Wooley, K. L. J. Am. Chem. Soc. 2000, 122, 3642. (9) Thurmond, K. B., II; Kowalewski, T.; Wooley, K. L. J. Am. Chem. Soc. 1997, 119, 6656. (10) Henselwood, F.; Liu, G. Macromolecules 1997, 30, 488. (11) Bosman, A. W.; Vestberg, R.; Heumann, A.; Frechet, J. M. J.; Hawker, C. J. J. Am. Chem. Soc. 2000, 125, 715. (12) Sumerlin, B. S.; Lowe, A. B.; Thomas, D. B.; Convertine, A. J.; Donovan, M. S.; McCormick, C. L. J. Polym. Sci., Part A: Polym. Chem. 2004, 42, 1724. (13) Heise, A.; Hedrick, J. L.; Frank, C. W.; Miller, R. D. J. Am. Chem. Soc. 1999, 121, 8647. (14) Yoo, M.; Heise, A.; Hedrick, J. L.; Miller, R. D.; Frank, C. W. Macromolecules 2003, 36, 268.
10.1021/la060169b CCC: $33.50 © 2006 American Chemical Society Published on Web 06/07/2006
Thermally ResponsiVe Star Polymers
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Figure 1. Schematic of using four-arm star polymers that form tetrafunctional nanoparticles when the polymer is in a collapsed conformation. In this work, the inner arm is composed of NIPAM, which can be collapsed by heating above its phase transition temperature. The outer arm is composed of DMA, which remains hydrophilic upon increasing the temperature. It is also possible that the collapsed conformation of the polymer may further aggregate into a supramolecular assembly.
block composition affects the solution conformation of the copolymers when one of the blocks becomes insoluble. Herein, the synthesis and characterization of thermoresponsive linear and star diblock copolymers is reported. Linear and fourarm star N,N′-dimethylacrylamide (DMA) homopolymers were prepared by reversible addition-fragmentation chain transfer (RAFT) polymerization and used as macro chain transfer agents for block copolymerization with N-isopropylacrylamide (NIPAM). PolyNIPAM is a thermoresponsive polymer, displaying lower critical solution temperature (LCST) behavior at ca. 32 °C,15 while polyDMA is a water-soluble polymer. For the star block copolymers, the interior block consisted of NIPAM while the exterior blocks consisted of DMA. The DMA block length was held constant while the NIPAM block length was varied. The molecular weight and molecular weight distribution of the polymers was determined by gel permeation chromatography (GPC). Differential scanning calorimetry (DSC), dynamic light scattering (DLS), and static light scattering (SLS) were used to study the aggregation behavior of the polymers in an aqueous pH 4 buffer solution as a function of temperature. Our studies show that for the block lengths chosen, when the LCST of polyNIPAM is exceeded, the star polymers aggregate into monodisperse particles as revealed by dynamic light scattering. We show that a simple model based on optimal area per headgroup developed for linear block copolymer micelles is successful in predicting the number of linear and star unimers per aggregate in the final structure and the size of the aggregated micelles of the four-arm stars. These studies reveal interesting methods for synthesizing amphiphilic star block copolymers whose aggregation behavior can be controlled by chemical design and positioning of the block segment lengths. 2. Experimental Section 2.1. Materials. Unless otherwise noted, all materials were used as received. NIPAM was recrystallized from petroleum ether/benzene 7:3 (v/v). Azobis(isobutyronitrile) was recrystallized twice from methanol. DMA and chlorobenzene were dried over CaH2 and vacuum distilled prior to use. Pentaerythritoltetrakis(3-(S-benzyltrithiocarbonyl)propionate) (1) was synthesized as described previously.16 Trithiocarbonic acid benzyl ester butyl ester (2) was synthesized in a similar manner. 2.2. Analysis. The molecular weight and polydispersity of the polymers were estimated in a mixture of tetrahydrofuran (THF) (89%), MeOH (10%), and triethylamine (1%) at 30 °C with a Waters 515 HPLC pump, Viscotek TDA Model 300 triple detector, and a (15) Taylor, L. D.; Cerankowski, L. D. J. Polym. Sci., Part A: Polym. Chem. 1975, 13, 2551. (16) Mayadunne, R. T. A.; Jeffery, J.; Moad, G.; Rizzardo, E. Macromolecules 2003, 36, 1505.
