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Dec 16, 2011 - Lett. 1996, 36, 289. (20) Bates, F.; Rosedale, J.; Fredrickson, G. J. Chem. Phys. 1990, 92,. 6255−6270. (21) Holzer, B.; Lehmann, A.;...
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Thermodynamic and Structural Changes in Ion-Containing Symmetric Diblock Copolymers: A Small-Angle X-ray Scattering Study Ilja Gunkel and Thomas Thurn-Albrecht* Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany S Supporting Information *

ABSTRACT: We present temperature-dependent SAXS measurements on symmetric poly(styrene-block-2-vinylpyridine) and poly(styrene-block-ethylene oxide) with added lithium triflate. Salt doping led to a strong increase of the order−disorder transition temperatures and increased domain spacings. Based on a detailed analysis of the scattering data close to the order−disorder transition, three contributions to the structural changes can be distinguished: an increased incompatibility between the different monomers, the additional volume of the added salt, and chain stretching due to coordination between polymer and salt. At the phase transition, i.e. at constant interaction parameter χ, for low concentrations the increase in domain size is quantitatively explained by the volume of the added salt, and at higher concentrations chain stretching sets in. Structural and thermodynamic effects are considerably stronger in PEO than in P2VP.

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INTRODUCTION Block copolymers with added ions which selectively dissolve in one block became of interest recently as nanostructured polymer electrolytes for use in batteries or fuel cells.1−3 In the microphase-separated state such a system offers the possibility to simultaneously optimize different properties which would normally exclude each other. One block, being in a solid state, can give mechanical strength while the other block, typically in the liquid state, can be designed to achieve good ion transport.4,5 Several studies on different ion-containing block copolymers have shown that the addition of salt also strongly changed the thermodynamic and structural properties. In the ordered state addition of salt induced modifications of the phase behavior and large increases in domain spacing.6−11 These changes were attributed to an increased value of the interaction parameter χ due to the added salt, based on the established relation d ∼ aN2/3χ1/6 which relates domain spacing d with χ and is valid in the strong segregation limit.6−8,11 Here N is the degree of polymerization and a the segment length. Similar conclusions were drawn from temperature-dependent studies in the weak segregation regime showing strongly increased order-to-disorder transition temperatures and again increased domain spacings.6,7,12−15 Wang et al.16 quantitatively analyzed the temperature dependence of χ from scattering experiments on ion-complexed block copolymers in the disordered state in the framework of the Leibler theory.17 For their analysis, which confirmed the salt-induced increase of χ, they also had to assume salt-induced changes of the segment lengths. For pure block copolymers it is well-known that also in the weak segregation regime the domain spacing respectively the position of the peak in the structure factor depends on the incompatibility. Thus, an increase of N18,19 and a decrease in temperature, leading to an increase of χ, were found to result in chain stretching.20−26 Recently, in a theoretical study27 significant changes in χ were © 2011 American Chemical Society

predicted also for polymer blends with added ions. On the other hand, changes in structure can also be related to changes in conformation directly caused by coordination of ions with polymer chains. Lee et al.13,28 presented direct evidence for such an effect. They demonstrated that coordination can either induce an increase or a decrease of the domain spacing depending on the type of coordination (inter- vs intramolecular coordination). Also, as a third point it should be taken into account that the additional volume of the added salt leads to an increase of the domain spacing. In general, separation of the above-mentioned different possible causes for chain stretching is difficult. We here present detailed measurements of two block copolymers, poly(styrene-block-2-vinylpyridine) (PS−P2VP) and poly(styrene-block-ethylene oxide) (PS−PEO), both doped with LiCF3SO3, in the vicinity of the order−disorder transition, together with an analysis of the scattering data which allows partial separation of the different salt-induced effects. As a starting point we assume that also for ion-containing block copolymers the value of the incompatibility at the order− disorder transition is constant and, in particular, independent of salt concentration. We will show experimental evidence that this a reasonable assumption. On the basis of this approach, we were able to separate chain stretching originating from an increased incompatibility from the other effects by comparing values of the domain spacing directly at the order−disorder transition. As we will show, for low concentrations the increase in domain size can be quantitatively explained by the volume of the added salt, while at higher concentrations additional chain stretching sets in. The analysis of the transition temperatures as a function of Received: June 19, 2011 Revised: November 5, 2011 Published: December 16, 2011 283

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salt concentration shows that the salt-induced changes in χ are much larger for PEO than for P2VP.

