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Solution behavior of 4-arm poly(tert-butyl acrylate) star polymers
European Polymer Journal 46 (2010) 2341–2351
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Solution behavior of 4-arm poly(tert-butyl acrylate) star polymers Barbara Mendrek a,b, Barbara Trzebicka a,⇑, Wojciech Wałach a, Andrzej Dworak a,b a b
Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Skłodowskiej 34, 41-819 Zabrze, Poland University of Opole, Faculty of Chemistry, Oleska 48, 45-052 Opole, Poland
a r t i c l e
i n f o
Article history: Received 14 June 2010 Received in revised form 14 September 2010 Accepted 30 September 2010 Available online 8 October 2010 Keywords: Star polymers Poly(tert-butyl acrylate) Intrinsic viscosity Branching parameters q Ratio
a b s t r a c t This paper reports the synthesis of 4-arm poly(tert-butyl acrylate) stars of different molar masses up to 106 g/mol by the ‘‘core-first” method using ATRP. All obtained stars have a monomodal and narrow molar-mass distribution (<1.2). The dilute-solution properties of these star polymers were investigated in good solvents (tetrahydrofuran and acetone). Gel permeation chromatography and dynamic and static light scattering were used to measure the hydrodynamic properties including intrinsic viscosity [g], radius of gyration Rg, hydrodynamic radius Rh, second virial coefficient A2 and diffusion coefficient D0. These data were used to establish relationships between these parameters and the molar mass of 4-arm poly(tert-butyl acrylate) stars. The branching parameters g and g0 and the shape factor q were calculated for all obtained star polymers. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Studying the properties of non-linear structures is essential to increase our understanding of the relationship between topology and polymer properties. These properties must also be studied to enable the tailored design of materials to specific applications. Branched structures are well known to have different properties from their linear analogues [1,2]. Star polymers are a special class of branched polymers that have a lower hydrodynamic volume, smaller size and higher segment density than linear polymers of the same molar mass [1,2]. The studies of star polymers with exactly known arm numbers and lengths have been useful to understand how the arm number and length influence the properties of these types of polymers in solution and in the melt. To gain a better understanding of the effect of branching, it is important to investigate simple models and to proceed step by step to more complex structures. Regular stars are the simplest branching architecture, containing f arms of equal molar mass. Such stars have
⇑ Corresponding author. Tel.: +48 32 271 60 70; fax: +48 32 271 29 69. E-mail address: [email protected] (B. Trzebicka). 0014-3057/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2010.09.042
been synthesized since the 1970s using anionic living polymerization to obtain arms followed by reaction with a linking agent to create the star polymer [3,4]. This method has been used to obtain polybutadiene [5,6], poly(ethylene oxide) [7], polyisoprene [8] and polystyrene [3,4,9,10] stars with arm numbers ranging from 3 to ca. 270. Controlled radical polymerization (CRP) such as atom transfer radical polymerization (ATRP) [11–13], nitroxidemediated radical polymerization (NMP) [14], reversible addition-fragmentation chain transfer polymerization (RAFT) [15,16] have been versatile techniques for star polymer synthesis using both the ‘‘arm-first” and ‘‘core-first” methods [17]. CRP methods have many advantages including their ability to be used for many different monomers, their far greater simplicity compared with anionic polymerization, and the far shorter time necessary to prepare star polymers. Star polymers have a more compact structure in solution compared to linear analogues with the same molar mass, leading to smaller sizes and lower viscosities [1,2,17]. This effect becomes more pronounced with increasing arm number [2,17,18]. Similarly to linear polymers, studying the conformational characteristics of star polymers leads to the
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so-called scaling equation relationships between molar mass on the one hand and the radius of gyration, hydrodynamic radius, second virial coefficient, diffusion coefficient and intrinsic viscosity on the other. These relationships are power law type relationships of the form P = KMm where P is the property that depends on molar mass, M is the molar mass, and K and m are constants depending on the polymer–solvent system and on temperature [1,19,20]. When the excluded volume region is reached in a good solvent, in scaling equation of radius of gyration the value of m proposed by Flory is 0.6 [21], whereas renormalization group calculations delivered a more precise value of 0.588 [22]. Scaling equations were established inter alia for polystyrene stars with 3 and 12 arms [35], for poly(ethylene oxide) stars with 4, 8 and 16 arms [7] and for polyisoprene stars with arm numbers from 3 to 18 [8]. Scaling equations for star polymers were determined for properties such as the diffusion coefficient, intrinsic viscosity and radius of gyration [7,8,35]. For non-linear structures the so called branching parameters g and g0 [23,24] are often calculated as well as the shape factor q [19,25,26]. The values of the branching parameters and the factor q are influenced by polymer architecture [18,20,27,28]. To characterize star structures it is important to establish the relationship between these factors and molar mass and the number of arms and to compare the measured values with theoretically predicted values [1,18,28]. In a previous paper [29] we discussed the synthesis and solution properties of poly(tert-butyl acrylate) star polymers with 3, 4, 6, 12 and 16 arms and different arm lengths. The current paper concentrates on the synthesis of 4arm poly(tert-butyl acrylate) star polymers with high molar masses (>105 g/mol) using the core-first method via ATRP. Molar masses, dispersities, radii of gyration and intrinsic viscosity were measured using gel permeation chromatography with refractive index, multiangle laser light scattering and viscosimetric detectors. The properties of these star polymers were characterized using static and dynamic light scattering to measure radii of gyration Rg, hydrodynamic radii Rh, second virial coefficients A2 and diffusion coefficients D0 in a good solvent. The results were used to establish scaling equations for poly(tert-butyl acrylate) star polymers with four arms. The branching parameters g and g0 were calculated and the shape factor q was estimated. All obtained values for the PTBA stars were compared with theoretically and experimentally obtained values for similar polymers.
prior to use. Benzene (pure p.a) was purchased from POCh and was purified by distillation prior to use. DOWEX MARATHON MSC ion exchange resin (Aldrich) was transformed into the H+ type using 1.6 M HNO3.
2. Experimental
2.5. Radical polymerization of tert-butyl acrylate
2.1. Materials
Benzoyl peroxide (BPO) (3.3 mg, 0.01365 mmol), tertbutyl acrylate (1.75 g, 13.65 mmol, 2 mL) and benzene (2 mL) were placed in the reactor equipped with a magnetic stirrer. The mixture was degassed using three freeze-vacuum-thaw cycles. The reactor was placed in an oil bath and held at 60 °C. The reaction was stopped after 15 min. The polymer was precipitated in a methanol/water mixture (1:1) and then dried.
N,N,N0 ,N0 ,N00 -pentamethyldiethylenetriamine (PMDETA, 99%) and copper (I) bromide (CuBr, 99.999%) were purchased from Aldrich and used as received. Benzoyl peroxide (BPO, 97%) was purchased from Fluka and used as received. tert-Butyl acrylate (tBuA, 98%) and anisole (99%) were purchased from Aldrich and purified by distillation
2.2. Synthesis of ditrimethylolpropane tetrakis(2bromopropionate) (Br4DTMP) Ditrimethylolpropane tetrakis(2-bromopropionate) was used as the initiator for atom transfer radical polymerization of tert-butyl acrylate. Synthesis of the ditrimethylolpropane tetrakis(2-bromopropionate) and the confirmation of its structure were performed according to our previous publication [29]. 2.3. Star synthesis via ATRP of tert-butyl acrylate The polymerization was carried out in a reactor equipped with a magnetic stirrer. The Br4DTMP (14 103 g, 1.772 105 mol) was dissolved separately in 4 mL of anisole under nitrogen. CuBr (1.27 103 g, 8.86 106 mol) was placed in a reactor. The dissolved initiator and PMDETA (1.53 103 g, 8.86 106 mol, 1.85 103 mL) were added. The solution was stirred until the Cu complex formed (the solution turned green) and then the tert-butyl acrylate (36.3 g, 0.28 mol, 41.5 mL) was added. The mixture was degassed three times using a high-vacuum technique, left for a night and degassed two more times. The reactor was placed in an oil bath and held at 100 °C. Samples were taken during the polymerization and analyzed without purification using gas chromatography to check the monomer conversion. The rest of the sample was dissolved in THF (40 mL). The solution was passed through a column with a DOWEX-MSC-1 ion exchange resin to remove copper. The polymer was precipitated several times in a methanol/water mixture (1:1) and then dried. 2.4. Selective alkaline hydrolysis of ester bonds between the arms and the core of the stars The star polymer sample (0.3 g) was dissolved in THF (20 mL) in a round-bottom flask fitted with a condenser and a nitrogen inlet. A KOH solution (2 mL, 1 M in ethanol) was added to the flask and the reaction mixture was refluxed at 80 °C for 10 min. The solvent was evaporated without heating under reduced pressure; the remaining polymer was dissolved in THF, precipitated in a methanol/water mixture (1:1) and dried.