series of three ViskoGEL HR high-resolution columns (1 × G3000 HR, 2 × GMHHR-H mixed bed) at a flow rate of 1.0 mL/min. Molecular weight data are reported as polystyrene equivalents. Dynamic light scattering (DLS) and static light scattering (SLS) were performed with a 10 W Lexel Model 95 argon ion laser at a wavelength of 514.5 nm and at a power of 150-1000 mW. A Brookhaven Instruments BI-200 goniometer was used to measure the scattered light intensity at scattering angles from 40° to 140° for SLS, while DLS was performed predominantly at 40°, 90°, and 140°. The θ range of 40° to 140° corresponds to 0.011 to 0.031 nm-1, respectively. Samples were dispersed in pH 4 buffer and filtered through a 0.45 µm nylon filter into Fisherbrand 10 mm o.d. glass tubes prior to the experiment. The temperature of the sample was maintained at a constant value ((0.2 °C) by recirculating water from a temperature-controlled water bath through the sample holder. Light intensity was measured with a photomultiplier tube, and the output signal was processed by a Brookhaven BI-9000AT digital correlator. Correlation functions were measured over delay times ranging from 0.5 µs to 9 ms for a few minutes. Hydrodynamic diameters were extracted from the measured correlation function using the second cumulant method. The measured “polydispersity” from DLS was e0.3, which validates the second cumulant method.17 The weight-average molecular weight (Mw) and radius of gyration (Rg) were extracted from Zimm plots. DSC measurements were performed on a Mettler-Toledo DSC821 at heating and cooling rates of 5 °C/min. Measurement of dn/dc for the four-arm star polymers of DMA/NIPAM and for the linear polymers was performed using a Wyatt Optilab DSP refractometer at a wavelength of 488 nm and at 25 °C. 2.3. Typical DMA Homopolymerization. To a 250 mL Schlenk flask under N2 atmosphere was added 1 (104 mg, 0.090 mmol) and a 1.12 mg/mL stock solution of AIBN in chlorobenzene (0.66 mL, 0.0045 mmol). DMA (12.47 mL, 121 mmol) and chlorobenzene (90 mL) were added via syringe. The flask was sealed with a glass stopper, degassed, and then backfilled with argon followed by three freeze-pump-thaw cycles under argon. The flask was placed in an oil bath at 65 °C and stirred for 10 h. Solvent was removed under high vacuum, and the remaining solid was redissolved in ethyl acetate (100 mL). The solution was precipitated by dropwise addition into diethyl ether (800 mL). The precipitate was collected by vacuum filtration and dried under high vacuum. 2.4. Typical NIPAM Copolymerization from PolyDMA Macro Chain Transfer Agent. To a 100 mL Schlenk flask under N2 atmosphere was added polyDMA (95 700 g/mol based on percent conversion) (1.0 g, 0.010 mmol), a 1.0 mg/mL solution of AIBN in chlorobenzene (0.086 mL, 0.00052 mmol), NIPAM (2.0 g, 17.6 mmol), and chlorobenzene (50 mL). The flask was sealed with a glass stopper, degassed, and then backfilled with argon followed by three freeze-pump-thaw cycles under argon. The flask was placed in an oil bath at 65 °C and stirred for 12 h. Solvent was removed (17) Instruction Manual V2.2 for Model BI-9000AT Digital Correlator; Brookhaven Instrument Corporation: 1992.
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Lambeth et al. Scheme 1. Star Polymer Synthesis
under high vacuum, and the remaining solid was redissolved in ethyl acetate (40 mL). The solution was precipitated by dropwise addition into 400 mL of diethyl ether. The precipitate was collected by vacuum filtration and dried under high vacuum. 2.5. Arm Cleavage from Star Polymers. A typical procedure is as follows: a sample of polymer (ca. 200 mg) and dithiothreitol (1 mg) was dissolved in 40 mL of the GPC eluent described above, and piperdine (100 µL) was added. The reaction was maintained at room temperature and monitored by GPC and in all cases was complete after 9 h.