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Here (∂χeff/∂xm)|ODT = 0 according to eq 4. The remaining contribution (∂/∂xm)d(xm)|ODT represents both changes of the domain spacing related to conformational changes of the ioncontaining blocks and changes due to the additional volume of the salt. Structure Factor of Block Copolymers in the Disordered State. According to Leibler,17 in the mean-field approximation the structure factor S(q) in the disordered state is given by

THEORY

Ordering Transition. The local interactions in block copolymer melts are described by an interaction parameter χ with a temperature dependence

A +B (1) T For ion-containing block copolymers it is often assumed that the ions, which are dissolved in only one of the blocks, simply modify the segmental interactions such that the whole system can still be described as a binary system with a new effective interaction parameter χeff χ=

S−1(q) = N −1F(x , f ) − 2χ

where f = NA/N describes the composition of the copolymer and x = q2Rg2 with Rg denoting the radius of gyration of a Gaussian chain. The function F(x,f) was calculated by Leibler in the framework of the random phase approximation and is given in terms of Debye functions. The function F(x,f) has a minimum at x*, corresponding to a maximum in the structure factor S(q) at a scattering vector q*. The maximum of the structure factor diverges at the spinodal where F(x*,f) = 2(χN)s. In case of a symmetric (f = 1/2) composition x* = 3.7852 and (χN)s = 10.495. The period of the lamellar phase (d = 2π/q*) is predicted to be d ≈ 3.23Rg. Accounting for composition fluctuations, Fredrickson and Helfand 29 corrected the structure factor S(q) in a Hartree approximation. The corrected structure factor S(q) possesses the same form as Leibler’s structure factor and satisfies 30

A (x m ) + B (x m ) (2) T where xm denotes the molar ratio between ions and the monomers of the ion-containing block. As already mentioned in the Introduction, an increased value of χeff > χ should lead to an increased value of domain spacing d(χeff), even at constant temperature. Generally, the domain spacing d in ion-containing symmetric block copolymers should therefore depend on the salt concentration (molar ratio) xm as follows: χeff (xm) =

d = d(χeff (xm), xm) (3) On the one hand, there is an explicit dependence on xm originating from either conformational changes or from the additional volume of the salt. On the other hand, d implicitly depends on xm via the modified segmental interactions in the ion-containing block copolymer that are described by χeff(xm). We propose to separate implicit and explicit effects based on simple arguments from the thermodynamics of block copolymers. As originally shown by Leibler,17 there is a critical point at (χN)ODT = 10.495 at which a symmetric diblock copolymer melt undergoes a second-order phase transition from the disordered to a lamellar phase. This scenario was later modified by Fredrickson and Helfand,29 who showed that fluctuations induce a weakly first-order phase transition and shift the transition to a larger (χN)ODT = 10.495 + 41.022N̅ −1/3, where N̅ ≡ Na6v−2 is the invariant polymerization index (a and v are the statistical segment length and volume, respectively). In any case, if the added salt only changes χ, the value of (χN)ODT, i.e., the incompatibility at the order−disorder transition, remains unchanged and independent of salt concentration. (χeff N )ODT = const

S−1(q) = N −1F(x , f ) − 2χren

where c, g, and λ are constants. In case of a symmetric composition these constants attain the following values 29

g=

≡

∂ ∂ χ d ∂χeff ∂xm eff ∂ d(xm) ∂xm

ODT

∂ d ∂xm

(9)

λ = 106.19

Please note that the shape of the scattering curve and the position of the maximum q* remain unchanged. The parameter χN, however, is renormalized, and thus the peak height changes such that S(q*) is finite at the transition. Please note that neither in eq 6 nor in eq 7 the value x* depends on χ. Hence, a change in peak position due to chain stretching is not described within the framework of these theories. Expanding the function F(x,f) in eq 6 around its extremum at q* the structure factor S(q) can be approximated as21,31

ODT

S(q) ≈ ODT

= 1.1019,

x=x*

ODT

+

3x* = 1.8073, 2π

⎡ 1 ∂ 2F ⎤1/2 c = ⎢ x 2⎥ ⎣ 3 ∂x ⎦

Consequently, salt-induced changes of the domain spacing at the order−disorder transition should obey the following equation:

