2160
J. Phys. Chem. B 2002, 106, 2160-2165
Encapsulation of Self-Assembled Bicopper Complex Filaments in Thermoreversible Gel Fibrils: Effect of the Solvent Isomer Daniel Lo´ pez† and Jean-Michel Guenet* Institut Charles Sadron, CNRS UPR 22, 6, rue Boussingault, F-67083 Strasbourg, Cedex, France ReceiVed: July 3, 2001; In Final Form: December 17, 2001
The encapsulation process of a filament-forming bicopper complex within the fibrils of an isotactic polystyrene (iPS) thermoreversible gel has been studied as a function of the solvent isomer. Differential scanning calorimetry (DSC) and small-angle neutron scattering (SANS) have been used. It is observed through the evolution of the gelation threshold and the alteration of the molecular structure of both the gel fibrils and the bicopper complex threads that the latter act as a nucleating agent for the fibrils growth in gels from iPS/trans-decalin but not in gels from iPS/cis-decalin. Molecular encapsulation of the bicopper complex filaments by a polymer sheath is therefore achieved in trans-decalin, whereas in cis-decalin, the 1-D filaments are not stable and eventually the bicopper complex crystallizes under the form of 3-D crystals. The possible origin of these differing types of behavior is briefly discussed.
Introduction Hot, low-concentrated solutions in organic solvents of copper (II) tetra-2-ethylhexanoate form viscous jellies on cooling to room temperature.1,2 This effect arises from the piling up in one dimension of the complex molecules which produces long threads similar to polymeric chains (see Figure 1). Yet, unlike covalent polymers, the interaction energy between complex molecules is about kT so that the threads continuously break up while new ones are formed with a typical lifetime of less than 1 s. These threads are described by theories developed for so-called “living” polymers.3,4 These filaments are very rigid as the estimated persistence length is larger than 15 nm.5 Apart from the “living” polymer aspect, the one-dimensional arrangement of copper atoms can be of further interest as specific magnetic properties may be observed under these conditions (spin ladders).6 We have recently devised a method to prevent the filament structures from breaking up which consists of encapsulating the bicopper complex threads in the fibrils of a thermoreversible gel from isotactic polystyrene.7 Thermoreversible gels are produced by cooling moderately concentrated polymer solutions (typically 2 to 20% w/w) to below a well-defined temperature designated as the gelation threshold.8 These gels possess a network morphology made up of interconnected fibrils.8,9,10 The mesh size of this network is located typically somewhere between 0.1 and 1 µm, whereas the fibrils possess cross-section radii in the range 1-10 nm. As only van der Waals interactions are involved both in the internal cohesion of the fibrils and in establishing connections between fibrils, these gels are thermally reversible: they can be melted and reformed at will without altering the system, and as a result can be studied by DSC. Isotactic polystyrene produces this type of gels in a large variety of solvents, of which transand cis-decalin.8 These two solvents differ only slightly at the level of their conformation and yet they produce gels of * To whom correspondence should be addressed. E-mail: guenet@ ics.u-strasbg.fr. Tel: +33 (0) 388 41 40 87. Fax: +33 (0) 388 41 40 99. † Permanent address: Instituto de Ciencia y Tecnologı´a de Polı´meros, CSIC, Juan de la Cierva, 3, E-28006 MADRID Spain.
Figure 1. Schematic drawing of a bicopper complex molecule, namely bicopper ethyl-2-hexanoate (left), and the way these molecules pile up to form long monomolecular filaments (right). Grey-filled circles stand for copper atoms, open circles for oxigen atoms and black circles for carbon atoms. For the sake of clarity, hydrogen atoms are omitted. The chemical formula is Cu2(O2C-C7H15)4.
markedly differing properties (note that there is no physical possibility of transforming the cis isomer into the trans isomer, and vice-versa). The conformation of the iPS chains constituting the fibrils has been determined by small-angle neutron scattering and found to be wormlike with a corresponding persistence length close to lp ≈ 4 nm, namely about four times larger than that observed in the usual flexible state of this polymer. Gelation occurs in this polymer through the bunching of these wormlike chains because chain-folding, as would be required for producing crystals and eventually spherulites, is precluded.11,12 In a previous paper, we have described how the bicopper complex filaments can act as a heterogeneous nucleation agent for the formation of the fibrils of the iPS thermoreversible gel in trans-decalin.7 Isotactic polystyrene and the bicopper complex form homogeneous solutions above 120 °C. On cooling such ternary solutions, the bicopper complex filaments grow first, and eventually trigger the formation of the fibrils. A composite material is thus produced wherein one monomolecular filament of the bicopper complex is encapsulated into a nanosized polymer fibril. In this paper, we report on an investigation by DSC analysis and small-angle neutron scattering on the effect of Decalin isomers (cis-decahydronaphthalene and trans-decahydronaphthalene) on the encapsulation process. We shall show that
10.1021/jp012523e CCC: $22.00 © 2002 American Chemical Society Published on Web 02/01/2002
Effect of the Solvent Isomer the encapsulation process is not favored in cis-decahydronaphthalene unlike what was reported for trans-decahydronaphthalene.
