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Novel map for polymer miscibility as revealed by neutron reflectometry
Physica B 276}278 (2000) 365}366
Novel map for polymer miscibility as revealed by neutron re#ectometry D.W. Schubert *, M. Pannek , A.H.E. MuK ller GKSS Research Centre, Max-Planck-Strasse, 21502 Geesthacht, Germany Macromol. Chem.II, Universita( tsstr. 30, 95440 Bayreuth, Germany
Abstract During annealing, above the glass transition temperatures the interface width between incompatible polymers increases with time, reaching an equilibrium value (typically 2 and 15 nm), which according to mean-"eld theory is determined by the Flory}Huggins}Stavermann interaction parameter v. The quantity v is a measure of polymer compatibility, although it is not well understood on a molecular basis and is often used as an empirical parameter. The purpose of this work is to reveal a correlation of chemical structure and the interaction parameter v. A novel scheme is used for a graphical representation of this correlation. The interaction parameters are calculated consistently from interfacial width values and from the compositions of coexisting phases, accessible by neutron re#ectometry. This is an important fact because interfaces might be enlarged due to capillary waves and would result in wrong values for the interaction parameter. A useful di!erential equation is presented connecting compositions of coexisting phases and interfacial pro"le. 2000 Elsevier Science B.V. All rights reserved. Keywords: Interfaces; Polymer "lms; Polymers; Re#ectometry
1. Theory The volume fraction pro"le (z) at the interface between incompatible polymers is described by the following "rst-order di!erential equation:
g
d F( )!F( ) ( ! ) "F( )! dz
!
#F( ) , with b g" , and 24 (1! )
ln (1! ) ln (1! ) F" # #s( ) (1! ), N N
* Corresponding author. Fax: #49-4152-87-1338. E-mail address: [email protected] (D.W. Schubert)
(1)
where and are the compositions of coexisting phases, v interaction parameter, b the segment length (0.73 nm used [1]) and N and N the chain length of used polymers. z is the coordinate perpendicular to the interface. Eq. (1) ensures the boundary condition d /dz"0 for the pro"le reaching the compositions of coexisting phases. The numerical treatment of Eq. (1) is very simple and enables a rapid calculation of interfacial width a for a given interaction parameter and corre' sponding coexisting phases.
2. Results For example, a result from a neutron re#ection (NR) experiment is shown (Fig. 1) utilizing a bilayer of a statistical copolymer of poly(ethylmethacrylateco-methylmethacrylate) (P(EMA -co-MMA )) and a deuterated polystyrene (PS(D)). The compositions of coexisting phases and the interface widths are obtained after annealing (1423C for 24 h) by "tting the experimental re#ection curve using a matrix formalism. Thus,
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 4 9 8 - 2
366
D.W. Schubert et al. / Physica B 276}278 (2000) 365}366
Fig. 2. Distances mirror the square root of interaction parameters at 1423C.
Fig. 1. Neutron refractive index pro"les of the PS(D)/ P(EMA -co-MMA ) bilayer sample before and after an nealing.