3. Results 3.1. Polymer Synthesis and GPC Characterization. The structure of trithiocarbonate chain transfer agents (CTAs) determines the direction of fragmentation in star polymer synthesis. The direction of fragmentation depends on the relative stability of the carbon-centered radicals generated by dissociation from of the trithiocarbonate.16 In this case, since the benzyl radical is more stable than the primary alkyl radical, fragmentation occurs in the direction of the benzyl group resulting in a species that propagates away from the CTA core. The advantage of having a propagating species that is not attached to the CTA core is that no star-star coupled impurities resulting from bimolecular termination will be present.16 Using this strategy, DMA was homopolymerized in the presence of the tetrafunctional trithiocarbonate (1) using a [CTA]:[AIBN] of 80:1 with a target molecular weight of 100 kDa at 75% conversion. The DMA homopolymer (S1) was subsequently used as a “macroCTA” for chain extension with NIPAM to form star block copolymers S2 and S3. Since propagation occurs away from the CTA core, the NIPAM block will be attached to the CTA core (Scheme 1). A linear DMA homopolymer (L1) was also synthesized using a monofunctional CTA (2) under similar conditions and was used as a macroCTA for block compolymerization with NIPAM to form the linear block copolymer L2. The theoretical molecular weight of the polymers based on percent conversion of monomer was determined from the following equation:
Mn(calc) )
[M]MWmon [CTA]
% conversion + MWCTA
GPC traces are unimodal and symmetrical, indicating the polymers were not in an aggregated state (Figure 2). Some tailing was observed in the low molecular weight region of each sample, indicating that chain-chain coupling may have occurred to a small degree during the homopolymerization and subsequent block copolymerization. Nonetheless each polymer synthesized had a relatively low polydispersity index (Mw/Mn) (Table 1). It should be noted that there are some differences between the predicted molecular weights based on percent conversion and what was observed from GPC analysis. For the linear DMA homopolymer, GPC analysis using conventional calibration gives significantly lower molecular weights than what was calculated while the molecular weight estimated by GPC for the DMANIPAM block copolymer matches well with the calculated molecular weight. The discrepancy between the calculated and observed Mn values for the DMA could be due to interactions
(1)
where Mn is the number-average molecular weight, MWmon and MWCTA are the molecular weights of the monomer and CTA, respectively and [M] and [CTA] are the initial concentrations of monomer and CTA, respectively. The molecular weight and polydispersity of each polymer was characterized by GPC eluting with a solvent mixture of THF (89%), methanol (10%), and triethylamine (1%). This unusual solvent composition was essential for analysis because characterization of polymers containing NIPAM by GPC in pure THF is often associated with various problems such as irreversible chain aggregation.18 With the above-mentioned solvent mixture,
Figure 2. (A) GPC traces for star DMA homopolymer (S1) and chain extended block copolymers (S2, S3). (B) GPC traces for linear DMA homopolymer (L1) and chain extended block copolymer (L2).
Thermally ResponsiVe Star Polymers
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Table 1. Molecular Weight and Polydispersity Data for Linear and Star Homopolymers and Block Copolymers as Determined by GPC structure star linear
polymer
Mn(calcd)a (kDa)
Mn(GPC)b (kDa)
Mw/Mn (GPC)
PDMA965 (S1) P(DMA965-b-NIPAM506) (S2) P(DMA965-b-NIPAM126) (S3) PDMA229 (L1) P(DMA229-b-NIPAM117) (L2)
95.7 153.0 110.0 22.7 36.0
47.3 76.0 55.3 15.6 35.3
1.14 1.40 1.22 1.07 1.12
compositionc (DMA:NIPAM) 1.9:1 7.7:1 2.0:1
a
Calculated from eq 1 based on monomer conversion determined gravimetrically. b See Experimental Section for GPC conditions. c Weight of fraction of NIPAM determined by SLS.
Scheme 2. Base Cleavage of Star Polymer Arms
between the column packing material and the polymer itself, causing longer retention times than expected. In the case of the star polymers, the differences in the calculated and observed molecular weights can be explained by the differences in hydrodynamic volume between linear and star polymers. Star polymers have a smaller hydrodynamic volume compared to linear polymers of the same molecular weight, so polymer analysis by conventional calibration based on linear polystyrene standards will cause the measured molecular weight to be lower than the true molecular weight. One method to verify the overall molecular weight and purity of the star polymers is to cleave the arms from the CTA and characterize the individual arms by GPC.16 To accomplish this cleavage, the polymers were reacted with piperidine in the presence of dithiothreitol (DTT) for 9 h (Scheme 2). It was necessary to include DTT in the reaction mixture to prevent disulfide formation of the thiol endgroups produced during the cleavage reaction.19 As can be seen in Figure 3, the molecular
Table 2. Molecular Weight and Polydispersity Data for Star Polymers Cleaved with Piperdine in the Presence of DTT as Determined by GPC polymer
Mn(calcd)a (kDa)
Mn(GPC)b (kDa)
Mw/Mn (GPC)
S1 S2 S3
23.9 38.3 27.5
16.1 36.2 22.8
1.13 1.42 1.28
a Calculated by dividing M (calcd) from Table 1 by 4. b See n Experimental Section for GPC conditions.
Figure 4. DSC data for a 100 mg/mL solution of S1 in pH 4 buffer.