B. Mendrek et al. / European Polymer Journal 46 (2010) 2341–2351
2.6. Characterization 2.6.1. Gas chromatography Gas chromatography was used to determine the conversion by measuring the residual monomer content with anisole as the internal standard using a VARIAN 3400 gas chromatograph with a J&W Scientific DB-5 (30 m 0.32 mm) column. 2.6.2. Gel permeation chromatography The GPC systems were used to determine the molar masses, molar-mass distributions and solution viscosities of the obtained polymers. GPC was performed in THF at 35 °C with a nominal flow rate of 1 mL/min using three detectors: a differential refractive index detector Dn2010 RI WGE Dr. Bures, a viscosimetric detector g-2010 WGE Dr. Bures and a multiangle light scattering detector DAWN EOS from Wyatt Technologies. The column set from Polymer Standard Service (PSS) contained four SDV columns: 1 105 Å + 1 103 Å + 2 102 Å. The second GPC system ran in DMF with 5 mM LiBr at 45 °C with a nominal flow rate of 1 mL/min with two detectors: a differential refractive index Dn-2010 RI WGE Dr. Bures and multiangle light scattering DAWN HELEOS from Wyatt Technologies. The column set consisted of PL gel guard, 2 PL gel MIXED-C from Polymer Laboratories and a 1 102 Å PSS GRAM column from PSS. Results were evaluated using the ASTRA software from Wyatt Technologies and the WinGPC Unity software from PSS. All GPC-MALLS data were evaluated using Zimm method from ASTRA software. The previously measured refractive index increment dn/ dc for 4-arm star polymers in THF was used (dn/ dc = 0.0539 mL/g) [29]. Independently, the dn/dc value was measured for 4-arm star polymers with Mn = 822,600 g/mol in acetone (dn/ dc = 0.092 mL/g) and for linear PTBA (Mn = 8700 g/mol) in DMF (dn/dc = 0.031 mL/g). The intrinsic viscosity of the star polymer solution in THF was measured using a viscosimetric detector connected to the GPC system. Measurements were performed at 35 °C. The integral of the measured slice viscosities (gsp)i over concentration (ci) yielded the viscosity of the whole sample [g], called the total intrinsic viscosity:
P ðgsp Þi DV ½g ¼ P c i DV
ð1Þ
2.6.3. Dynamic light scattering (DLS) DLS measurements were performed on a Brookhaven BI-200 goniometer with vertically polarized incident light of wavelength k = 632.8 nm supplied by a He–Ne laser operating at 35 mW and a Brookhaven BI-9000 AT digital auto-correlator. The light scattered by the star polymer solutions in acetone was measured at different concentrations (0.2–3 g/L) at angles h ranging from 30° to 150°. The autocorrelation functions were analyzed using the constrained regularized algorithm CONTIN to obtain the distributions of relaxation times (s). The relaxation rates U = s-1 give the distributions of the apparent diffusion coefficient
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(D = U/q2). Here q is the magnitude of the scattering vector given by q=(4pn/k)sin(h/2) and n is the refractive index of the medium. The mean hydrodynamic radius is obtained by the Stokes–Einstein equation:
Rh ¼ kT=ð6pgD0 Þ
ð2Þ
where k is the Boltzmann constant, g is the solvent viscosity at temperature T in K, and D0 is the diffusion coefficient at an infinite dilution. 2.6.4. Static Light Scattering (SLS) SLS measurements were carried out using the same light scattering setup and the same angle range as DLS measurements. The SLS data were analyzed using the Zimm plot software (BI-ZPW) provided by Brookhaven Instruments. Information on the weight-average molar mass Mw, the radius of gyration Rg, and the second virial coefficient were obtained from the dependence of the quantity Kc/Rh on the concentration c and the scattering angle h. Here the optical constant is defined as:
K ¼ 4p2 n20 ðdn=dcÞ2 =NA k4
ð3Þ
where n0 is the refractive index of acetone, NA is Avogadro’s constant, k is the laser wavelength and dn/dc is the refractive index increment measured using the differential refractive index detector Dn-2010 RI WGE Dr. Bures. The sample solutions used for SLS and DLS measurements were filtered through membrane filters with nominal pore sizes of 0.2 lm just before measurements. Acetone used to prepare the samples was first filtered through membrane filters with a 0.02 lm pore size. 3. Results and discussion 3.1. Synthesis of ditrimethylolpropane tetrakis(2-bromopropionate) (Br4DTMP) The initiator with four initiating centers (Br4DTMP) was obtained by the esterification of the hydroxyl group of ditrimethylolpropane with 2-bromopropionic acid as previously described [29]. The structure of the Br4DTMP was confirmed by 1H NMR and MS(ESI). 3.2. Synthesis of the tert-butyl acrylate star polymers with four arms (PTBA stars) The tetra-functional Br4DTMP was used as the initiator of tert-butyl acrylate for the preparation of stars with long arms via atom transfer radical polymerization (Scheme 1). The star polymers were obtained using the ‘‘core-first” method [2] where functional groups of the core initiate the polymerization of the tert-butyl acrylate monomer. The catalytic system was CuBr/PMDTA (N,N,N0 ,N0 ,N00 -pentamethyldiethylenetriamine). Control over the polymerization of tert-butyl acrylate was ensured by using a molar ratio of [I]:[CuBr]:[PMDTA] of [1]:[0.5]:[0.5]. A high initial monomer to initiator ratio ([M0]/[I0]) of 16,000 was used to obtain stars with long arms and to avoid ‘‘star-star coupling” reactions by the combination of active radical species, which is a significant reaction when most of the
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Scheme 1. Schematic representation of the synthetic route to poly(tert-butyl acrylate) (PTBA) stars with four arms.
monomer is consumed. This corresponds to 4000 mol of monomer per one mol of initiating sites. The reaction was stopped at a relatively low monomer conversion (<41%). The molar masses of the obtained star polymers were measured by GPC equipped with a MALLS detector. GPC measurements indicate an increase in molar mass with increasing monomer conversion (Fig. 1) and demonstrate that no significant star-star coupling occurred. The plot of log([M]0/[M]t) versus time is nearly linear (Fig. 2) indicating that the concentration of the radicals remains constant during polymerization. Table 1 reports the molar masses and the distributions of molar mass of the star polymers determined from GPC with light scattering detection (GPC-MALLS) as well as the theoretical molar masses calculated from monomer conversion. The GPC measurements for all synthesized stars were done both THF and DMF. The theoretical molar masses are in good agreement with the molar masses obtained with the absolute method (GPC-MALLS) (Table 1). The first-order rate of propagation in the kinetic plot (Fig. 2), the good correlation of the theoretical and measured molar masses and the rather low dispersity of the obtained star polymers confirmed the controlled character of the polymerization.
Fig. 2. Monomer consumption versus time in the polymerization of tertbutyl acrylate using Br4DTMP as the initiator.
The presence of the ester links between the core and the arms could be used to estimate the number of star arms [30,31]. These linkages were cleaved under basic conditions. Four of the obtained stars were hydrolyzed in THF using a KOH solution in ethanol in 80 °C for a few minutes. After reaction, the isolated polymers were purified by precipitation and characterized by GPC-MALLS in THF. The ratio of the molar mass before and after hydrolysis yields the number of star arms:
fcalcd ¼ ðMn
star
Mn
core Þ=M n arm
ð4Þ
Table 2 reports results obtained for 4-arm star polymers from Eq. (4) and from GPC-MALLS in THF. The experimentally determined number of arms is close to the assumed number of initiating sites in the macroinitiators (Table 2), indicating that almost all of the 2-bromoester groups initiate the polymerization of tert-butyl acrylate. 3.3. Dilute-solution properties of 4-arm PTBA star polymers
Fig. 1. Chromatograms (RI traces) of the 4-arm stars during polymerization of tert-butyl acrylate using Br4DTMP.
Static and dynamic light scattering were used to measure the radius of gyration, hydrodynamic radius, second virial coefficient and diffusion coefficient of synthesized 4-arm PTBA star polymers with molar masses ranging from 105 to 106 g/mol (Stars from 1 to 5). Those measurements
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B. Mendrek et al. / European Polymer Journal 46 (2010) 2341–2351 Table 1 Synthesis of 4-arm PTBA stars. Sample
Time [h]
Conversion [%]
Mteor.a [g/mol]
Mn GPC-MALLSb [g/mol]
Mw GPC-MALLSb [g/mol]
Mw/Mn
Mn GPC-MALLS [g/mol]
Star Star Star Star Star
24 48 55 75 90
8 17 22 37 41
164,800 349,400 452,000 759,600 840,800
156,000 356,000 440,000 752,000 822,600
166,000 390,000 500,000 850,000 926,000
1.07 1.10 1.13 1.13 1.13
152,000 330,000 480,000 790,000 832,000
1 2 3 4 5
c
Mw GPC-MALLS [g/mol]
c
Mw/Mn
160,000 350,000 500,000 890,000 920,000
1.05 1.06 1.04 1.13 1.10
a M theor: ¼ Mi þ ð½C tBuA 0 =½C i 0 Þ DC tBuA MtBuA Þ where: Mtheor., the theoretical molar mass of the star polymer; Mi, the molar mass of the initiator; [CtBuA]0, the initial molar concentration of tert-butyl acrylate; [Ci]0, the initial molar concentration of the initiator; DCtBuA, the consumption of tert-butyl acrylate; MtBuA, the molar mass of tert-butyl acrylate. b Values obtained in THF with dn/dc = 0.0539 mL/g. c Values obtained in DMF with dn/dc = 0.031 mL/g.
Table 2 The functionality of 4-arm PTBA stars. Sample
Star Star Star Star
Star
2 3 4 5
Arms
Mn [g/mol]
Mw/Mn
Mn [g/mol]
Mw/Mn
356,000 440,000 752,000 822,600
1.10 1.13 1.13 1.13
96,300 119,000 200,700 216,300
1.1 1.1 1.1 1.1
were used to establish the relationships between these parameters and molar mass for 4-arm stars. The above parameters characterize the conformation and behavior of these polymers in dilute solution. SLS and DLS measurements were carried out at 25 °C in acetone, which is a good solvent for poly(tert-butyl acrylate) [32]. In acetone poly(tert-butyl acrylate) also scatters light stronger than in THF, and the light scattering results are more precise. Five samples of 4-arm PTBA stars (Table 3) were measured by static and dynamic light scattering below the critical overlapping concentration (C* = 3Mw/4pRg3NA) in the concentration range from 0.2 to 3 g/L. Zimm plots of stars obtained by static light scattering (SLS) yielded weight-average molar masses, radii of gyration and the second virial coefficient. Fig. 3 shows a typical Zimm plot for Star 5. The values of Mw obtained from the Zimm plots are in good agreement with the values from GPC-MALLS (Table 3). The particle radii increase with the molar mass of the stars. In the case of Star 1, the sizes of the polymer particles were lower than 15 nm and no angular dependence was observed on the Zimm plot. Mw values obtained from Zimm plots were used to construct the scaling equations.
ftheor
fcalcd
4 4 4 4
3.7 3.7 3.7 3.8
from (4)
Fig. 3. Zimm plot of Star 5 in acetone at 25 °C. Experimental points are open symbols, extrapolated points are closed symbols.