=

(7)

with a renormalized interaction parameter χren, given by v χren = χ − 3 c 3g λN −2[N −1F(x*, f ) − 2χren]−1/2 (8) 2b

(4)

d d(χeff (xm), xm) dx m

(6)

(5) 284

S(q*) 1 + ξ2(q − q*)2

(10)

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where the correlation length ξ and the peak height S(q*) are given by ξ2 =

c 2Nb2 , 2[(χN )s − χN ]

S(q*) =

N 2[(χN )s − χN ]

glycol methyl ether acetate (PGMEA) obtained from Aldrich was filtered using 0.2 μm syringe filters. Lithium triflate (LiCF3SO3) from Aldrich was dried at 170 °C under vacuum for 24 h before use. Sample Preparation. To prepare ion-containing block copolymers, we at first dissolved block copolymer (PS−P2VP/PS−PEO) and lithium triflate in PGMEA, followed by continuous stirring and moderate heating at 70 °C until the solutions became clear. Polymer and salt solutions were then mixed at a given ratio. Subsequently, most of the PGMEA was evaporated by heating again to 70 °C for several days. During this process precipitation of the salt did not occur. Before the SAXS measurements the samples were heated to 140 °C under vacuum for 24 h to remove remaining PGMEA and water. PS−P2VP was LiCF3SO3-doped at mass ratios from 5.3 × 10−3 to 4.3 × 10−2 and PS−PEO at mass ratios from 2.0 × 10−3 to 2.3 × 10−2. Assuming that no salt was dissolved in PS, these values correspond to molar ratios of [LiCF3SO3]:[2VP] = 1.32−5.83% and [LiCF3SO3]:[EO] = 0.23− 1.31%. We used different methods to keep the samples in the X-ray beam during the SAXS experiments. In the case of PS−P2VP the sample (thickness some 10 μm) was held on a simple aluminum foil with a thickness of 12.5 μm. In the case of PS−PEO aluminum disks with holes of 1 mm and a thickness of 2 mm were used to carry the samples. Small-Angle X-ray Scattering (SAXS). All SAXS measurements were performed using an X-ray generator of rotating anode type with Cu target from Rigaku, operated at 2.4 kW. A confocal optics from Osmic provided monochromatic Cu Kα radiation. The X-ray beam was collimated by a system of three pinholes. At the position of the sample the size of the beam was ∼350 μm. The flight path was fully evacuated, and the scattered radiation was detected by a Bruker Hi-Star multiwire proportional chamber. The data were collected as frames of 1024 × 1024 pixels and later on calibrated using silver behenate. The accessible q-range was 0.01 Å−1 < q < 0.14 Å−1. To control the temperature of the samples, a hot stage from Linkam was used. Heat conduction paste was used for good thermal contact between the holder and the hot stage in vacuum. Exposure times were 500 s for PS−P2VP and 1200 s in the case of PS−PEO. Before every measurement the samples were given 60 s (PS−P2VP) and 300 s (PS−PEO) at the new temperature to equilibrate. Scattering data for the different ion-containing block copolymer samples were taken within a temperature range of about ±20 °C around the respective TODT(xm). Here TODT(xm) denotes the salt concentration-dependent temperature of the order−disorder transition. Measurements were generally taken during cooling runs. After each measurement the temperature was reduced by 3 K at a rate of 5 K min−1 (neat PS− P2VP was exceptionally measured in 5 K steps).

(11)

Inserting the temperature dependence of the Flory−Huggins interaction parameter χ, which is given by eq 1, leads to the following relations:

1 ξ2

∼

−2

1 1 − , Ts T

1 1 1 ∼ − S(q∗) Ts T

(12)

−1

ξ and S (q*) show the same linear dependence on 1/T (Ts denotes the spinodal temperature). In the vicinity of the phase transition, however, one expects deviations from the linear dependence on 1/T because of the fluctuation correction according to eqs 7 and 8. Model Function. All scattering data were fitted at temperatures T ≥ TODT as well as T < TODT to the following function:

y = y0 +

w 2A + bx c π 4(x − xc)2 + w 2

(13)

In addition to a Lorentzian function, we used a power law in eq 13 to take the background scattering at low angles into account.21 The fit parameters were the offset y0, the area A of the Lorentz peak, the width w of the peak, its position xc, the power law amplitude b, and the exponent c. Comparing eq 13 with eq 11, one finds the following relations:

2[(χN )s − (χN )] w2 = , 4 c 2Nb2 2[(χN )s − (χN )] πw = (14) N 2A So the interaction parameter χN is essentially given by the inverse peak height (2A/πw)−1 and width squared w2 while the radius of gyration of the chain Rg is given by the inverse peak position xc−1.