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2161 The position sensitive detector was calibrated by means of hydrogenous cis-decalin which gives off only incoherent scattering. Under these conditions, the absolute intensity, IA(q) is written
Experimental Section Materials. The hydrogenous (iPSH) and deuterated (iPSD) isotactic polystyrene samples used in this study were synthesized by the method of Natta.13 The weight-average molecular weight was found to be Mw) 427 000 g/mol with Mw/Mn) 2.5 for iPSH and Mw) 166 000 g/mol with Mw/Mn) 2.92 for iPSD as determined by self-exclusion chromatography in THF at 25 °C. The bicopper complex (copper (II) 2-ethylhexanoate) was synthesized and purified by means of a method described elsewhere.14 It will be designated as CuS8 in what follows. Hydrogenous trans-decalin and cis-decalin were purchased from Fluka and Aldrich, respectively. Deuterated trans-decalin and cis-decalin were purchased from Eurisotop (Saclay, France) and Acros, respectively. They were used without further purification. Sample Preparation and Techniques. Differential Scanning Calorimetry (DSC). Homogeneous solutions were prepared by heating a mixture of iPSH, bicopper complex and solvent at 150 °C in hermetically closed test tubes. Gels were formed by subsequent quenching of these solutions at room temperature. Pieces of gel, approximately 15 mg, were then transferred into aluminum DSC pans that were hermetically sealed. Thermal analysis was carried out with a DSC 30 instrument from METTLER equipped with the TA9000 pilot system and a TA72 software for processing the raw data. Prior to any measurement, the gels were melted in the DSC pans in order to erase all structures. Samples were then scanned from 150 to -70 °C at different cooling rates: 15, 10, 5 and 2.5 K min-1. Small-Angle Neutron Scattering (SANS). The experiments were performed on the PAXE camera located at the Laboratoire Le´on Brillouin (LLB) (CEN Saclay, France). A wavelength of λm ) 0.6 nm was used with a wavelength distribution characterized by a full width at half-maximum, ∆λ/λ, of about 10%. Neutron detection and counting was achieved with a built-in two-dimensional sensitive detector composed of 64 × 64 cells (further details are available on http://www-llb.cea.fr). By varying the sample-detector distance, the available q-range was 0.1 < q (nm-1) < 2.5 where q ) (4π/λ) sin (θ/2), θ being the scattering angle. Gel samples were prepared directly in sealable quartz cells from HELLMA of optical paths of 1 and 2 mm. After introducing appropriate mixtures of the different components, the system was heated to 150 °C to obtain homogeneous solutions. Gelation was achieved by a quench to 0 °C. By toying with the different isotopic-labeled components the nanostructure of either the polymer gel or the bicopper complex can be determined. (i) Polymer gel structure: a match of the coherent scattering amplitude of the bicopper complex can be achieved by using a solvent isotopic mixture of deuterated (tdecaD) and hydrogenous trans-decalin (tdecaH) where tdecaD/ tdecaH ) 8/92 in v/v or a mixture of deuterated (cdecaD) and hydrogenous cis-decalin (cdecaH) where (cdecaD/cdecaH ) 8/92 in v:v) leaving only the coherent intensity arising from the deuterated polymer gel. (ii) Bicopper complex structure: A highly deuterated solvent mixture (tdecaD/tdecaH) 91/9 in v/v or cdecaD/ cdecaH) 89.5/10.5 in v/v) was used so as to match the coherent scattering amplitude of the deuterated polymer gel, thus leaving only the coherent scattering arises from the bicopper complex. The incoherent scattering due to the hydrogenous complex has been calculated by means of a relation established experimentally by Fazel et al.15
IA(q) ) IN(q)/K
(1)
in which IN(q) is the intensity obtained after background subtraction, transmission corrections and detector normalization, and K is a constant which reads
K)
4π (ai - yas)2δdecTdecNA g(λm)(1 - Tdec)mi2
(2)