GPC-MALLS measurements performed in THF yielded the average radius of gyration of stars in THF. The results
Table 3 Dynamic and static light scattering (DLS, SLS) data for 4-arm PTBA stars in comparison with data obtained from GPC-MALLS. Sample
SLS acetone Mw
Star Star Star Star Star
1 2 3 4 5
Zimm
178,000 376,000 490,000 900,000 930,000
[g/mol]
DLS acetone Rg [nm] – 18.0 20.6 30.0 31.0
A2[mL mol g2] 4
2.90 10 2.17 104 1.76 104 2.02 104 2.06 104
Rh [nm] 7.3 12.0 13.6 17.9 18.8
GPC-MALLS THF D0 [m2s1] 11
9.16 10 5.57 1011 4.86 1011 3.70 1011 3.53 1011
q = Rg/Rh
Mw
– 1.5 1.5 1.7 1.7
166,000 390,000 500,000 850,000 926,000
GPC
[g/mol]
Rg [nm] – 18.8 21.0 29.0 31.5
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presented in Table 3 are very close to those obtained by SLS in acetone. The values of the second virial coefficients A2 obtained from SLS (Table 3) are positive indicates favorable polymer/solvent interactions and good solvent behavior [1,19]. Dynamic light scattering (DLS) was used to measure the hydrodynamic radius Rh and diffusion coefficient D0 (Table 3). The relaxation rates C were measured for five concentrations and different angles from 30° to 150°, yielding Rh and D0. The distribution of hydrodynamic radii of the star polymers in acetone solutions are monomodal and symmetri cal. The intensity distribution obtained for h = 90° (R90 h ) is shown in Fig. 4 for Star 2. For all stars, the distribution of particle sizes is given as l2 is the average value of C and l2 is its second , where C 2 C moment, and ranges from 0.067 to 0.097. These values were obtained based on cumulant analysis. The apparent diffusion coefficients D (from CONTIN algorithm) for each concentration were determined as the slopes of the linear fit of the relaxation rates U versus sin2(h/2) as shown in Fig. 5(a). Then the values of D were plotted against concentration (Fig. 5(b)) and extrapolated to zero concentration (D0 ¼ limc!0 D). The mean hydrodynamic radii were derived from Eq. (2), taking into account the diffusion coefficient D0 obtained as the intercept from Fig. 5(b). The results are reported in Table 3. The dimensionless shape parameter q defined as [25,27]:
q ¼ Rg =Rh
ð5Þ
is often used to describe the structure of macromolecules in solution. The value of q is influenced by the type of structure (sphere, rigid rod, flexible coil) [27], the nature of the solvent [25], the segment density in the polymer
Fig. 4. Distribution of hydrodynamic radii of Star 2 in acetone at 25 °C at 90°.
Fig. 5. (a) Relaxation rate as a function of sin2(h/2) for a 0.468 g/L solution of Star 4, (b) concentration dependence of apparent diffusion coefficients D for Star 4. The dashed lines through the data points are the linear fits.
chain [27] and the dispersity of the system [26,27,33]. Table 3 also reports the q ratios calculated for PTBA 4-arm stars. Different theories predict different q ratio values, and the reasons for the discrepancies are interpreted differently. Park and Chang have discussed this in detail [25]. The literature reports values of the q ratio calculated on the basis of Kirkwood’s approximation [27] for 4-arm stars in h conditions. Theoretical values for stars with uniform arm lengths are 1.333 and with non-uniform lengths is 1.534. There are no theoretically predicted q ratio values for 4-arm stars in a good solvent. For linear polymers, the q ratio is predicted to be 1.78 for a uniform random coil and 2.05 for a non-uniform random coil in good solvents [27]. The experimental q ratio values (Table 3) increase with molar mass from 1.5 to 1.7 for stars with Mw P 390 000 g/mol, reflecting the more compact structure of stars with shorter arms. Huber and others [9] obtained q = 1.33 for 3-arm polystyrene star polymers in a good solvent whereas Strandman [26] reported q 1.5 for
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4-arm PMMA-block-PAA stars in aqueous solutions. In comparison with experimental values obtained for 6arm polystyrene stars (q from 1.16 to 1.45) [34], our q ratio values are higher but have the same tendency of increasing q ratio with arm length. This also confirms that for stars with fixed numbers of arms, the structure changes towards a structure characteristic of a random coil as the molar mass and the excluded volume of the star increase [34]. Fig. 6 presents the double logarithmic plots of the second virial coefficient, diffusion coefficient and both radii (Rg and Rh) as a function of the weight-average molar masses of 4-arm PTBA stars. Scaling equations for poly (tert-butyl acrylate) star polymers with four arms are derived from these graphs. The scaling equation for the second virial coefficient is:
A2 ¼ 7:45 103 M 0:27 w
½mL:mol:g2
ð6Þ
The dependence of logA2 on logMw is shown in Fig 6(a). Flexible linear polymers in good solvent have mA2 values from 0.2 to 0.3 [36,37]. Bauer et al. [8] obtained mA2 ¼ 0:238 for 4-arm polyisoprene stars in cyclohexane. The mA2 value given by our equation 6 for PTBA 4-arm star polymers is mA2 ¼ 0:27, which fits very well with values for other polymers in good solvents. The following relationship was obtained for the diffusion coefficient:
D0 ¼ 7:57 108 M 0:55 w
½m2 :s1
ð7Þ
while the hydrodynamic radius (Rh 1/D0) can be expressed as:
Rh ¼ 9:47 103 M 0:55 w
½nm
ð8Þ
The exponents in the diffusion coefficient scaling equation for the range of star molar masses investigated here is 0.55 (Eq. (7)), what gives 0.55 for the hydrodynamic radius scaling equation (Eq. (8)). Similar results were obtained by Roovers for 4-arm poly(ethylene oxide) stars in methanol (mD = 0.567) [7]. According to theory [21,22,38–40], exponent m in the scaling equation for the sizes (Rg and Rh) should change from 0.5 in a h solvent to 0.6 [21] (0.588 predicted by scaling theories [22,38–40]) in a good solvent and when the excluded volume region is reached. At the asymptotic limit ðM ! 1Þ, mRg ¼ mRh . This asymptotic value is known to be a consequence of chain swelling due to the gradual increase of the intrachain excluded volume [21,40]. It has been revealed [27,38,41] that the radius of gyration reaches the asymptotic limit at smaller values of molar masses than hydrodynamic radius. In most cases, the polymer is not sufficiently flexible and the solvent is not sufficiently good for mRh to reach its asymptotic value in the experimental range of molar masses where mRg is already equal to the predicted value of m. For some polymer/solvent systems, this region is reached when the molar mass is in the range of several million [19]. The linear fit of logRg versus logMw yields the scaling equation for the radius of gyration:
Rg ¼ 7:82 103 M 0:60 w
½nm
ð9Þ
Fig. 6. The dependence of the weight-average molar mass on the second virial coefficient (a), diffusion coefficient (b) and radius of gyration and hydrodynamic radius (c) for the 4-arm PTBA stars in acetone at 25 °C. The lines through the data points represent linear fits to the data.
The value of m in the scaling equation of the radius of gyration (9) is exactly the same as predicted by Flory [21] but slightly higher than the value predicted by scaling theory [22,38–40]. Bauer et al. [8] obtained m values of
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0.546, 0.555 and 0.558 for polyisoprene stars with 8, 12 and 18 arms, respectively, in toluene. Willner et al. [42] investigated polybutadiene and polyisoprene star polymers with f P 8 by small angle neutron scattering (SANS) and obtained values higher than 0.6 (from 0.64 to 0.67). These high values were attributed to the stretched configuration of the arms in these star polymers [42]. mRg values higher than theoretical predictions were also seen for linear polymers with relatively high molar masses in good solvents, for instance, for chitosan in water solution [43] and for polyglicidol in water [19]. The authors explained that this behavior is due to the ellipsoidal shape of the macromolecules [43] or to the high dispersity of the polyglicidol samples[19]. Linear poly(tert-butyl acrylate) was synthesized separately using conventional radical polymerization. It has Mn = 252,000 g/mol, Mw = 743,700 g/mol and a broad molar-mass distribution (Mw/Mn = 2.95, dn/dc = 0.0593 mL/g in THF). The ASTRA software is able to determine the Rg values of polymer fractions with different weight-average molar masses. The linear PTBA has a sufficient dispersity to cover the range of molar masses studied here. The Rg values for linear chains in THF, obtained using Zimm method from ASTRA software, are placed in Fig. 7 as open circles. The same method was used to calculate Rg of stars (Fig. 7 closed circles). The GPC-MALLS measurements of linear PTBA and PTBA stars enabled the calculation of scaling parameters in THF at 35 °C (Fig. 7). The linear fits for both polymers shown in Fig. 7 yielded the following equations:
value of 0.59 for PTBA stars in THF. This value of mRg is the same as the value obtained by fitting the results from GPC-MALLS. 3.4. Branching parameters of 4-arm star polymers The intrinsic viscosity of the synthesized stars was measured using a viscosimetric detector connected on-line to the GPC system in THF solutions at 35 °C. Integrating the measured slice viscosities (gsp)i over concentration yields the total intrinsic viscosity of the sample [g] (see Eq. (1)). Intrinsic viscosity measurements were performed for linear PTBA standards to compare them with those obtained for stars and to determine the branching parameter g0 . As shown in our previous paper [29], the linear fit of experimental values of log[g] versus logMw shown in Fig. 8 yields the Kuhn-Mark-Houwink-Sakurada equation for linear PTBA in THF at 35 °C:
½g ¼ 4:2 103 M0:78 w
ð12Þ 3
The exponents mRg have the same value for linear as for star polymers and are in agreement with values predicted by scaling theory [22,38–40]. The known relationship between the exponent a from the Kuhn-Mark-HouwinkSakurada equation and mRg , a ¼ ð3mRg 1Þ [38], gives a mRg
The obtained values of K = 4.2 10 and a = 0.78 are consistent with those for linear PTBA measured by Mrkvickova et al. in THF at 25 °C [44]. Fig. 8 presents the intrinsic viscosities of the 4-arm PTBA stars discussed in this paper and those described previously [29]. The intrinsic viscosities of the stars are lower than those of the linear analogues, and the viscosities increase linearly with the arm length, parallel to the graph of linear PTBA. Parallel or nearly parallel lines on the logarithmic plot of intrinsic viscosity versus weight-average molar mass were also observed for poly(ethylene oxide) [7], polybutadiene [5,6], polyisoprene [8,45] and polystyrene [3,4,30,35] star polymers with different functionalities in good solvent. Fitting all of the star polymer points in Fig. 8 to a linear function gave the value of the exponent a in the KuhnMark-Houwink-Sakurada of 0.78. Branching parameters are often calculated to characterize branched structures. Zimm and Stockmayer defined the
Fig. 7. Radius of gyration versus the weight-average molar mass for the 4-arm PTBA stars and linear PTBA obtained by GPC-MALLS.
Fig. 8. Log–log plot of intrinsic viscosities versus the weight-average molar mass for 4-arm PTBA stars and linear PTBA.