Figure 3. GPC traces for S1, S2, and S3 after treatment with piperidine in the presence of DTT.
weight distributions of the cleaved arms are unimodal, further indicating that the polymers were prepared in high purity. The molecular weight data are presented in Table 2. Again, GPC analysis using conventional calibration underestimates Mn for (18) Ganachaud, F.; Monteiro, M. J.; Gilbert, R. G.; Dourges, M. A.; Thang, S. H.; Rizzardo, E. Macromolecules 2000, 33, 6738. (19) Cleland, W. W. Biochemistry 1964, 4, 480.
the cleaved DMA chains but estimates Mn for the cleaved DMAb-NIPAM chains well. 3.2. Differential Scanning Calorimetry (DSC). The enthalpic changes associated with the transition from the extended to the collapsed state of star polymer S1 were studied by DSC. Three heating and cooling cycles were performed on the sample at a concentration of 100 mg/mL in pH 4 buffer (Figure 4). An endothermic transition was observed at 33.0 ( 0.1 °C upon heating, and an exothermic transition was observed at 28.6 ( 0.1 °C upon cooling. The enthalpy changes observed are associated with the breaking and making of hydrogen bonds between NIPAM monomer units and water,20 and they appear to be completely reversible with no significant hysteresis. 3.3. Static Light Scattering (SLS). The polymers listed in Table 1 were studied by SLS. For each polymer, a series of concentrations was made up ranging from 2 to 35 mg/mL (20) Heskins, M.; Guillet, J. E. J. Macromol. Sci. Chem. 1968, 2, 1441.
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Figure 5. Zimm plot of S3 polymer at 27 °C.
(minimum of six concentrations) and each concentration was studied as a function of temperature from 25 to 44 °C. Figure 5 is a characteristic Zimm plot of S3 polymer at 27 °C in pH 4 buffer. In a Zimm plot, the measured Rayleigh Ratio (Rθ) calculated at different angles (θ) and concentrations (c) is plotted as a function of sin2(θ/2).21
)[
(
2
2
16π Rg Kc 1 ) + 2A2c 1 + sin2(θ/2) Rθ Mw 3λ2
]
(2)
where Mw is molecular weight, A2 is the second virial coefficient, Rg is the radius of gyration, λ is the wavelength of radiation, and K is an optical constant. This approximation is valid in the low concentration limit. For higher concentrations the right-hand side of eq 2 increases nonlinearly with c. In the above equation, the optical constant K is given by
K)
4π2no2(dn/dc)2 NAλ4
(3)
where no is the refractive index of solvent (1.33 for pH 4 buffer) and dn/dc is the specific refractive index increment of the solution. The dn/dc was found to be a constant for the different polymers at 0.17 mL/g and is the value used in this work. The variation of dn/dc with temperature (25-44 °C) is neglected. Rg is calculated from a plot of Kc/Rθ taken in the limit c f 0 as a function of sin2(θ/2), A2 is calculated from Kc/Rθ in the limit θ f 0 as a function of c, and Mw is obtained from a double extrapolation to c f 0 and θ f 0. For the linear polymers and four-arm star polymers at room temperature, due to their low molecular weight, the variation of Kc/Rθ with sin2(θ/2) is negligible at a λ of 514 nm; hence an Rg for these polymers could not be determined. The results of the SLS measurements are presented in Figure 6. Figure 6A compares the changes in molecular weight as a function of temperature, while Figure 6B is a plot of the aggregation number (Xagg) as a function of temperature. Xagg is the ratio of the molecular weight at temperature T divided by the molecular weight at 25 °C ((Mw)T/(Mw)25). As can be seen from Figure 6, the DMA homopolymer S1 is in a nonaggregated state at both 25 and 40 °C as defined by a constant molecular weight and Xagg. The star diblock copolymers S2 and S3 and the linear diblock copolymer L2 showed an increase in Mw and Xagg upon raising the temperature above the LCST of polyNIPAM, which we treat as having a micellar structure. As can be seen from Figure 6A, the temperature at which aggregation begins is a function of the relative block length of (21) Zimm, B. J. Chem. Phys. 1948, 16, 1093.
Figure 6. (A) Weight-average molecular weight (Mw) of the different polymers as determined by static light scattering as a function of temperature. (B) Number of aggregates (Xagg) of the different polymers as a function of temperature. Xagg is calculated from the data in (A) as the ratio of the weight-average molecular weights at temperature T and at 25 °C ((Mw)T/(Mw)25)).