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EXPERIMENTAL SECTION

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Materials. We used symmetric poly(styrene-block-2-vinylpyridine) (PS−P2VP) block copolymers and symmetric poly(styrene-blockethylene oxide) (PS−PEO) block copolymers from Polymer Source. The molecular and thermodynamic characteristics of PS−P2VP and PS−PEO are shown in Table 1. SAXS patterns of both materials at

RESULTS AND DISCUSSION Neat PS−P2VP and PS−PEO. Figure 1a shows SAXS profiles obtained for neat PS−P2VP at different temperatures during stepwise cooling. At the ordering transition the peak width decreased discontinuously accompanied by an increase of the peak intensity. For a quantitative analysis of the scattering data we fitted the SAXS profiles to eq 13 as can be seen exemplarily in Figure 1b for two curves in the immediate vicinity of the transition. To determine TODT, the peak width squared and the reciprocal peak intensity were plotted as a function of the reciprocal temperature as can be seen in Figure 2a for neat PS−P2VP. The discontinuity similarly observed in both curves corresponds to TODT.20 We found TODT = 161 ± 3 °C for neat PS−P2VP, which is consistent with reported values for PS− P2VP of similar molecular weight.32 The peak position decreased continuously with decreasing temperature. This known phenomenon of an increased domain spacing at lower temperatures20−26 can be attributed to chain stretching caused by an increasing segmental interaction parameter χ. Figure 3a shows the peak width squared and the reciprocal peak intensity versus the reciprocal temperature for neat PS−PEO with TODT

Table 1. Characteristics of the Block Polymers Used in This Studya polymer

Mn [g mol−1]

f PS

PDI

TODT [°C]

dODT [nm]

PS−PEO PS−P2VP

9500−8000 8200−8300

0.54 0.50

1.07 1.09

145 ± 2 161 ± 3

16.7 13.8

a

The values of the number-average molecular weight (Mn) and the polydispersity index (PDI) were provided by the supplier. f PS denotes the composition of the block copolymer. The order−disorder transition temperature (TODT) and the corresponding value of the domain spacing (dODT) were determined using small-angle X-ray scattering (data shown in Figures 2 and 3). Scattering patterns in the ordered state indicative of a lamellar microstructure are shown in the Supporting Information. room temperature in the ordered state show higher order reflections indicative of lamellar structures (see Supporting Information). Propylene 285

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Figure 1. (a) Temperature dependence of the SAXS profiles for neat PS−P2VP in the vicinity of the order−disorder transition. (b) SAXS profiles (open circles) of neat PS−P2VP in the disordered (T = 164 °C) and the ordered state (T = 159 °C). The solid lines were obtained by curve fitting SAXS profiles to eq 13. Curves are shifted vertically for clarity.

Figure 3. (a) Neat PS−PEO. Square of peak width w and inverse peak maximum πw/2A vs inverse temperature. (b) Peak position xc vs inverse temperature. Error bars represent fitting errors.

Figure 2. Scattering parameters as obtained from curve fitting SAXS profiles to eq 13 for neat PS−P2VP. (a) Square of peak width w2 and reciprocal peak height πw/2A as a function of reciprocal temperature. (b) Peak position xc versus reciprocal temperature. Error bars represent fitting errors.

PS−P2VP with LiCF3SO3. Figure 4 shows the SAXS results for LiCF3SO3-doped PS−P2VP with molar ratios between 1.32% and 5.83%. In Figure 4a, the peak width squared is plotted as a function of the reciprocal temperature. Here and in the following we only consider the peak width since this parameter is more robust than the peak intensity. For each sample TODT was determined as shown in Figure 2. The value of the squared width at the order−disorder transition is independent of the salt concentration. The strong increase of TODT with

at 145 ± 2 °C. For neat PS−PEO we also found a decreasing peak position with decreasing temperature as can be seen in Figure 3b. For both systems the value of the peak width w in the ordered phase corresponds to the resolution of the scattering setup. Please note that the fitting errors of the parameters shown in Figures 2 and 3 are smaller than the statistical uncertainties of each measurement and will be omitted in the following. 286