RgðLinÞ ¼ 1:18 102 M 0:59 w
ð10Þ
RgðStarÞ ¼ 8:77 103 M0:59 w
ð11Þ
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branching parameter g0 [23] as the ratio of the intrinsic viscosities of branched and linear polymers of the same molar mass (Eq. (13)). The same authors also defined the branching parameter g [23] as the ratio of the mean square radius of gyration of branched and linear polymers of the same molar mass (Eq. (14)). According to this definition, the factor g can only be determined when the radius of gyration is measurable.
g0 ¼
½gbranched ½glinear at
R2gbranched g¼ 2 Rg linear
ð13Þ the same M
ð14Þ at the same M
The measured intrinsic viscosities of stars and those calculated for linear chains of the same molar mass were used to obtain the g0 parameter. The results are collected in Table 4. The same table contains g0 values calculated based on the relationship derived by Zimm and Kilb [24] (Eq. (15)), Roovers [28] (Eq. (16)) and Douglas and Freed [46] (Eq. (17)).
g 0ZK ¼
ð2=f Þ1:5 ½0:396ðf 1Þ þ 0:196 0:586
ð15Þ
log g 0 ¼ 0:36 0:8 log f
ð16Þ
" 0:58 # 3f 2 1 0:276 0:015ðf 1Þ g ¼ 2 f 1 0:276 0
ð17Þ
The Zimm and Kilb Eq. (15) gives g0 equal to 0.83, but this prediction is limited to a h solvent. No theoretical value of g0 (or g) is proposed for stars in a good solvent. Roovers [28] and Douglas and Freed [46] proposed empirical relations (Eqs. (16 and 17), respectively) correlating g0 with the number of arms in good solvents. The average of all values of g0 obtained for 4-arm PTBA stars is equal to 0.754, which is very close to the value calculated from empirical dependence derived by Roovers (Eq. (16)) (0.756) and is lower than that calculated from the Zimm and Kilb equation for h conditions (0.83). A similar result was observed for other star polymers in good solvents [18,28,33]. 4-arm PTBA stars with long arms (Stars 1 to 5 from Table 3) have values of g0 (Table 4) that are in good correlation with results obtained by Hirao [47] for stars with four poly(methyl methacrylate) arms (g0 = 0.77 in THF) and Hwang [48] for polybutadiene 4-arm stars (g0 between 0.75–0.76 in toluene). Angot [30] reported even higher g0 values for 4-arm polystyrene stars in toluene close to 0.85. Rglin was measured for each slice of chromatographic separation by GPC using ASTRA software as shown in Table 4 Experimental values of g0 for 4-arm PTBA stars in THF. Sample
Mw
Star Star Star Star Star
166,000 390,000 500,000 850,000 926,000
1 2 3 4 5
GPC–MALLS
[g/mol]
g0 0.76 0.76 0.76 0.75 0.74
Table 5 Experimental values of the radius of gyration of stars and their linear analogues and parameter g for 4-arm PTBA stars in THF.
a b
Sample
Mw GPC-MALLSa [g/mol]
Rg_starb
Rg_lin.b
g
Star Star Star Star
390,000 500,000 850,000 926,000
18.8 21.0 29.0 31.5
26.4 29.6 37.7 40.0
0.51 0.50 0.59 0.62
2 3 4 5
dn/dc = 0,0539 mL/g (THF) From Zimm plot
Fig. 7. The Rg of PTBA stars (except for Star 1) and their R2g could be obbranching parameter g ¼ Rbranched 2 g linear
at the same M
tained. All results are shown in Table 5. Zimm and Stockmayer [23] predicted the branching parameter g for a star with f equal arms (h condition):
g ZS ¼
3f 2 f2
ð18Þ
The branching parameter gZS calculated from Eq. (18) for 4-arm stars is equal to 0.625. Douglas and Freed [49] used renormalization group calculation to predict g for star polymers in good solvents. Performing this calculation for 4-arm stars in good solvent conditions gives a g value of 0.631 [49]. The average value obtained here for 4-arm PTBA stars is gav = 0.555 and is lower than calculated by Douglas and Freed [49]. The experimental values of branching parameter reported for four arm stars in good solvent ranging from 0.56 for polystyrene stars in toluene to 0.72 for polybutadiene stars in cyclohexane [46]. 4. Conclusions A synthetic approach based on ATRP was used to obtain 4-arm PTBA star polymers with high molar masses and low molar mass dispersities not exceeding 1.13. The process was well controlled, with molar masses increasing with conversion in good agreement with theoretical calculations from monomer conversion. Polymerization was stopped before the star-star coupling reaction could occur. The well-defined structure was proven by alkaline hydrolysis, and almost all initiating groups were involved in the polymerization. The solution behavior of the obtained star polymers was investigated by static and dynamic light scattering and by GPC with three detectors. The SLS and DLS measurements in acetone at 25 °C delivered weight-average molar masses, sizes (Rg and Rh), diffusion coefficients (D0) and second virial coefficients (A2). The measured values were used to establish scaling equations between these parameters and molar mass. The values of the exponents in the scaling equations for A2, D0 and Rh indicated that the asymptotic excluded volume limit for 4-arm stars in acetone has not been reached. The exponent in the Rg scaling equation fit with the value predicted by Flory. The observations demonstrate that the radius of gyration reaches the asymptotic value faster than hydrodynamic radius. The
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values of m for the obtained stars and their linear analogues in THF were determined from the logarithmic dependence of Rg versus weight-average molar mass, and these values are consistent with those predicted by scaling theory for the excluded volume region. The values of the shape parameter q increase from 1.5 to 1.7 with the molar mass of the star, indicating that the conformation of the obtained stars in acetone resemble a coil more than a sphere. The intrinsic viscosities measured for star polymers and linear poly(tert-butyl acrylates)in THF indicated the scaling parameters of the Kuhn-Mark-Houwink-Sakurada equations. The intrinsic viscosities of the 4-arm star polymers are lower than those of the analogous linear polymers with the same molar mass. The exponents have the same values for star polymers as for their linear counterparts. The average branching ratio g0 is in good agreement with the predicted values for star polymers in good solvents. The values of branching parameters g in THF calculated for 4-arm stars proved their non-linear structure. Acknowledgements This work was supported by Polish Ministry of Science and Higher Education grant NN 204 153136. The authors wish to thank Prof. Walter Burchard (University of Freiburg) for the stimulative and helpful discussion. References [1] Burchard W. Solution properties of branched macromolecules. Adv Polym Sci 1999;143:113–94. [2] Mishra MK, Kobayashi S, editors. Star and hyperbranched polymers. New York, Basel: Marcel Dekker, Inc.; 1999. [3] Roovers J, Bywater S. Preparation and characterization of fourbranched star polystyrene. Macromolecules 1972;5:384–8. [4] Roovers J, Bywater S. Preparation of six-branched star polystyrene. Thermodynamic and hydrodynamic properties of four and sixbranched star polystyrenes. Macromolecules 1974;4:443–9. [5] Roovers J, Zhou LL, Van der Zwan M, Iatrou H, Hadjichristidis N, Toporowski PM. Regular star polymers with 64 and 128 arms. Models for polymeric micelles. Macromolecules 1993;26:4324–31. [6] Roovers J, Toporowski P, Martin J. Synthesis and characterization of multiarm star polybutadienes. Macromolecules 1989;22:1897–903. [7] Comanita B, Noren B, Roovers J. Star poly(ethylene oxide)s from carbosilane dendrimers. Macromolecules 1999;32:1069–72. [8] Bauer BJ, Fetters LJ, Graessley WW, Hadjichristidis N, Quack GF. Chain dimension in dilute polymer solutions: a light-scattering and viscometric study of multiarmed polyisoprene stars in good and h solvents. Macromolecules 1989;22:2337–47. [9] Huber K, Burchard W, Fetters LJ. Dynamic light scattering from regular star-branched molecules. Macromolecules 1984;17:541–8. [10] Roovers J, Hadjichristidis N, Fetters LJ. Analysis and dilute solution properties of 12- and 18-arm-star polystyrenes. Macromolecules 1983;16:214–20. [11] Matyjaszewski K, Xia J. Atom transfer polymerization. Chem Rev 2001;101:2921–90. [12] Tsarevsky NV, Matyjaszewski K. ‘‘Green” atom transfer radical polymerization: from process design to preparation of welldefined environmentally friendly polymeric materials. Chem Rev 2007;107:2270–99. [13] Braunecker WA, Matyjaszewski K. Controlled/living radical polymerization: features, developments, and perspectives. Prog Polym Sci 2007;32:93–146. [14] Hawker CJ, Bosman AW, Harth E. New polymer synthesis by nitroxide mediated living radical polymerizations. Chem Rev 2001;101:3661–88.
[15] Colombani D. Driving forces in free radical addition–fragmentation processes. Prog Polym Sci 1999;24:425–80. [16] Lowe AB, McCormick CL. Reversible addition–fragmentation chain transfer (RAFT) radical polymerization and the synthesis of watersoluble (co)polymers under homogeneous conditions in organic and aqueous media. Prog Polym Sci 2007;32:283–351. [17] Hadjichristidis N, Pitsikalis M, Iatrou H. In: Matyjaszewski K, Gnanou Y, Leibler L, editors. Macromolecular Engineering, vol. 2. Weinheim, Germany: Wiley-VCH; 2007. p. 909–72. [18] Grest S, Fetters L, Huang JS, Richter D. Star polymers: experiment, theory and simulation. Adv Chem Phys 1996;XCIV:67–163. [19] Rangelov S, Trzebicka B, Jamóz-Piegza M, Dworak A. Hydrodynamic behavior of high molar mass linear polyglycidol in dilute aqueous solution. J Phys Chem.B 2007;111:11127–33. [20] Bercea M, Ioan C, Ioan S, Simionescu BC, Simionescu CI. Ultrahigh molecular weight polymers in dilute solutions. Prog Polym Sci 1999;24:379–424. [21] Flory PJ. Principles of polymer chemistry. New York, Ithaca: Cornell University Press; 1953. [22] Le Guillou J, Zinn-Justin J. Critical exponents for the n-vector model in three dimensions from field theory. Phys Rev Lett 1977;39:95–8. [23] Zimm BH, Stockmayer WH. The dimensions of chain molecules containing branches and rings. J Chem Phys 1949;17:1301–14. [24] Zimm BH, Kilb RW. Dynamiccs of branched polymer molecules in dilute solution. J Polym Sci 1959;37:19–42. [25] Park S, Chang T, Park ICH. Static and hydrodynamic size of polystyrene coils in various solvents. Macromolecules 1991;24:5729–31. [26] Stradman S, Hietala S, Aseyev V, Koli B, Butcher SJ, Tenhu H. Supramolecular assemblies of amphiphylic PMMA-block-PAA stars in aqueous solutions. Polymer 2006;47:6524–35. [27] Burchard W. In: Borsali R, Pecora R, editors. Soft-matter characterization. Berlin-Heidelberg: Springer; 2008. p. 465–603. [28] Roovers J. In: Mishra MK, Kobayashi S, editors. Star and hyperbranched polymers. New York, Basel: Marcel Dekker Inc.; 1999. p. 285–341. [29] Mendrek B, Trzebicka B. Synthesis and characterization of welldefined poly(tert-butyl acrylate) star polymers. Eur Polym J 2009;45:1979–93. [30] Angot S, Murthy KS, Taton D, Gnanou Y. Scope of copper halide/ bipyridyl system associated with calixarene-based multihalides for synthesis of well-defined polystyrene and poly(meth)acrylate stars. Macromolecules 2000;33:7261–74. [31] Stradman S, Tenhu H. Star polymers synthesised with flexible resorcinarene-derived ATRP initiators. Polymer 2007;48:3938–51. [32] Jerome R, Desreux V. Hydrodynamic properties and unperturbed dimensions of poly(tert-butyl acrylate) in different solvents. Eur Polym J 1970;6:411–21. [33] Burchard W. Static and dynamic light scattering from branched polymers and biopolymers. Adv Polym Sci 1983;48:1–124. [34] Weber V, Duval M, Ederle Y, Mathis C. Physico-chemical behavior in solution of star-shaped polystyrene with a C60 core. Carbon 1998;36(5, 6):839–42. [35] Khasat N, Pennisi RW, Hadjichristidis N, Fetters LJ. Dilute solution behavior of asymmetric three-arm and regular three- and twelvearm polystyrene stars. Macromolecules 1988;21:1100–6. [36] Fujita H. Some unsolved problems on dilute polymer solutions. Macromolecules 1988;21:179–85. [37] Fujita H, Norisuye T. Molecular weight dependence of the second virial coefficient for linear flexible polymers in good solvents. Macromolecules 1985;18:1637–8. [38] Weill G, des Cloizeaux J. Dynamics of polymers in dilute solutions: an explanation of anomalous indices by cross-over effect. J Phys (Paris) 1979;40:99–105. [39] deGennes PG. Scaling concepts in polymer physics. NewYork, Ithaca: Cornell University Press; 1979. [40] Yamakawa H. Modern theory of polymer solutions. New York: Harper&Row, Publishers Inc.; 1971. [41] Adam M, Delsanti M. Light scattering by dilute solution of polystyrene in good solvent. J Phys (Paris) 1976;37:1045–9. [42] Willner L, Jucknischke O, Richter D, Roovers J, Zhou L-L, Toporowski PM, et al. Structural investigation of star polymers in solution by small angle neutron scattering. Macromolecules 1994;27:3821–9. [43] Cölfen H, Berth G, Dautzenberg H. Hydrodynamic studies on chitosans in aqueous solution. Carbohydrate Polymers 2001;45:373–83. [44] Mrkvickova L, Danhelka J. Characterization of poly(tert-butyl acrylate) by SEC. J Appl Polym Sci 1990;41:1929–31. [45] Hadjichristidis N, Roovers J. Synthesis and solution properties of linear, four-branched, and six-branched star polyisoprenes. J Poly Sci, Polym Phys Ed 1974;12:2521–33.