one calculates on the basis of the refractive index pro"le (Fig. 1) the binodal composition as "0.06$0.01 (initial pure PS(D) layer) with respect to the P(EMA co-MMA ) volume fraction. The composition of the P(EMA -co-MMA ) layer after annealing is essen tially the same as before annealing. The polymer/polymer interface is determined to 2.8$0.4 and 13.2$0.8 nm before and after annealing, respectively. NR experiments are performed at room temperature after annealing and quenching using TOREMA II at Geesthacht [1,2]. An important point is that from the interfacial width and the compositions of coexisting phases one calculates consistently the same interaction parameter v" 0.0055$0.0003 [2]. If capillary wave contributions would be important for this system a much larger interfacial width would be expected [3,4]. Comparing this interaction parameter with other studies using a novel scheme (Fig. 2), one "nds an excellent consistence with the interaction parameters between the pure components PS/PEMA, PS/PMMA and PMMA/PEMA [2]. Also shown are some other polyalkylmethacrylates, polyisopropylmethacrylate (PiPrMA), poly(n/t)butylmethacrylate (PnBMA, PtBMA) in the map with respect to their interaction parameter to PS and PMMA [1]. The basis of the scheme (Fig. 2) is given by PS and PMMA plotted at the distance of (s . Geometrically, the .1 .++ position of the polyalkylmethacrylates are given by the
intersection of two circles (centres at PS and PMMA, respectively) where the radii are given by the square root of corresponding interaction parameters. Due to experimental errors the intersection points degenerate to intersection areas. This scheme also mirrors directly the position of statistical copolymers [5]. For example, from the knowledge of the PEMA position one can estimate the position of the P(EMA -co-MMA ) to be on the connecting line between PEMA and PMMA given by its copolymer composition, in our case 0.28. The distance PEMA/P(EMA -co-MMA ) is 28% of the PEMA/ PMMA distance. This predicted position is given by the dot (Fig. 2) in the area of P(EMA -co-MMA ), and "ts nicely to the experimental area determined by analysing the interaction parameter P(EMA -co MMA )/PS(D) and P(EMA -co-MMA )/ PMMA(D) [2]. Fig. 2 reveals that the shift in compatibility increasing the length of the alkyl group is nearly `quantizeda and that compatibility is at least a two-dimensional problem [1]. References [1] D.W. Schubert, M. Stamm, A.H.E. MuK ller, Polymer Eng. Sci. 39 (1999) 1501. [2] D.W. Schubert, M. Pannek, A.H.E. MuK ller, Macromol. Symp. (2000), in press. [3] T. Kerle, J. Klein, K. Binder, Phys. Rev. Lett. 77 (1996) 1318. [4] M. Sferrazza, C. Xiao, R.A.L. Jones, D.G. Bucknall, J. Webster, J. Penfold, Phys. Rev. Lett. 78 (1997) 3693. [5] D.W. Schubert, Polymer Bull. 41 (1998) 737.
Novel map for polymer miscibility as revealed by neutron re#ectometry D.W. Schubert *, M. Pannek , A.H.E. MuK ller GKSS Research Centre, Max-Planck-Strasse, 21502 Geesthacht, Germany Macromol. Chem.II, Universita( tsstr. 30, 95440 Bayreuth, Germany
Abstract During annealing, above the glass transition temperatures the interface width between incompatible polymers increases with time, reaching an equilibrium value (typically 2 and 15 nm), which according to mean-"eld theory is determined by the Flory}Huggins}Stavermann interaction parameter v. The quantity v is a measure of polymer compatibility, although it is not well understood on a molecular basis and is often used as an empirical parameter. The purpose of this work is to reveal a correlation of chemical structure and the interaction parameter v. A novel scheme is used for a graphical representation of this correlation. The interaction parameters are calculated consistently from interfacial width values and from the compositions of coexisting phases, accessible by neutron re#ectometry. This is an important fact because interfaces might be enlarged due to capillary waves and would result in wrong values for the interaction parameter. A useful di!erential equation is presented connecting compositions of coexisting phases and interfacial pro"le. 2000 Elsevier Science B.V. All rights reserved. Keywords: Interfaces; Polymer "lms; Polymers; Re#ectometry
1. Theory The volume fraction pro"le (z) at the interface between incompatible polymers is described by the following "rst-order di!erential equation:
g
d F( )!F( ) ( ! ) "F( )! dz
!
#F( ) , with b g" , and 24 (1! )
ln (1! ) ln (1! ) F" # #s( ) (1! ), N N
* Corresponding author. Fax: #49-4152-87-1338. E-mail address: [email protected] (D.W. Schubert)
(1)
where and are the compositions of coexisting phases, v interaction parameter, b the segment length (0.73 nm used [1]) and N and N the chain length of used polymers. z is the coordinate perpendicular to the interface. Eq. (1) ensures the boundary condition d /dz"0 for the pro"le reaching the compositions of coexisting phases. The numerical treatment of Eq. (1) is very simple and enables a rapid calculation of interfacial width a for a given interaction parameter and corre' sponding coexisting phases.