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Figure 4. Results of SAXS data analysis for LiCF3SO3-doped PS−P2VP (molar ratios given in the legend). (a) Peak width squared w2 as a function of reciprocal temperature. The dashed line indicates the value of w2 at ODT. (b) Peak position xc versus reciprocal temperature. (c) Peak width squared w2 versus reduced reciprocal temperature 1000/T − 1000/TODT. (d) Peak position xc versus reduced reciprocal temperature.

increasing salt content can be attributed to the stronger incompatibility between the PS blocks and the ion-containing P2VP blocks. Figure 4b shows the peak position xc versus the reciprocal temperature. For all salt concentrations the peak position decreased with decreasing temperature. The xc curves run approximately parallel to each other with curves of higher salt concentrations at lower xc values. To analyze the salt-induced changes further, we compare the values of the domain spacing at the order−disorder transition dODT as discussed above (cf. eqs 3−5). We replotted the squared widths from Figure 4a versus a reduced reciprocal temperature 1000/T − 1000/TODT as shown in Figure 4c. Please note the reduced reciprocal temperature 1000/T − 1000/TODT corresponds to χN − (χN)ODT according to eqs 1 and 2. In Figure 4c, the curves of the squared widths coincidein particular at TODTindicating a constant value of χN at the transition (cf. eq 14). This result confirms our assumption that LiCF3SO3-doped PS−P2VP can be treated as a block copolymer with an effective interaction parameter χeff in the range of salt concentrations studied here. In Figure 4d, the peak positions xc from Figure 4b were replotted versus 1000/T − 1000/TODT. The xc curves do not overlap. According to eqs 4 and 5, the remaining differences in the domain spacings dODT at TODT should originate from direct effects of the salt, i.e., coordination or effect of added volume. For a discussion of these direct effects, we plotted TODT and dODT in Figure 5 vs xm. Both parameters increase with increasing salt concentration. To distinguish between coordination and volume effects, we assumed in a first approximation that the volume of the polymer and the volume of the salt simply add up in the mixture. In this case the increase of the domain spacing dODT due to the volume of the added salt can be estimated as follows:

d dBCP

=1+

ρ Vsalt = 1 + xm BCP VBCP ρsalt

Figure 5. (a) The order−disorder transition temperature TODT (as shown by the open circles) for LiCF3SO3-doped PS−P2VP as a function of the molar ratio between LiCF3SO3 molecules and 2VP monomers. The corresponding linear fit is shown by the straight line and yields TODT = 166 ± 3 °C + 1669 ± 78 °C × xm, where xm denotes the molar ratio. (b) The domain spacings d = 2π/xc (open squares) at the corresponding TODT are shown versus the molar ratio. The dashed line represents the estimated increase of the domain spacing due to the volume of the added salt.

Here dBCP denotes the domain spacing in the neat block copolymer, VBCP its volume, and xm the mass ratio known from the sample preparation. For the densities of LiCF3SO333 and

(15) 287

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Figure 6. Results of SAXS data analysis for LiCF3SO3-doped PS−PEO (molar ratios given in the legend). (a) Peak width squared w2 as a function of reciprocal temperature. The dashed line indicates the value of w2 at ODT. (b) Peak position xc versus reciprocal temperature. (c) Peak width squared w2 versus reduced reciprocal temperature 1000/T − 1000/TODT. (d) Peak position xc versus reduced reciprocal temperature.