NIPAM to DMA. For the S2 and L2 polymers, aggregation starts at ca. 29 °C whereas the S3 polymer begins aggregating at ca. 36 °C. The temperature dependence of the onset of aggregation with NIPAM molecular weight is consistent with previous reports. Xia and co-workers22 demonstrated that the LCST of well-defined NIPAM homopolymers decreases with increasing molecular weight. Convertine and co-workers23 also observed a similar relationship between temperature and aggregation behavior of various DMA-NIPAM di- and triblock copolymers. When comparing polymers of similar block composition but different architecture, namely S2 and L2, the aggregation behavior is very different. To compare the number of linear chains in the micelles of S2 and L2, Xagg for S2 is multiplied by 4, the number of arms of the star polymer. The number of linear chains in the S2 micelle is 88, which is still less than half the number of linear chains (Xagg ) 220) in the micelle formed from the L2 polymer. The large difference in the number of linear polymer chains in the aggregates of L2 and S2 is most likely because star polymers are entropically disfavored in the micellar state compared to linear polymers.24 Aggregation results from a reduction in free energy of the system. For homogeneous polymers, this occurs as segment attractions become larger than segment-solvent attractions. As (22) Xia, Y.; Yin, X.; Burke, N. A. D.; Stover, H. D. H. Macromolecules 2005, 38, 5937. (23) Convertine, A. J.; Lokitz, B. S.; Vasileva, Y.; Myrick, L. J.; Scales, C. W.; Lowe, A. B.; McCormick, C. L. Macromolecules 2006, 39, 1724. (24) Narrainen, A. P.; Pascual, S.; Haddleton, D. M. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 439.
Thermally ResponsiVe Star Polymers
Figure 7. Second virial coefficient (A2) as a function of temperature for the different polymers as determined by static light scattering.
the segment-segment attractions overwhelm the segmentsolvent attractions, the polymer becomes increasingly more likely to aggregate. Typically the edge of stability occurs at the theta point where A2 in eq 2 goes to zero. At this point the effects of volume exclusion are balanced by the net attraction between the polymer segments. A negative value of A2 indicates increasingly strong attractions and reduced segment solubility. For block copolymers and star block copolymers, stability will be a balance of the theta state of each block.25-28 An averaged value of the theta state of the star copolymers and their aggregates can be found by measuring A2. A plot of A2 as a function of temperature is shown in Figure 7 for the different polymers used in this work. For the DMA star copolymer (S1) A2 is independent of temperature, indicating that this star is well solvated independent of temperature in the range tested. For the star and linear diblock copolymers, A2 shows a constant value and then decreases toward zero with increasing temperature. The onset of the decrease in A2 corresponds to the onset of the increase in molecular weight (aggregation) of the species in solution. Interpreting the absolute values of A2 requires knowledge of the structure of the polymers and their aggregates. If we treat the polymers as spheres, the natural scaling is A2HS ) (2π/3)σ3NA/ Mw2, where σ is the sphere diameter and NA is Avogadro’s number. If A2 takes on a value of A2HS, the objects are assumed to experience only hard sphere or purely excluded volume interactions. A decrease in A2 from A2HS is an indication of attraction between the polymers. For the star copolymers studied as a function of temperature here, we are working with systems where both σ and Mw change with temperature, thus complicating the interpretation of A2. If the density of the sphere is independent of its size, then A2HS ∼ Mw-1. Of course the star polymers are not spheres of uniform density. However, if we look at another extremesa straight chain, random coil polymer under dilute poorsolvent conditionsswe expect σ ∼ Mw1/2 yielding A2HS ∼ Mw-1/2. Either choice of A2 scaling indicates that the formation of aggregates alone will reduce A2. Thus the decrease in A2 with increasing temperature is to some extent a measure of the onset of increasing molecular weight. If we assume that the star copolymers and their aggregates can be treated as particles with a constant density, then A2/A2HS ∼ A2(T)Xagg/A2(T)25 °C). Deviations of A2/A2HS from unity are a measure of the strength of attraction or repulsion between the star copolymers or their (25) Lee, A. S.; Butun, V.; Vamvakaki, M.; Armes, S. P.; Pople, J. A.; Gast, A. P. Macromolecules 2002, 35, 8540. (26) Nagarajan, R.; Ganesh, K. J. Chem. Phys. 1989, 90, 5843. (27) Jain, S.; Bates, F. S. Science 2003, 300, 460. (28) Munch, M. R.; Gast, A. P. Macromolecules 1988, 21, 1360.
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aggregates. For S2 and S3, at all temperatures we find A2/A2HS to be 0.9 ( 0.3, while for L2 the absolute values of A2 are so close to zero that the experimental uncertainties make calculation of A2/A2HS meaningless. These estimates show that, as the polyNIPAM cores change their theta state and the star copolymers aggregate, the resulting structures retain approximately the same interaggregate interactions and that this keeps the aggregates behaving as hard spheres; i.e., as the temperature is raised, the star copolymers adjust their state of aggregation in such a way that they experience primarily volume exclusion interactions with no substantial interaggregate attractions within the temperature range tested. 3.4. Dynamic Light Scattering (DLS). The diffusion coefficient of the solute can be measured from the autocorrelation function of light intensity fluctuations, G2(τ),29 which is an ensemble average of the product of the intensity at time t and t + τ.