in which ai is the coherent scattering amplitude of either the polymer or the bicopper complex, and as the scattering coherent amplitude of the solvent mixture, δdec and Tdec the thickness and the transmission of the calibration cis-decalin sample, mi the molecular weight of the scattering unit (polymer or bicopper complex), and g(λm) a constant which is camera-dependent and was measured by using Cotton’s method.16 The intensities are expressed in dimensionless units. Results As has been emphasized in the Introduction section, the gelation behavior of isotactic polystyrene is very sensitive to the isomer of Decalin. Gels with differing properties (thermal, rheological,..) are obtained whether cis- or trans-decalin is used. This essentially stems from the occurrence of polymer-solvent compounds,8,17,18,19 whose stoichiometry depends on the isomer (≈ 2 solvent molecules /monomer in cis-decalin and ∼1 solvent molecule/monomer in trans-decalin). The isomer type also affects the formation of the bicopper complex threads as observed from rheological experiments: the viscosity of the jellies obtained with cis-decalin is much lower than that in transdecalin.20 In a recent paper,5 Lopez and Guenet have suggested that these jellies consist actually of a mixture of very long filaments and of very short filaments. The lower viscosity in cis-decalin is therefore attributed to the late appearance of very long filaments at concentration much higher than in transdecalin. So far, the reason for these differing types of behavior of the bicopper complex in either isomer is not known. As expected, and as will be discussed in what follows, the isomer effect is also observed for ternary systems iPS/CuS8/decalin. Thermal Behavior. As has been reported in a previous paper, the variation of the gelation threshold has been studied as a function of the bicopper complex fraction in the ternary system.7 The gelation threshold of pure isotactic polystyrene solutions in trans-decalin stands close to 20 °C and to 15 °C in cis-decalin8 for the polymer concentrations under consideration. In Figure 2 is represented the relative evolution of the gelation threshold (∆Tgel ) Tgel - Tgelo) for the ternary systems iPS/ CuS8/cis-decalin as a function of the bicoppper complex molar fraction fCu after proper extrapolation to zero cooling rate. The gelation threshold is nonvariant for low bicopper contents, whereas it significantly increases above some critical mole fraction f /Cu. This behavior is quite conspicuous for the lowest polymer concentration (Cpol ) 0.02 g/cm3). The critical mole fraction f /Cuis dependent upon polymer concentration: the larger the polymer concentration the smaller the critical mole fraction. Figure 3 highlights that the behavior in cis-decalin is markedly different from that previously reported in trans-decalin. In the latter ∆Tgel is first seen to increase and then levels off at another
2162 J. Phys. Chem. B, Vol. 106, No. 9, 2002
Figure 2. Relative variation of the gelation threshold of iPS, ∆Tgel in cis-decalin as a function of the bicopper complex mole fraction fCu with respect to the polymer. (]) Cpol ) 0.02 g/cm3; (b) Cpol ) 0.04 g/cm3; (O) Cpol ) 0.08 g/cm3.
Figure 3. Relative variation of the gelation threshold of iPS, ∆Tgel as a function of the bicopper complex mole fraction with respect to the polymer. Cpol ) 0.04 g/cm3; (b) gels in cis-decalin and (9) gels in trans-decalin.
Figure 4. Relative variation of the gelation threshold of iPS, ∆Tgel as a function of the bicopper complex concentration. in trans-decalin (]) Cpol ) 0.04 g/cm3; ([) Cpol ) 0.08 g/cm3; in cis-decalin (+) Cpol ) 0.02 g/cm3, (0) Cpol ) 0.04 g/cm3 (O) Cpol ) 0.08 g/cm3.
critical mole fraction f /Cu. The increase of the gelation threshold in trans-decalin was assigned to a heterogeneous nucleation effect, whereas the leveling-off was shown to be due to an additional phase separation.7 To be sure, the plateau regime is reached when the bicopper complex filaments and the polymer are no longer compatible and further addition of complex is merely rejected into a polymer-poor phase where it becomes useless for nucleation purposes. The behavior observed with cis-decalin strongly suggests that the increase of the gelation threshold in this solvent beyond f /Cu, as opposed to what is seen for trans-decalin, has most probably another origin than a heterogeneous nucleation effect. The differences observed between the two isomers are certainly connected with their differing behavior toward both the polymer and the complex. Plotting the results as a function of the concentration of CuS8 instead of the mole fraction (Figure 4) reveals two salient features: (i) the critical concentration C/Cu at which the leveling-off is observed in trans-decalin is virtually independent of
Lo´pez and Guenet
Figure 5. Relative variation of the gelation threshold of iPS, ∆Tgel as a function of the bicopper complex molar fraction with respect to the polymer’s fCu in trans-decalin: (]) Cpol ) 0.04 g/cm3, ([) Cpol ) 0.08 g/cm3; (9) Cpol ) 0.16 g/cm3.