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Contents lists available at ScienceDirect
European Polymer Journal journal homepage: www.elsevier.com/locate/europolj
Solution behavior of 4-arm poly(tert-butyl acrylate) star polymers Barbara Mendrek a,b, Barbara Trzebicka a,⇑, Wojciech Wałach a, Andrzej Dworak a,b a b
Centre of Polymer and Carbon Materials, Polish Academy of Sciences, M. Curie-Skłodowskiej 34, 41-819 Zabrze, Poland University of Opole, Faculty of Chemistry, Oleska 48, 45-052 Opole, Poland
a r t i c l e
i n f o
Article history: Received 14 June 2010 Received in revised form 14 September 2010 Accepted 30 September 2010 Available online 8 October 2010 Keywords: Star polymers Poly(tert-butyl acrylate) Intrinsic viscosity Branching parameters q Ratio
a b s t r a c t This paper reports the synthesis of 4-arm poly(tert-butyl acrylate) stars of different molar masses up to 106 g/mol by the ‘‘core-first” method using ATRP. All obtained stars have a monomodal and narrow molar-mass distribution (<1.2). The dilute-solution properties of these star polymers were investigated in good solvents (tetrahydrofuran and acetone). Gel permeation chromatography and dynamic and static light scattering were used to measure the hydrodynamic properties including intrinsic viscosity [g], radius of gyration Rg, hydrodynamic radius Rh, second virial coefficient A2 and diffusion coefficient D0. These data were used to establish relationships between these parameters and the molar mass of 4-arm poly(tert-butyl acrylate) stars. The branching parameters g and g0 and the shape factor q were calculated for all obtained star polymers. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Studying the properties of non-linear structures is essential to increase our understanding of the relationship between topology and polymer properties. These properties must also be studied to enable the tailored design of materials to specific applications. Branched structures are well known to have different properties from their linear analogues [1,2]. Star polymers are a special class of branched polymers that have a lower hydrodynamic volume, smaller size and higher segment density than linear polymers of the same molar mass [1,2]. The studies of star polymers with exactly known arm numbers and lengths have been useful to understand how the arm number and length influence the properties of these types of polymers in solution and in the melt. To gain a better understanding of the effect of branching, it is important to investigate simple models and to proceed step by step to more complex structures. Regular stars are the simplest branching architecture, containing f arms of equal molar mass. Such stars have
⇑ Corresponding author. Tel.: +48 32 271 60 70; fax: +48 32 271 29 69. E-mail address: [email protected] (B. Trzebicka). 0014-3057/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2010.09.042
been synthesized since the 1970s using anionic living polymerization to obtain arms followed by reaction with a linking agent to create the star polymer [3,4]. This method has been used to obtain polybutadiene [5,6], poly(ethylene oxide) [7], polyisoprene [8] and polystyrene [3,4,9,10] stars with arm numbers ranging from 3 to ca. 270. Controlled radical polymerization (CRP) such as atom transfer radical polymerization (ATRP) [11–13], nitroxidemediated radical polymerization (NMP) [14], reversible addition-fragmentation chain transfer polymerization (RAFT) [15,16] have been versatile techniques for star polymer synthesis using both the ‘‘arm-first” and ‘‘core-first” methods [17]. CRP methods have many advantages including their ability to be used for many different monomers, their far greater simplicity compared with anionic polymerization, and the far shorter time necessary to prepare star polymers. Star polymers have a more compact structure in solution compared to linear analogues with the same molar mass, leading to smaller sizes and lower viscosities [1,2,17]. This effect becomes more pronounced with increasing arm number [2,17,18]. Similarly to linear polymers, studying the conformational characteristics of star polymers leads to the
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so-called scaling equation relationships between molar mass on the one hand and the radius of gyration, hydrodynamic radius, second virial coefficient, diffusion coefficient and intrinsic viscosity on the other. These relationships are power law type relationships of the form P = KMm where P is the property that depends on molar mass, M is the molar mass, and K and m are constants depending on the polymer–solvent system and on temperature [1,19,20]. When the excluded volume region is reached in a good solvent, in scaling equation of radius of gyration the value of m proposed by Flory is 0.6 [21], whereas renormalization group calculations delivered a more precise value of 0.588 [22]. Scaling equations were established inter alia for polystyrene stars with 3 and 12 arms [35], for poly(ethylene oxide) stars with 4, 8 and 16 arms [7] and for polyisoprene stars with arm numbers from 3 to 18 [8]. Scaling equations for star polymers were determined for properties such as the diffusion coefficient, intrinsic viscosity and radius of gyration [7,8,35]. For non-linear structures the so called branching parameters g and g0 [23,24] are often calculated as well as the shape factor q [19,25,26]. The values of the branching parameters and the factor q are influenced by polymer architecture [18,20,27,28]. To characterize star structures it is important to establish the relationship between these factors and molar mass and the number of arms and to compare the measured values with theoretically predicted values [1,18,28]. In a previous paper [29] we discussed the synthesis and solution properties of poly(tert-butyl acrylate) star polymers with 3, 4, 6, 12 and 16 arms and different arm lengths. The current paper concentrates on the synthesis of 4arm poly(tert-butyl acrylate) star polymers with high molar masses (>105 g/mol) using the core-first method via ATRP. Molar masses, dispersities, radii of gyration and intrinsic viscosity were measured using gel permeation chromatography with refractive index, multiangle laser light scattering and viscosimetric detectors. The properties of these star polymers were characterized using static and dynamic light scattering to measure radii of gyration Rg, hydrodynamic radii Rh, second virial coefficients A2 and diffusion coefficients D0 in a good solvent. The results were used to establish scaling equations for poly(tert-butyl acrylate) star polymers with four arms. The branching parameters g and g0 were calculated and the shape factor q was estimated. All obtained values for the PTBA stars were compared with theoretically and experimentally obtained values for similar polymers.
prior to use. Benzene (pure p.a) was purchased from POCh and was purified by distillation prior to use. DOWEX MARATHON MSC ion exchange resin (Aldrich) was transformed into the H+ type using 1.6 M HNO3.
2. Experimental
2.5. Radical polymerization of tert-butyl acrylate
2.1. Materials
Benzoyl peroxide (BPO) (3.3 mg, 0.01365 mmol), tertbutyl acrylate (1.75 g, 13.65 mmol, 2 mL) and benzene (2 mL) were placed in the reactor equipped with a magnetic stirrer. The mixture was degassed using three freeze-vacuum-thaw cycles. The reactor was placed in an oil bath and held at 60 °C. The reaction was stopped after 15 min. The polymer was precipitated in a methanol/water mixture (1:1) and then dried.
N,N,N0 ,N0 ,N00 -pentamethyldiethylenetriamine (PMDETA, 99%) and copper (I) bromide (CuBr, 99.999%) were purchased from Aldrich and used as received. Benzoyl peroxide (BPO, 97%) was purchased from Fluka and used as received. tert-Butyl acrylate (tBuA, 98%) and anisole (99%) were purchased from Aldrich and purified by distillation
2.2. Synthesis of ditrimethylolpropane tetrakis(2bromopropionate) (Br4DTMP) Ditrimethylolpropane tetrakis(2-bromopropionate) was used as the initiator for atom transfer radical polymerization of tert-butyl acrylate. Synthesis of the ditrimethylolpropane tetrakis(2-bromopropionate) and the confirmation of its structure were performed according to our previous publication [29]. 2.3. Star synthesis via ATRP of tert-butyl acrylate The polymerization was carried out in a reactor equipped with a magnetic stirrer. The Br4DTMP (14 103 g, 1.772 105 mol) was dissolved separately in 4 mL of anisole under nitrogen. CuBr (1.27 103 g, 8.86 106 mol) was placed in a reactor. The dissolved initiator and PMDETA (1.53 103 g, 8.86 106 mol, 1.85 103 mL) were added. The solution was stirred until the Cu complex formed (the solution turned green) and then the tert-butyl acrylate (36.3 g, 0.28 mol, 41.5 mL) was added. The mixture was degassed three times using a high-vacuum technique, left for a night and degassed two more times. The reactor was placed in an oil bath and held at 100 °C. Samples were taken during the polymerization and analyzed without purification using gas chromatography to check the monomer conversion. The rest of the sample was dissolved in THF (40 mL). The solution was passed through a column with a DOWEX-MSC-1 ion exchange resin to remove copper. The polymer was precipitated several times in a methanol/water mixture (1:1) and then dried. 2.4. Selective alkaline hydrolysis of ester bonds between the arms and the core of the stars The star polymer sample (0.3 g) was dissolved in THF (20 mL) in a round-bottom flask fitted with a condenser and a nitrogen inlet. A KOH solution (2 mL, 1 M in ethanol) was added to the flask and the reaction mixture was refluxed at 80 °C for 10 min. The solvent was evaporated without heating under reduced pressure; the remaining polymer was dissolved in THF, precipitated in a methanol/water mixture (1:1) and dried.