G2(τ) ) 〈I(t)I(t+τ)〉
(4)
The angular brackets indicate an average has been taken for many values of t. For monodisperse particles in Brownian motion
G2(τ) ) B[1 + A exp(-2Γτ)]
(5)
where B is the baseline, A is a constant, and Γ is the exponential decay constant. Γ is related to the diffusion coefficient (D) by
Γ ) Dq2
(6)
where q is the scattering vector
q)
4πno sin(θ/2) λ
(7)
where no is the solvent refractive index, λ is the wavelength of laser used (514 nm), and θ is the scattering angle. Figure 8A is a representative plot of Γ vs q2 for S2 polymer at 44 °C at concentrations of 2.2 and 8.8 mg/mL, respectively. As can be seen from Figure 8A, Γ is a linear function of q2 for the concentrations studied, indicating that G2(τ) decays as a single exponential in delay time (indicating that the samples have a single diffusivity and thus have a narrow size distribution). The slope of Figure 8A gives the diffusion coefficient (D) at different concentrations. Extrapolations of D are made to zero concentration to determine the diffusivity at infinite dilution Do (Figure 8B). The hydrodynamic diameter Dh is then determined from Do using the Stokes-Einstein relation
Dh )
kT 3πηcDo
(8)
where T is the temperature and ηc is the viscosity of the suspending medium (pH 4 buffer) at temperature T. The measured hydrodynamic diameters of the polymers are shown in Figure 8C. As temperature is increased, the polymers that contain NIPAM aggregate into a monodisperse structure and in keeping with the SLS measurements the diffusivities indicate that the hydrodynamic diameters increase with temperature. The four-arm stars which contain a shorter length of NIPAM (S3) aggregate to a smaller size than S2. At higher temperatures (>40 °C) Dh reaches a constant value, as can be seen from Figure 8C, indicating that a high-temperature limit of aggregation has been reached. (29) Finsy, R. AdV. Colloid Interface Sci. 1994, 52, 79.
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Figure 9. D/Do as a function of concentration for S2 at different temperatures: 25 (0), 27.2 (O), 28.9 (4), 30.9 (3), 32.7 ([), 35.7 (b), and 44 °C (×).
Figure 10. D2′(T)/D2′(25 °C) as a function of temperature for S1, S2, and S3 four-arm star polymers.
Figure 8. (A) Exponential decay constant (Γ) as determined by dynamic light scattering as a function of q2 for S2 polymer at two different concentrations of 2.2 (circles) and 8.8 mg/mL (squares) at 44 °C. (B) Diffusivity (D) as a function of concentration for S2 at 44 °C. (C) Hydrodynamic diameter (Dh) as determined by dynamic light scattering for the different polymers as a function of temperature (T).
The concentration dependence of the aggregate diffusivity can also be used to characterize the strength of interaction of the aggregates. As shown in Figure 8B, the diffusivity is a linear function of polymer concentration. If we assume that the aggregates have sizes that are independent of concentration, we can write the diffusivity as
D/Do ) 1 + D2′c ) 1 + D2φ
(9)
where D2 ) 6D2′Mw/(πNADh3) and φ is the volume fraction of the particles with hydrodynamic diameter Dh and mass concentration c. A plot of D/Do as a function of c for S2 is given
in Figure 9. Similar to the analysis of the second virial coefficient (A2), if we assume a particle density that is independent of size and temperature, we expect D2′(T)/D2′(25 °C) ) D2(T)/D2(25 °C) to be a measure of changes in strengths of interaction between the star copolymers and their aggregates at each temperature. A plot of D2′(T)/D2′(25 °C) at different temperatures for the polymers studied in this work is given in Figure 10. The value of D2′(T)/ D2′(25 °C) lies between -1 and 2 for the different polymers studied in this work. The values of D2′(T)/D2′(25 °C) at the higher temperatures for the four-arm polymers S1 and S2 are nearly the same within error limits and are between 0.5 and 1. As the particles increase in size with temperature, the value of qDh at an angle of 140° also changes and is found to lie between 1 and 2 for the polymers studied in this work. Detailed calculations and measurements on hard sphere particles in the qDh range of 1-2 reveal D2 to lie between 0 and 1.4. The similarities of D2 values measured on the star copolymers and their aggregates and the values expected for hard spheres is consistent with the second virial coefficient measurements, indicating that with increasing temperature the four-arm star polymers aggregate to shield the hydrophobic core while leaving the hydrophilic chains to provide stability. Final size is reached when there is no greater change in chemical potential to provide stability, and the value of D2 at this size is very close to that expected for particles experiencing only volume exclusion interactions. Thus, while the degree of aggregation grows tremendously as temperature is raised, the DMA-NIPAM star polymers aggregate in a way that minimizes interaggregate interactions.