2. Results For example, a result from a neutron re#ection (NR) experiment is shown (Fig. 1) utilizing a bilayer of a statistical copolymer of poly(ethylmethacrylateco-methylmethacrylate) (P(EMA -co-MMA )) and a deuterated polystyrene (PS(D)). The compositions of coexisting phases and the interface widths are obtained after annealing (1423C for 24 h) by "tting the experimental re#ection curve using a matrix formalism. Thus,
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 4 9 8 - 2
366
D.W. Schubert et al. / Physica B 276}278 (2000) 365}366
Fig. 2. Distances mirror the square root of interaction parameters at 1423C.
Fig. 1. Neutron refractive index pro"les of the PS(D)/ P(EMA -co-MMA ) bilayer sample before and after an nealing.
one calculates on the basis of the refractive index pro"le (Fig. 1) the binodal composition as "0.06$0.01 (initial pure PS(D) layer) with respect to the P(EMA co-MMA ) volume fraction. The composition of the P(EMA -co-MMA ) layer after annealing is essen tially the same as before annealing. The polymer/polymer interface is determined to 2.8$0.4 and 13.2$0.8 nm before and after annealing, respectively. NR experiments are performed at room temperature after annealing and quenching using TOREMA II at Geesthacht [1,2]. An important point is that from the interfacial width and the compositions of coexisting phases one calculates consistently the same interaction parameter v" 0.0055$0.0003 [2]. If capillary wave contributions would be important for this system a much larger interfacial width would be expected [3,4]. Comparing this interaction parameter with other studies using a novel scheme (Fig. 2), one "nds an excellent consistence with the interaction parameters between the pure components PS/PEMA, PS/PMMA and PMMA/PEMA [2]. Also shown are some other polyalkylmethacrylates, polyisopropylmethacrylate (PiPrMA), poly(n/t)butylmethacrylate (PnBMA, PtBMA) in the map with respect to their interaction parameter to PS and PMMA [1]. The basis of the scheme (Fig. 2) is given by PS and PMMA plotted at the distance of (s . Geometrically, the .1 .++ position of the polyalkylmethacrylates are given by the
intersection of two circles (centres at PS and PMMA, respectively) where the radii are given by the square root of corresponding interaction parameters. Due to experimental errors the intersection points degenerate to intersection areas. This scheme also mirrors directly the position of statistical copolymers [5]. For example, from the knowledge of the PEMA position one can estimate the position of the P(EMA -co-MMA ) to be on the connecting line between PEMA and PMMA given by its copolymer composition, in our case 0.28. The distance PEMA/P(EMA -co-MMA ) is 28% of the PEMA/ PMMA distance. This predicted position is given by the dot (Fig. 2) in the area of P(EMA -co-MMA ), and "ts nicely to the experimental area determined by analysing the interaction parameter P(EMA -co MMA )/PS(D) and P(EMA -co-MMA )/ PMMA(D) [2]. Fig. 2 reveals that the shift in compatibility increasing the length of the alkyl group is nearly `quantizeda and that compatibility is at least a two-dimensional problem [1]. References [1] D.W. Schubert, M. Stamm, A.H.E. MuK ller, Polymer Eng. Sci. 39 (1999) 1501. [2] D.W. Schubert, M. Pannek, A.H.E. MuK ller, Macromol. Symp. (2000), in press. [3] T. Kerle, J. Klein, K. Binder, Phys. Rev. Lett. 77 (1996) 1318. [4] M. Sferrazza, C. Xiao, R.A.L. Jones, D.G. Bucknall, J. Webster, J. Penfold, Phys. Rev. Lett. 78 (1997) 3693. [5] D.W. Schubert, Polymer Bull. 41 (1998) 737.