B. Mendrek et al. / European Polymer Journal 46 (2010) 2341–2351
2.6. Characterization 2.6.1. Gas chromatography Gas chromatography was used to determine the conversion by measuring the residual monomer content with anisole as the internal standard using a VARIAN 3400 gas chromatograph with a J&W Scientific DB-5 (30 m 0.32 mm) column. 2.6.2. Gel permeation chromatography The GPC systems were used to determine the molar masses, molar-mass distributions and solution viscosities of the obtained polymers. GPC was performed in THF at 35 °C with a nominal flow rate of 1 mL/min using three detectors: a differential refractive index detector Dn2010 RI WGE Dr. Bures, a viscosimetric detector g-2010 WGE Dr. Bures and a multiangle light scattering detector DAWN EOS from Wyatt Technologies. The column set from Polymer Standard Service (PSS) contained four SDV columns: 1 105 Å + 1 103 Å + 2 102 Å. The second GPC system ran in DMF with 5 mM LiBr at 45 °C with a nominal flow rate of 1 mL/min with two detectors: a differential refractive index Dn-2010 RI WGE Dr. Bures and multiangle light scattering DAWN HELEOS from Wyatt Technologies. The column set consisted of PL gel guard, 2 PL gel MIXED-C from Polymer Laboratories and a 1 102 Å PSS GRAM column from PSS. Results were evaluated using the ASTRA software from Wyatt Technologies and the WinGPC Unity software from PSS. All GPC-MALLS data were evaluated using Zimm method from ASTRA software. The previously measured refractive index increment dn/ dc for 4-arm star polymers in THF was used (dn/ dc = 0.0539 mL/g) [29]. Independently, the dn/dc value was measured for 4-arm star polymers with Mn = 822,600 g/mol in acetone (dn/ dc = 0.092 mL/g) and for linear PTBA (Mn = 8700 g/mol) in DMF (dn/dc = 0.031 mL/g). The intrinsic viscosity of the star polymer solution in THF was measured using a viscosimetric detector connected to the GPC system. Measurements were performed at 35 °C. The integral of the measured slice viscosities (gsp)i over concentration (ci) yielded the viscosity of the whole sample [g], called the total intrinsic viscosity:
P ðgsp Þi DV ½g ¼ P c i DV
ð1Þ
2.6.3. Dynamic light scattering (DLS) DLS measurements were performed on a Brookhaven BI-200 goniometer with vertically polarized incident light of wavelength k = 632.8 nm supplied by a He–Ne laser operating at 35 mW and a Brookhaven BI-9000 AT digital auto-correlator. The light scattered by the star polymer solutions in acetone was measured at different concentrations (0.2–3 g/L) at angles h ranging from 30° to 150°. The autocorrelation functions were analyzed using the constrained regularized algorithm CONTIN to obtain the distributions of relaxation times (s). The relaxation rates U = s-1 give the distributions of the apparent diffusion coefficient
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(D = U/q2). Here q is the magnitude of the scattering vector given by q=(4pn/k)sin(h/2) and n is the refractive index of the medium. The mean hydrodynamic radius is obtained by the Stokes–Einstein equation:
Rh ¼ kT=ð6pgD0 Þ
ð2Þ
where k is the Boltzmann constant, g is the solvent viscosity at temperature T in K, and D0 is the diffusion coefficient at an infinite dilution. 2.6.4. Static Light Scattering (SLS) SLS measurements were carried out using the same light scattering setup and the same angle range as DLS measurements. The SLS data were analyzed using the Zimm plot software (BI-ZPW) provided by Brookhaven Instruments. Information on the weight-average molar mass Mw, the radius of gyration Rg, and the second virial coefficient were obtained from the dependence of the quantity Kc/Rh on the concentration c and the scattering angle h. Here the optical constant is defined as:
K ¼ 4p2 n20 ðdn=dcÞ2 =NA k4
ð3Þ
where n0 is the refractive index of acetone, NA is Avogadro’s constant, k is the laser wavelength and dn/dc is the refractive index increment measured using the differential refractive index detector Dn-2010 RI WGE Dr. Bures. The sample solutions used for SLS and DLS measurements were filtered through membrane filters with nominal pore sizes of 0.2 lm just before measurements. Acetone used to prepare the samples was first filtered through membrane filters with a 0.02 lm pore size. 3. Results and discussion 3.1. Synthesis of ditrimethylolpropane tetrakis(2-bromopropionate) (Br4DTMP) The initiator with four initiating centers (Br4DTMP) was obtained by the esterification of the hydroxyl group of ditrimethylolpropane with 2-bromopropionic acid as previously described [29]. The structure of the Br4DTMP was confirmed by 1H NMR and MS(ESI). 3.2. Synthesis of the tert-butyl acrylate star polymers with four arms (PTBA stars) The tetra-functional Br4DTMP was used as the initiator of tert-butyl acrylate for the preparation of stars with long arms via atom transfer radical polymerization (Scheme 1). The star polymers were obtained using the ‘‘core-first” method [2] where functional groups of the core initiate the polymerization of the tert-butyl acrylate monomer. The catalytic system was CuBr/PMDTA (N,N,N0 ,N0 ,N00 -pentamethyldiethylenetriamine). Control over the polymerization of tert-butyl acrylate was ensured by using a molar ratio of [I]:[CuBr]:[PMDTA] of [1]:[0.5]:[0.5]. A high initial monomer to initiator ratio ([M0]/[I0]) of 16,000 was used to obtain stars with long arms and to avoid ‘‘star-star coupling” reactions by the combination of active radical species, which is a significant reaction when most of the
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Scheme 1. Schematic representation of the synthetic route to poly(tert-butyl acrylate) (PTBA) stars with four arms.
monomer is consumed. This corresponds to 4000 mol of monomer per one mol of initiating sites. The reaction was stopped at a relatively low monomer conversion (<41%). The molar masses of the obtained star polymers were measured by GPC equipped with a MALLS detector. GPC measurements indicate an increase in molar mass with increasing monomer conversion (Fig. 1) and demonstrate that no significant star-star coupling occurred. The plot of log([M]0/[M]t) versus time is nearly linear (Fig. 2) indicating that the concentration of the radicals remains constant during polymerization. Table 1 reports the molar masses and the distributions of molar mass of the star polymers determined from GPC with light scattering detection (GPC-MALLS) as well as the theoretical molar masses calculated from monomer conversion. The GPC measurements for all synthesized stars were done both THF and DMF. The theoretical molar masses are in good agreement with the molar masses obtained with the absolute method (GPC-MALLS) (Table 1). The first-order rate of propagation in the kinetic plot (Fig. 2), the good correlation of the theoretical and measured molar masses and the rather low dispersity of the obtained star polymers confirmed the controlled character of the polymerization.
Fig. 2. Monomer consumption versus time in the polymerization of tertbutyl acrylate using Br4DTMP as the initiator.
The presence of the ester links between the core and the arms could be used to estimate the number of star arms [30,31]. These linkages were cleaved under basic conditions. Four of the obtained stars were hydrolyzed in THF using a KOH solution in ethanol in 80 °C for a few minutes. After reaction, the isolated polymers were purified by precipitation and characterized by GPC-MALLS in THF. The ratio of the molar mass before and after hydrolysis yields the number of star arms:
fcalcd ¼ ðMn
star
Mn
core Þ=M n arm
ð4Þ
Table 2 reports results obtained for 4-arm star polymers from Eq. (4) and from GPC-MALLS in THF. The experimentally determined number of arms is close to the assumed number of initiating sites in the macroinitiators (Table 2), indicating that almost all of the 2-bromoester groups initiate the polymerization of tert-butyl acrylate. 3.3. Dilute-solution properties of 4-arm PTBA star polymers
Fig. 1. Chromatograms (RI traces) of the 4-arm stars during polymerization of tert-butyl acrylate using Br4DTMP.
Static and dynamic light scattering were used to measure the radius of gyration, hydrodynamic radius, second virial coefficient and diffusion coefficient of synthesized 4-arm PTBA star polymers with molar masses ranging from 105 to 106 g/mol (Stars from 1 to 5). Those measurements
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B. Mendrek et al. / European Polymer Journal 46 (2010) 2341–2351 Table 1 Synthesis of 4-arm PTBA stars. Sample
Time [h]
Conversion [%]
Mteor.a [g/mol]
Mn GPC-MALLSb [g/mol]
Mw GPC-MALLSb [g/mol]
Mw/Mn
Mn GPC-MALLS [g/mol]
Star Star Star Star Star
24 48 55 75 90
8 17 22 37 41
164,800 349,400 452,000 759,600 840,800
156,000 356,000 440,000 752,000 822,600
166,000 390,000 500,000 850,000 926,000
1.07 1.10 1.13 1.13 1.13
152,000 330,000 480,000 790,000 832,000
1 2 3 4 5
c
Mw GPC-MALLS [g/mol]
c
Mw/Mn
160,000 350,000 500,000 890,000 920,000
1.05 1.06 1.04 1.13 1.10
a M theor: ¼ Mi þ ð½C tBuA 0 =½C i 0 Þ DC tBuA MtBuA Þ where: Mtheor., the theoretical molar mass of the star polymer; Mi, the molar mass of the initiator; [CtBuA]0, the initial molar concentration of tert-butyl acrylate; [Ci]0, the initial molar concentration of the initiator; DCtBuA, the consumption of tert-butyl acrylate; MtBuA, the molar mass of tert-butyl acrylate. b Values obtained in THF with dn/dc = 0.0539 mL/g. c Values obtained in DMF with dn/dc = 0.031 mL/g.