Thermally ResponsiVe Star Polymers
Langmuir, Vol. 22, No. 14, 2006 6359
4. Discussion A considerable effort has been devoted to describing the thermodynamics of block copolymer micelles and the size of these micelles.25-28 These block copolymers are suspended in a solvent that is good for one block but poor for the other; hence they arrange into micelles with a core formed by the insoluble blocks and a corona consisting of the soluble blocks. These micelles can take on a variety of shapes but are commonly spheres, cylinders, and lamellae. States of association depend on a number of parameters such as the ratio of block lengths and relative solvent compatibility. Micellar structure and size are predicted by minimizing the total free energy of the system, which consists of a number of terms such as the elastic deformation of polymer chains in the micelle and free energy of mixing of the solvent molecules with the monomer units of the polymer.28 Predictions of size and structure from these models require a detailed knowledge of the thermodynamic properties of the individual polymeric units and are beyond the scope of this work. However, from these models we can extract a number of concepts to determine if the star copolymer aggregates studied here can be described in ways similar to those developed to describe the structures of straight chain copolymer micelles. To this end we model the aggregates at temperatures above 40 °C as consisting of a spherical hydrophobic core of NIPAM with a corona of DMA chains and test predictions expected for such structures. Qin and co-workers30 performed a detailed characterization of polystyrene-poly(methacrylic acid) (PS-PMA) block copolymer (diblock and triblock) micelles using static light scattering, dynamic light scattering, viscometry, sedimentation velocity, and densitometry. When the block copolymers were suspended in a dioxin/water mixture, the styrene block was hydrophobic while the methacrylic acid block was hydrophilic and hence micelles were formed. The molecular weight of these monomeric block copolymers varied from 30 to 182 kDa, and the resulting micelles had molecular weights up to 30 000 kDa, depending on the initial molecular weight and ratio of block lengths. Comparisons of the experimental data with a simple spherical model of a collapsed core surrounded by a corona of the PMA chains resulted in good agreement between the measured and predicted sizes. A surprising finding that resulted from the analysis of the data was that the fraction of the core surface area per tethered chain (Ac) (for a dry core) fell in a narrow range of 9-11 nm2 per chain. Another variable that was approximately constant was the coiling ratio Cr, defined as the ratio of the thickness of the shell and the length of the fully stretched PMA blocks. Table 3 lists the area of the core per tethered chain for the three polymers used in this work. The following steps and assumptions are used in calculating Ac and the stretching ratio βDMA. The volume of the collapsed core of a single nanoparticle (Vc1) is first calculated using the formula
Table 3. Calculations of Fraction of the Core Surface Area per Tethered Chain (Ac) and Stretching Ratio (βDMA) from Experimental Data
polymer
radius of core (nm)
Ac (nm2)
Dh(measd) (nm)
thickness of shell (nm)
βDMA
S3 S2 L2
3.96 9.09 14.43
12.58 12.62 11.90
33.77 47.17 63.93
12.92 14.50 17.53
1.69 1.89 1.79
with the number of aggregates and assuming a packing efficiency of 0.64:
[Mw]44°C 1 Vc ) Vc1 [Mw]25°C 0.64
(11)
The radius of the core Rc is then given by
Rc )
[ ] 3Vc 4π
1/3
(12)
The core surface area per tethered chain (Ac) follows from
Ac )
4πRc2 NDMAXagg
(13)
where NDMA is the number of DMA chains in a given polymer (4 for a four-arm star polymer and 1 for a linear chain) and Xagg is the number of aggregates in the final particle (Xagg ) [Mw]44°C/ [Mw]25°C). Once Rc is calculated, the following formula is used in evaluating βDMA:
βDMA )
Dh - 2Rc 4Rh,DMA
(14)
where [Mw]25°C is the molecular weight of the polymer at 25 °C, wNIPAM is the weight fraction of NIPAM in the polymer, FNIPAM is the particle density of NIPAM (a value of 0.965 g/cm3 is used in this work), and NA is Avogadro’s number. The number 0.87 arises from the assumption that, in the collapsed nanoparticle, 87% of the total volume is polymer and 13% is water.31 The total volume of the core (Vc) is then calculated by multiplying Vc1
where Dh is the measured hydrodynamic diameter of the micelle and Rh,DMA is the hydrodynamic radius of the free-floating DMA chain in solution. In this work, Rh,DMA of sample L1 is determined to be 3.7 nm and the values of hydrodynamic radii for different molecular weight DMA are calculated using a scaling law for polymers in a good solvent (Rh ∼ Mw0.6) since pH 4 buffer is a good solvent for DMA at all temperatures. As can be seen from Table 3, the value of Ac is constant at ca. 12 nm2. The stretching ratio (βDMA) of the DMA chains on the surface is also given in Table 3. βDMA is defined as the hydrodynamic thickness of the shell that contains the DMA chains divided by the hydrodynamic diameter of the free-floating DMA chains of the same molecular weight. The stretching ratio is a measure of how much the chains are stretched when they are attached to the surface. βDMA is approximately constant at a value of 1.7-1.9. This result is in agreement with the work of Qin and co-workers,30 where a constant value of Cr is seen. Table 4 lists the calculated final molecular weight and final hydrodynamic diameter of the aggregated micelles assuming a constant Ac of 12 nm2 and a stretching ratio of 1.8. As can be seen from this table, a constant value of Ac and βDMA captures the experimental values well. The existence of an optimal headgroup area has been extensively studied in the literature in order to understand the self-assembly of surfactants and block copolymers, and its value is determined through a competition between interfacial tension, headgroup repulsion (polymers in a good solvent), and entropic penalty for hydrophobic chain deformation. For the range of
(30) Qin, A. W.; Tian, M. M.; Ramireddy, C.; Webber, S. E.; Munk, P.; Tuzar, Z. Macromolecules 1994, 27, 120.