PS−P2VPa we used the values ρsalt = 1.9 g cm−3 and ρBCP = 0.96 g cm−3. At low salt concentrations up to ≈4% the values of dODT coincide with the increase of d according to eq 15 and above the increase is stronger. We attribute this effect to changes of chain conformation which could e.g. arise from coordination of 2VP with lithium ions. PS−PEO with LiCF3SO3. Generally, adding LiCF3SO3 to PS−PEO induced qualitatively quite similar effects as in PS− P2VP. For example, in Figure 6a,b the SAXS results for LiCF3SO3-doped PS−PEO show an increase of TODT as well as an increase of the domain spacing with increasing salt concentration. However, the corresponding changes of TODT in PS−PEO occurred at lower salt concentrations than in PS− P2VP. For a well-defined analysis of salt-induced thermodynamic and conformational changes in PS−PEO we again plotted the SAXS data as a function of a reduced reciprocal temperature 1000/T − 1000/TODT as shown in Figure 6c,d. In Figure 6c, the peak widths squared showed a common value at TODT, w2(TODT) = 3.6 × 10−5 Å2, for all salt concentrations. This in particular corresponds to the value of w2(TODT) for PS−P2VP. In Figure 6c the peak widths squared again overlapped above and at TODT, while below TODT the curves deviate from each other. It seems that for the salt containing systems the size of the ordered domain is limited. These last effects are beyond the scope of this work. Figure 6d shows that the values of the peak center xc at TODT decrease with increasing salt concentrationanalogously to the behavior in PS−P2VP. Figure 7 shows TODT and dODT vs xm. The increase of TODT with xm is about 4 times stronger in PS−PEO than in PS−P2VP. Figure 7b shows again dODT as a function of the molar ratio [LiCF3SO3]:[EO] together with the estimated effect of added salt volume (ρsalt = 1.9 g cm−3 and ρBCP = 0.97 g cm−3)b.33 Now, at molar ratios above ≈1% the values of the domain spacing significantly deviate from the trivial volume

Figure 7. (a) Order−disorder transition temperature TODT for LiCF3SO3doped PS−PEO as a function of the molar ratio between LiCF3SO3 molecules and EO monomers. Linear fit is shown by the straight line and yields TODT = 152 ± 3 °C + 7247 ± 386 °C × xm where xm denotes the molar ratio between the LiCF3SO3 molecules and the EO monomers. (b) The domain spacings d = 2π/xc at the corresponding TODT are shown versus the molar ratio between LiCF3SO3 and the EO monomers. The dashed line represents the increase of the domain spacing due to the volume of the added salt.

increase, indicating salt-induced chain stretching.c It might be surprising that also in PS−PEO changes of the chain conformation due to coordination with lithium ions should 288

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concentration:

increase the domain spacing. From molecular dynamics simulations as well as small-angle neutron scattering experiments on PEO/LiI melts it was shown that the (overall) radius of gyration of PEO chains decreased due to coordination with lithium ions.35,36 However, the detailed simulation analysis revealed that those chains with one to three EO-monomers coordinating with lithium ions can actually increase the radius of gyration while for numbers beyond three the radius of gyration decreased. Our results indicate that in PS−PEO block copolymers changes of the chain conformation due to coordination with lithium ions are different than in PEO homopolymers (suggesting e.g. a multichain coordination in block copolymers instead of the homopolymer single-chain coordination). Further (theoretical) work is needed to elaborate these differences between block copolymers and homopolymers. Interestingly, Gomez et al.37 showed that a change of the chain conformation also influences the coordination between lithium ions and PEO in mixtures of PS−PEO and LiTFSI. By means of energy filtered transmission electron microscopy, they observed that lithium ions were increasingly confined to the middle of the PEO lamellae with increasing values of χN. Please note, though, that our observations were performed at constant χN. The direct comparison of the salt-induced changes of TODT shown in Figure 8 suggests that the interaction with the salt is

0 TODT(xm) = TODT + mxm

(17)

To determine the values for χeff(xm), we assume that the enthalpic changes in χeff(xm) dominate and therefore set the entropic contribution as constant, i.e., B(xm) ≡ B in eq 16. This is certainly an approximation, but it is clear that there must be large changes in solvation energy27 of LiCF3SO3 in the mixed and demixed state of the block copolymer which should show up in A(xm). Equation 16 then reduces to

T (x m ) A(xm) = A ODT 0 TODT

(18)

Inserting eq 18 into eq 2 leads to the following expression for χeff(xm)

χeff (xm) =

A ⎛ TODT(xm) ⎞ ⎟⎟ + B ⎜⎜ 0 T ⎝ TODT ⎠

A ⎛ mx ⎞ = χ0 + ⎜⎜ 0 m ⎟⎟ T ⎝ TODT ⎠

(19)

Above, eqs 1 and 17 were inserted to obtain the final expression for χeff(xm). The change of the interaction parameter Δχ = χeff − χ0 is then given by

Δχ(xm) =

A ⎛ mxm ⎞ ⎜⎜ 0 ⎟⎟ T ⎝ TODT ⎠

(20)