Table 2 The functionality of 4-arm PTBA stars. Sample
Star Star Star Star
Star
2 3 4 5
Arms
Mn [g/mol]
Mw/Mn
Mn [g/mol]
Mw/Mn
356,000 440,000 752,000 822,600
1.10 1.13 1.13 1.13
96,300 119,000 200,700 216,300
1.1 1.1 1.1 1.1
were used to establish the relationships between these parameters and molar mass for 4-arm stars. The above parameters characterize the conformation and behavior of these polymers in dilute solution. SLS and DLS measurements were carried out at 25 °C in acetone, which is a good solvent for poly(tert-butyl acrylate) [32]. In acetone poly(tert-butyl acrylate) also scatters light stronger than in THF, and the light scattering results are more precise. Five samples of 4-arm PTBA stars (Table 3) were measured by static and dynamic light scattering below the critical overlapping concentration (C* = 3Mw/4pRg3NA) in the concentration range from 0.2 to 3 g/L. Zimm plots of stars obtained by static light scattering (SLS) yielded weight-average molar masses, radii of gyration and the second virial coefficient. Fig. 3 shows a typical Zimm plot for Star 5. The values of Mw obtained from the Zimm plots are in good agreement with the values from GPC-MALLS (Table 3). The particle radii increase with the molar mass of the stars. In the case of Star 1, the sizes of the polymer particles were lower than 15 nm and no angular dependence was observed on the Zimm plot. Mw values obtained from Zimm plots were used to construct the scaling equations.
ftheor
fcalcd
4 4 4 4
3.7 3.7 3.7 3.8
from (4)
Fig. 3. Zimm plot of Star 5 in acetone at 25 °C. Experimental points are open symbols, extrapolated points are closed symbols.
GPC-MALLS measurements performed in THF yielded the average radius of gyration of stars in THF. The results
Table 3 Dynamic and static light scattering (DLS, SLS) data for 4-arm PTBA stars in comparison with data obtained from GPC-MALLS. Sample
SLS acetone Mw
Star Star Star Star Star
1 2 3 4 5
Zimm
178,000 376,000 490,000 900,000 930,000
[g/mol]
DLS acetone Rg [nm] – 18.0 20.6 30.0 31.0
A2[mL mol g2] 4
2.90 10 2.17 104 1.76 104 2.02 104 2.06 104
Rh [nm] 7.3 12.0 13.6 17.9 18.8
GPC-MALLS THF D0 [m2s1] 11
9.16 10 5.57 1011 4.86 1011 3.70 1011 3.53 1011
q = Rg/Rh
Mw
– 1.5 1.5 1.7 1.7
166,000 390,000 500,000 850,000 926,000
GPC
[g/mol]
Rg [nm] – 18.8 21.0 29.0 31.5
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presented in Table 3 are very close to those obtained by SLS in acetone. The values of the second virial coefficients A2 obtained from SLS (Table 3) are positive indicates favorable polymer/solvent interactions and good solvent behavior [1,19]. Dynamic light scattering (DLS) was used to measure the hydrodynamic radius Rh and diffusion coefficient D0 (Table 3). The relaxation rates C were measured for five concentrations and different angles from 30° to 150°, yielding Rh and D0. The distribution of hydrodynamic radii of the star polymers in acetone solutions are monomodal and symmetri cal. The intensity distribution obtained for h = 90° (R90 h ) is shown in Fig. 4 for Star 2. For all stars, the distribution of particle sizes is given as l2 is the average value of C and l2 is its second , where C 2 C moment, and ranges from 0.067 to 0.097. These values were obtained based on cumulant analysis. The apparent diffusion coefficients D (from CONTIN algorithm) for each concentration were determined as the slopes of the linear fit of the relaxation rates U versus sin2(h/2) as shown in Fig. 5(a). Then the values of D were plotted against concentration (Fig. 5(b)) and extrapolated to zero concentration (D0 ¼ limc!0 D). The mean hydrodynamic radii were derived from Eq. (2), taking into account the diffusion coefficient D0 obtained as the intercept from Fig. 5(b). The results are reported in Table 3. The dimensionless shape parameter q defined as [25,27]:
q ¼ Rg =Rh
ð5Þ
is often used to describe the structure of macromolecules in solution. The value of q is influenced by the type of structure (sphere, rigid rod, flexible coil) [27], the nature of the solvent [25], the segment density in the polymer
Fig. 4. Distribution of hydrodynamic radii of Star 2 in acetone at 25 °C at 90°.
Fig. 5. (a) Relaxation rate as a function of sin2(h/2) for a 0.468 g/L solution of Star 4, (b) concentration dependence of apparent diffusion coefficients D for Star 4. The dashed lines through the data points are the linear fits.
chain [27] and the dispersity of the system [26,27,33]. Table 3 also reports the q ratios calculated for PTBA 4-arm stars. Different theories predict different q ratio values, and the reasons for the discrepancies are interpreted differently. Park and Chang have discussed this in detail [25]. The literature reports values of the q ratio calculated on the basis of Kirkwood’s approximation [27] for 4-arm stars in h conditions. Theoretical values for stars with uniform arm lengths are 1.333 and with non-uniform lengths is 1.534. There are no theoretically predicted q ratio values for 4-arm stars in a good solvent. For linear polymers, the q ratio is predicted to be 1.78 for a uniform random coil and 2.05 for a non-uniform random coil in good solvents [27]. The experimental q ratio values (Table 3) increase with molar mass from 1.5 to 1.7 for stars with Mw P 390 000 g/mol, reflecting the more compact structure of stars with shorter arms. Huber and others [9] obtained q = 1.33 for 3-arm polystyrene star polymers in a good solvent whereas Strandman [26] reported q 1.5 for
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4-arm PMMA-block-PAA stars in aqueous solutions. In comparison with experimental values obtained for 6arm polystyrene stars (q from 1.16 to 1.45) [34], our q ratio values are higher but have the same tendency of increasing q ratio with arm length. This also confirms that for stars with fixed numbers of arms, the structure changes towards a structure characteristic of a random coil as the molar mass and the excluded volume of the star increase [34]. Fig. 6 presents the double logarithmic plots of the second virial coefficient, diffusion coefficient and both radii (Rg and Rh) as a function of the weight-average molar masses of 4-arm PTBA stars. Scaling equations for poly (tert-butyl acrylate) star polymers with four arms are derived from these graphs. The scaling equation for the second virial coefficient is:
A2 ¼ 7:45 103 M 0:27 w
½mL:mol:g2
ð6Þ
The dependence of logA2 on logMw is shown in Fig 6(a). Flexible linear polymers in good solvent have mA2 values from 0.2 to 0.3 [36,37]. Bauer et al. [8] obtained mA2 ¼ 0:238 for 4-arm polyisoprene stars in cyclohexane. The mA2 value given by our equation 6 for PTBA 4-arm star polymers is mA2 ¼ 0:27, which fits very well with values for other polymers in good solvents. The following relationship was obtained for the diffusion coefficient:
D0 ¼ 7:57 108 M 0:55 w
½m2 :s1
ð7Þ
while the hydrodynamic radius (Rh 1/D0) can be expressed as:
Rh ¼ 9:47 103 M 0:55 w
½nm
ð8Þ
The exponents in the diffusion coefficient scaling equation for the range of star molar masses investigated here is 0.55 (Eq. (7)), what gives 0.55 for the hydrodynamic radius scaling equation (Eq. (8)). Similar results were obtained by Roovers for 4-arm poly(ethylene oxide) stars in methanol (mD = 0.567) [7]. According to theory [21,22,38–40], exponent m in the scaling equation for the sizes (Rg and Rh) should change from 0.5 in a h solvent to 0.6 [21] (0.588 predicted by scaling theories [22,38–40]) in a good solvent and when the excluded volume region is reached. At the asymptotic limit ðM ! 1Þ, mRg ¼ mRh . This asymptotic value is known to be a consequence of chain swelling due to the gradual increase of the intrachain excluded volume [21,40]. It has been revealed [27,38,41] that the radius of gyration reaches the asymptotic limit at smaller values of molar masses than hydrodynamic radius. In most cases, the polymer is not sufficiently flexible and the solvent is not sufficiently good for mRh to reach its asymptotic value in the experimental range of molar masses where mRg is already equal to the predicted value of m. For some polymer/solvent systems, this region is reached when the molar mass is in the range of several million [19]. The linear fit of logRg versus logMw yields the scaling equation for the radius of gyration:
Rg ¼ 7:82 103 M 0:60 w
½nm
ð9Þ
Fig. 6. The dependence of the weight-average molar mass on the second virial coefficient (a), diffusion coefficient (b) and radius of gyration and hydrodynamic radius (c) for the 4-arm PTBA stars in acetone at 25 °C. The lines through the data points represent linear fits to the data.
The value of m in the scaling equation of the radius of gyration (9) is exactly the same as predicted by Flory [21] but slightly higher than the value predicted by scaling theory [22,38–40]. Bauer et al. [8] obtained m values of
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0.546, 0.555 and 0.558 for polyisoprene stars with 8, 12 and 18 arms, respectively, in toluene. Willner et al. [42] investigated polybutadiene and polyisoprene star polymers with f P 8 by small angle neutron scattering (SANS) and obtained values higher than 0.6 (from 0.64 to 0.67). These high values were attributed to the stretched configuration of the arms in these star polymers [42]. mRg values higher than theoretical predictions were also seen for linear polymers with relatively high molar masses in good solvents, for instance, for chitosan in water solution [43] and for polyglicidol in water [19]. The authors explained that this behavior is due to the ellipsoidal shape of the macromolecules [43] or to the high dispersity of the polyglicidol samples[19]. Linear poly(tert-butyl acrylate) was synthesized separately using conventional radical polymerization. It has Mn = 252,000 g/mol, Mw = 743,700 g/mol and a broad molar-mass distribution (Mw/Mn = 2.95, dn/dc = 0.0593 mL/g in THF). The ASTRA software is able to determine the Rg values of polymer fractions with different weight-average molar masses. The linear PTBA has a sufficient dispersity to cover the range of molar masses studied here. The Rg values for linear chains in THF, obtained using Zimm method from ASTRA software, are placed in Fig. 7 as open circles. The same method was used to calculate Rg of stars (Fig. 7 closed circles). The GPC-MALLS measurements of linear PTBA and PTBA stars enabled the calculation of scaling parameters in THF at 35 °C (Fig. 7). The linear fits for both polymers shown in Fig. 7 yielded the following equations:
value of 0.59 for PTBA stars in THF. This value of mRg is the same as the value obtained by fitting the results from GPC-MALLS. 3.4. Branching parameters of 4-arm star polymers The intrinsic viscosity of the synthesized stars was measured using a viscosimetric detector connected on-line to the GPC system in THF solutions at 35 °C. Integrating the measured slice viscosities (gsp)i over concentration yields the total intrinsic viscosity of the sample [g] (see Eq. (1)). Intrinsic viscosity measurements were performed for linear PTBA standards to compare them with those obtained for stars and to determine the branching parameter g0 . As shown in our previous paper [29], the linear fit of experimental values of log[g] versus logMw shown in Fig. 8 yields the Kuhn-Mark-Houwink-Sakurada equation for linear PTBA in THF at 35 °C:
½g ¼ 4:2 103 M0:78 w
ð12Þ 3
The exponents mRg have the same value for linear as for star polymers and are in agreement with values predicted by scaling theory [22,38–40]. The known relationship between the exponent a from the Kuhn-Mark-HouwinkSakurada equation and mRg , a ¼ ð3mRg 1Þ [38], gives a mRg
The obtained values of K = 4.2 10 and a = 0.78 are consistent with those for linear PTBA measured by Mrkvickova et al. in THF at 25 °C [44]. Fig. 8 presents the intrinsic viscosities of the 4-arm PTBA stars discussed in this paper and those described previously [29]. The intrinsic viscosities of the stars are lower than those of the linear analogues, and the viscosities increase linearly with the arm length, parallel to the graph of linear PTBA. Parallel or nearly parallel lines on the logarithmic plot of intrinsic viscosity versus weight-average molar mass were also observed for poly(ethylene oxide) [7], polybutadiene [5,6], polyisoprene [8,45] and polystyrene [3,4,30,35] star polymers with different functionalities in good solvent. Fitting all of the star polymer points in Fig. 8 to a linear function gave the value of the exponent a in the KuhnMark-Houwink-Sakurada of 0.78. Branching parameters are often calculated to characterize branched structures. Zimm and Stockmayer defined the
Fig. 7. Radius of gyration versus the weight-average molar mass for the 4-arm PTBA stars and linear PTBA obtained by GPC-MALLS.