(31) Mullick, P. M. Ph.D. Thesis, Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 2004.
Vc1 )
[Mw]25°CwNIPAM 1 1 NA 0.87 FNIPAM
(10)
6360 Langmuir, Vol. 22, No. 14, 2006
Lambeth et al.
Table 4. Calculations of Final Molecular Weight and Hydrodynamic Diameter Using Constant Values of Ac (12 nm2) and βDMA (1.8) polymer
Mw(calcd) (g/mol)
% differencea
Dh(calcd) (nm)
% differencea
S3 S2 L2
479 166 3 160 000 11 400 000
7.2 8.35 -2.37
37.89 47.82 67.71
-9.67 -1.37 -5.59
a Percent difference calculated values and experimental values given in Tables 2 and 3.
DMA/NIPAM star polymers studied here, a value of 12 nm2 for Ac coupled with a stretching ratio of 1.8 captures the final micelle size well. The success of this simple model (which assumes a spherical core and a corona of chains) in capturing the size and number of aggregates of the experimental system further suggests the spherical nature of aggregates. In previous studies the core polymer resided in a very poor solvent such that the corona chains were strongly tethered. These models work well for our DMA/NIPAM polymers at the highest temperatures studied, while the models are less successful at lower temperatures where the solvent/NIPAM segment interactions are not so unfavorable. A possible explanation is that at lower temperatures, the NIPAM cores contain more water, which results in a higher Ac, and as the temperature is increased, the NIPAM core expels the water, causing the DMA chains to come together and stretch. That the models for strongly tethered corona polymers are applicable at the highest temperatures suggests that the constraint introduced by the presence of the star junction does not greatly alter the thermodynamics of aggregation and micelle formation for the range of star copolymers studied.
5. Conclusions and Future Directions In this study we have reported on the synthesis and characterization of linear and four-arm star block copolymers of NIPAM and DMA as a first step toward a final goal of synthesizing well-defined, unimolecular patchy nanoparticles. We find that when the four-arm star block copolymers are in a collapsed conformation they aggregate further into monodisperse supra-
molecular structures as revealed by SLS and DLS. Analysis of second virial coefficients and diffusion coefficients reveals that the star block copolymers aggregate until the interactions become hard-sphere-like independent of temperature. The corona of DMA chains essentially gives rise to short-range repulsions such that the micelles look like hard spheres. This is an important result if one is to study the assembly of these patchy nanoparticles at higher concentrations, as the nature of interactions between the particles is critical to the assembly step. Since the interactions are hard-sphere-like at different temperatures, one would also expect the sizes of the particles to be the same from dilute through high concentration. A simple model based on an optimum area per headgroup and a stretching ratio captures the thermodynamics of the assembly process and predicts the final molecular weight and aggregate size. Since our theoretical model has been verified experimentally, we would like to employ it as a predictive tool to rationally design a star polymer that will collapse into a monodisperse core-shell nanoparticle. Using eq 13, one can calculate the necessary core radius, and hence molecular weight, to prepare a unimolecular nanoparticle (Nagg ) 1). If the DMA block length is held constant and a value of 12 is used for Ac, then eq 13 predicts the formation of unimolecular nanoparticles with core radii of 1.95, 2.39, and 2.76 nm for four-, six-, and eight-arm star block copolymers, respectively. These values translate to total NIPAM core weight-average molecular weights of 16, 29, and 44 kDa, respectively. Detailed experimental investigations are being conducted to further confirm the validity of the model and to produce a collapsed patchy nanoparticle. The results of the investigations will be reported in future publications. Acknowledgment. This work was supported by the Nanoscale Science and Engineering Initiative of the National Science Foundation under NFS Award No. DMR-0117792. LA060169B