Δχ is shown in Figure 9 for the systems studied here.d Indeed, the interaction parameter in PS−PEO increases stronger with

Figure 8. The order−disorder transition temperature TODT as a function of the molar ratio xm in LiCF3SO3-doped PS−P2VP and PS− PEO block copolymers.

much stronger in the PEO-containing block copolymer than in the other system. To further analyze this effect, we suggest an approximation which eliminates the effect of molecular weight and allows an approximate determination of the effect of the salt on the interaction parameter χ. Assuming that N is constant, eqs 1, 2, and 4 reduce to the following relation

A 0 TODT

+B=

A (x m ) + B (x m ) TODT(xm)

0 Figure 9. The change Δχ of the interaction parameter at T = TODT due to LiCF3SO3 doping as a function of the molar ratio xm in PS− P2VP and PS−PEO block copolymers.

increasing LiCF3SO3 concentration than in case of PS−P2VP. This result reflects the strong coordination of lithium ions with oxygen in PEO. Our values for Δχ are significantly smaller than values in previous publications.10,11 Young et al.11 calculated Δχ based on domain spacing data and the relationship between domain spacing and Δχ in the strong segregation regime. As we have shown in the present work, the domain spacing also contains contributions from coordination and salt volume which could account for larger values in Δχ. Note that the analysis presented here is different from the analysis by

(16)

0 where TODT ≡ TODT(xm = 0) denotes the order−disorder transition temperature of the neat block copolymers. The values of A and B for the neat block copolymers are known from the literature:32,34 χS−EO = −7.03 × 10−3 + 21.3/T and χS−2VP = Vref(T)(−1.791 × 10−4 + 0.478/T). Here Vref(T) denotes a temperature-dependent reference molar volume. For both systems we obtained a linear dependence of TODT on salt

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of the domain spacing. GPC analysis of PS−PEO up to 200 °C did not show any indication of substantial degradation. d 0 To determine Δχ for PS−P2VP, Vref(TODT = 166 °C) ≈ 101 −3 mol cm was used.

Wanakule et al.10,15 As mentioned, the addition of salt that selectively dissolves in one block changes the volume fraction of the copolymer system. As the value of (χN)ODT, the incompatibility at the order−disorder transition, depends on the volume fraction,17 the addition of salt also changes (χN)ODT. Wanakule et al.10,15 calculated these changes of (χN)ODT and χODT in the framework of the Leibler theory.17 Asymmetric block copolymers can show large changes of (χN)ODT; for symmetric block copolymers, as they are used here, this effect is negligible. The effect on the value of Δχ in Figure 9 would be on the order 3 × 10−4 for the highest xm considered here.

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REFERENCES

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CONCLUSIONS We analyzed the effect of salt doping on the order−disorder transition in two symmetric block copolymers, PS−P2VP and PS−PEO. Both systems can be described as effective binary systems with an an effective interaction parameter χeff which depends on the salt concentration. The results indicate that the interaction of LiCF3SO3 with PEO is considerably stronger than with P2VP. Furthermore, both block copolymers show a salt-induced change in domain spacing at the transition which was determined from the position of the peak of the structure factor. Comparing the domain spacing at the transition removes effects of χ on the chain conformation and singles out direct salt-induced effects like the volume of the added salt and additional conformational changes due to the coordination with the salt. In first order the changes in domain spacing could be quantitatively explained by the added volume of the salt, assuming volume additivity during mixing. Additional conformational effects set in only at somewhat higher concentrations (molar ratio ∼1%) and are indicative of additional chain stretching. Further work is necessary to develop a theoretical understanding of this behavior. The method of analysis we propose seems generally applicable to study the effect of strongly selective additives on structure and thermodynamics of block copolymers. Examples could be ionic liquids or other strongly polar compounds.38,39

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ASSOCIATED CONTENT S Supporting Information * Additional SAXS results and DSC analyis of the transitions occurring in the investigated materials. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

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ACKNOWLEDGMENTS This work was supported by the state Sachsen-Anhalt (research network nanostructured materials) and the International Max Planck Research School for Science and Technology of Nanostructures.

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ADDITIONAL NOTES The density of PS−P2VP was approximated by its value for PS at 200 °C.34 b The density of PS−PEO was calculated using the values for PS respectively PEO at 200 °C.34 c Please note that degradation of PEO could not induce this effect since a lower molecular weight would lead to lower values a

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