Fig. 8. Log–log plot of intrinsic viscosities versus the weight-average molar mass for 4-arm PTBA stars and linear PTBA.
RgðLinÞ ¼ 1:18 102 M 0:59 w
ð10Þ
RgðStarÞ ¼ 8:77 103 M0:59 w
ð11Þ
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branching parameter g0 [23] as the ratio of the intrinsic viscosities of branched and linear polymers of the same molar mass (Eq. (13)). The same authors also defined the branching parameter g [23] as the ratio of the mean square radius of gyration of branched and linear polymers of the same molar mass (Eq. (14)). According to this definition, the factor g can only be determined when the radius of gyration is measurable.
g0 ¼
½gbranched ½glinear at
R2gbranched g¼ 2 Rg linear
ð13Þ the same M
ð14Þ at the same M
The measured intrinsic viscosities of stars and those calculated for linear chains of the same molar mass were used to obtain the g0 parameter. The results are collected in Table 4. The same table contains g0 values calculated based on the relationship derived by Zimm and Kilb [24] (Eq. (15)), Roovers [28] (Eq. (16)) and Douglas and Freed [46] (Eq. (17)).
g 0ZK ¼
ð2=f Þ1:5 ½0:396ðf 1Þ þ 0:196 0:586
ð15Þ
log g 0 ¼ 0:36 0:8 log f
ð16Þ
" 0:58 # 3f 2 1 0:276 0:015ðf 1Þ g ¼ 2 f 1 0:276 0
ð17Þ
The Zimm and Kilb Eq. (15) gives g0 equal to 0.83, but this prediction is limited to a h solvent. No theoretical value of g0 (or g) is proposed for stars in a good solvent. Roovers [28] and Douglas and Freed [46] proposed empirical relations (Eqs. (16 and 17), respectively) correlating g0 with the number of arms in good solvents. The average of all values of g0 obtained for 4-arm PTBA stars is equal to 0.754, which is very close to the value calculated from empirical dependence derived by Roovers (Eq. (16)) (0.756) and is lower than that calculated from the Zimm and Kilb equation for h conditions (0.83). A similar result was observed for other star polymers in good solvents [18,28,33]. 4-arm PTBA stars with long arms (Stars 1 to 5 from Table 3) have values of g0 (Table 4) that are in good correlation with results obtained by Hirao [47] for stars with four poly(methyl methacrylate) arms (g0 = 0.77 in THF) and Hwang [48] for polybutadiene 4-arm stars (g0 between 0.75–0.76 in toluene). Angot [30] reported even higher g0 values for 4-arm polystyrene stars in toluene close to 0.85. Rglin was measured for each slice of chromatographic separation by GPC using ASTRA software as shown in Table 4 Experimental values of g0 for 4-arm PTBA stars in THF. Sample
Mw
Star Star Star Star Star
166,000 390,000 500,000 850,000 926,000
1 2 3 4 5
GPC–MALLS
[g/mol]
g0 0.76 0.76 0.76 0.75 0.74
Table 5 Experimental values of the radius of gyration of stars and their linear analogues and parameter g for 4-arm PTBA stars in THF.
a b
Sample
Mw GPC-MALLSa [g/mol]
Rg_starb
Rg_lin.b
g
Star Star Star Star
390,000 500,000 850,000 926,000
18.8 21.0 29.0 31.5
26.4 29.6 37.7 40.0
0.51 0.50 0.59 0.62
2 3 4 5
dn/dc = 0,0539 mL/g (THF) From Zimm plot
Fig. 7. The Rg of PTBA stars (except for Star 1) and their R2g could be obbranching parameter g ¼ Rbranched 2 g linear
at the same M
tained. All results are shown in Table 5. Zimm and Stockmayer [23] predicted the branching parameter g for a star with f equal arms (h condition):
g ZS ¼
3f 2 f2
ð18Þ
The branching parameter gZS calculated from Eq. (18) for 4-arm stars is equal to 0.625. Douglas and Freed [49] used renormalization group calculation to predict g for star polymers in good solvents. Performing this calculation for 4-arm stars in good solvent conditions gives a g value of 0.631 [49]. The average value obtained here for 4-arm PTBA stars is gav = 0.555 and is lower than calculated by Douglas and Freed [49]. The experimental values of branching parameter reported for four arm stars in good solvent ranging from 0.56 for polystyrene stars in toluene to 0.72 for polybutadiene stars in cyclohexane [46]. 4. Conclusions A synthetic approach based on ATRP was used to obtain 4-arm PTBA star polymers with high molar masses and low molar mass dispersities not exceeding 1.13. The process was well controlled, with molar masses increasing with conversion in good agreement with theoretical calculations from monomer conversion. Polymerization was stopped before the star-star coupling reaction could occur. The well-defined structure was proven by alkaline hydrolysis, and almost all initiating groups were involved in the polymerization. The solution behavior of the obtained star polymers was investigated by static and dynamic light scattering and by GPC with three detectors. The SLS and DLS measurements in acetone at 25 °C delivered weight-average molar masses, sizes (Rg and Rh), diffusion coefficients (D0) and second virial coefficients (A2). The measured values were used to establish scaling equations between these parameters and molar mass. The values of the exponents in the scaling equations for A2, D0 and Rh indicated that the asymptotic excluded volume limit for 4-arm stars in acetone has not been reached. The exponent in the Rg scaling equation fit with the value predicted by Flory. The observations demonstrate that the radius of gyration reaches the asymptotic value faster than hydrodynamic radius. The
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values of m for the obtained stars and their linear analogues in THF were determined from the logarithmic dependence of Rg versus weight-average molar mass, and these values are consistent with those predicted by scaling theory for the excluded volume region. The values of the shape parameter q increase from 1.5 to 1.7 with the molar mass of the star, indicating that the conformation of the obtained stars in acetone resemble a coil more than a sphere. The intrinsic viscosities measured for star polymers and linear poly(tert-butyl acrylates)in THF indicated the scaling parameters of the Kuhn-Mark-Houwink-Sakurada equations. The intrinsic viscosities of the 4-arm star polymers are lower than those of the analogous linear polymers with the same molar mass. The exponents have the same values for star polymers as for their linear counterparts. The average branching ratio g0 is in good agreement with the predicted values for star polymers in good solvents. The values of branching parameters g in THF calculated for 4-arm stars proved their non-linear structure. Acknowledgements This work was supported by Polish Ministry of Science and Higher Education grant NN 204 153136. The authors wish to thank Prof. Walter Burchard (University of Freiburg) for the stimulative and helpful discussion. References [1] Burchard W. Solution properties of branched macromolecules. Adv Polym Sci 1999;143:113–94. [2] Mishra MK, Kobayashi S, editors. Star and hyperbranched polymers. New York, Basel: Marcel Dekker, Inc.; 1999. [3] Roovers J, Bywater S. Preparation and characterization of fourbranched star polystyrene. Macromolecules 1972;5:384–8. [4] Roovers J, Bywater S. Preparation of six-branched star polystyrene. Thermodynamic and hydrodynamic properties of four and sixbranched star polystyrenes. Macromolecules 1974;4:443–9. [5] Roovers J, Zhou LL, Van der Zwan M, Iatrou H, Hadjichristidis N, Toporowski PM. Regular star polymers with 64 and 128 arms. Models for polymeric micelles. Macromolecules 1993;26:4324–31. [6] Roovers J, Toporowski P, Martin J. Synthesis and characterization of multiarm star polybutadienes. Macromolecules 1989;22:1897–903. [7] Comanita B, Noren B, Roovers J. Star poly(ethylene oxide)s from carbosilane dendrimers. Macromolecules 1999;32:1069–72. [8] Bauer BJ, Fetters LJ, Graessley WW, Hadjichristidis N, Quack GF. Chain dimension in dilute polymer solutions: a light-scattering and viscometric study of multiarmed polyisoprene stars in good and h solvents. Macromolecules 1989;22:2337–47. [9] Huber K, Burchard W, Fetters LJ. Dynamic light scattering from regular star-branched molecules. Macromolecules 1984;17:541–8. [10] Roovers J, Hadjichristidis N, Fetters LJ. Analysis and dilute solution properties of 12- and 18-arm-star polystyrenes. Macromolecules 1983;16:214–20. [11] Matyjaszewski K, Xia J. Atom transfer polymerization. Chem Rev 2001;101:2921–90. [12] Tsarevsky NV, Matyjaszewski K. ‘‘Green” atom transfer radical polymerization: from process design to preparation of welldefined environmentally friendly polymeric materials. Chem Rev 2007;107:2270–99. [13] Braunecker WA, Matyjaszewski K. Controlled/living radical polymerization: features, developments, and perspectives. Prog Polym Sci 2007;32:93–146. [14] Hawker CJ, Bosman AW, Harth E. New polymer synthesis by nitroxide mediated living radical polymerizations. Chem Rev 2001;101:3661–88.
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