the polymer concentration, whereas the magnitude of ∆Tgel is; (ii) the behavior in cis-decalin is totally independent of bicopper complex concentration, namely both the critical concentration C/Cu and the ∆Tgel do not depend on polymer concentration. The critical bicopper complex concentration CCu* seems to be slightly lower in cis-decalin than in trans-decalin. If, at a given polymer concentration in trans-decalin, the increase in gelation threshold does arise from heterogeneous nucleation, then the relevant parameter is the number of bicopper complex “nuclei” per unit mass of polymer, a parameter directly proportional to the molar fraction of bicopper complex with respect to the polymer. As a matter of fact, it has been shown by Fillon et al.19,20 that the crystallization temperature Tc as determined by DSC depends directly upon the number of nuclei per unit volume. Plotting ∆Tgel vs fCu (Figure 5) does yield an universal behavior (the plateau regime is not considered as phase separation comes into play). The absence of an universal behavior for a similar plot in cis-decalin (Figure 2) definitely points out to an effect differing from heterogeneous nucleation. In trans-decalin, the behavior of the bicopper complex, particularly the growth of the filaments mean length when increasing its concentration, is inclined to determine the terminal behavior. In principle, the average length 〈L〉 of the filaments is supposed to increase when increasing the bicopper complex concentration as shown in the theory developed by Cates3,4 for “living” systems. This length is given through
∝ φR exp
Escis 2kT
(3)
where R is an exponent which depends on the filament statistics (generally 0.5 e R e 0.6), and Escis the scission energy. The growth of the filaments beyond some critical mean length * is likely to modify the entropy of the system which should trigger the mutual incompatibility between the polymer and the bicopper complex filaments.23 The observation of a plateau regime seen in trans-decalin, and correspondingly, the occurrence of a phase separation, is most probably directly related to this effect. Conversely, accounting for the behavior in cis-decalin is not so straightforward. As will be seen below from the study of the molecular structure, heterogeneous nucleation is probably not the driving phenomenon in the increase of the gelation threshold beyond CCu*. Molecular Structure. As has been emphasized above, the degree of solvation of the chains constituting the fibrils of the gel differs whether cis- or trans-decalin are used.8 This has a direct effect on the molecular structure of the gels as revealed by small-angle neutron scattering. In Figure 6 are plotted the
Effect of the Solvent Isomer
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2163
Figure 6. Scattering curve in q2IA(q) vs q for the binary systems (gels) in trans-decalin ([) and in cis-decalin (b). In both cases Cpol ) 0.04 g/cm3. The solid line stands for the “single” chain behavior for qlp > 1 (see relation 4).
Figure 7. Scattering curve in q2IA(q) vs q for systems in cis-decalin. The binary system (b); the ternary system where fCu ) f /Cu (9) and the ternary system where fCu ) 2f /Cu (O). Cpol ) 0.04 g/cm3 in all cases.
intensities for gels where all the chains are deuterium-labeled. In the low-q region, the scattered intensity is directly related to the fibrils cross-section, hence the prominent upturn. In this q-range the scattering curve can be fitted with a model where the fibrils have polydisperse cross-sectional radii24 (see below). Conversely, at larger q one observes the “single” chain scattering which indicates that the chains are significantly spaced apart. This is directly related to the solvation shell around the polymer chains. For qlp > 1, the intensity can be fitted with
J21(qrH)
q IA(q) ) πµLq 2
q2rH2
(4)
in which rH is the cross-sectional radius of the helical form involved and µL the mass per unit length. Both parameters correspond to a helical conformation close to the usual 31 helix(13) (µL ) 520 g/nmxmol; rH ) 0.4 nm). Interestingly, the “single” chain behavior is observed at q-values lower for cis-decalin than for trans-decalin. This simply means that chains are separated by a larger distance in the former solvent, a conclusion in agreement with the higher solvation degree as derived from the temperature-concentration phase diagrams.8 To investigate the structure of the polymer or of the bicopper complex in the ternary systems, we have used isotopic mixtures of solvents so as to match the coherent scattering of either compound (for details, see Experimental section). Polymer in the Ternary System. Typical scattering curves obtained for increasing amounts of bicopper complex are drawn in Figure 7 by means of a Kratky-representation (Cpol ) 0.04 g/cm3). Three curves are plotted standing for fCu ) 0, fCu ) f /Cu, and fCu ) 2f /Cu. For the sake of comparison, the counter-
Figure 8. Scattering curve in q2IA(q) vs q for systems in trans-decalin (from ref 6). The binary system (+); the ternary system where fCu ) f /Cu (0) and the ternary system where fCu ) 2f /Cu (b). Cpol ) 0.04 g/cm3 in all cases.
part systems in trans-decalin7 are drawn in Figure 8 (the solid line stands for a fit achieved with a molecular model where 4 extended polymer chains wrap around 1 CuS8 filament. Details are available in ref 7). In the case of cis-decalin, the upturn at small q-values never vanishes upon addition of bicopper complex unlike what is seen for trans-decalin. On the contrary, this upturn becomes more pronounced for the ternary system than for the pure polymer gel. Also, it increases for fCu ) f /Cu, and decreases for fCu ) 2f /Cu but still having a higher intensity than for fCu ) 0. The results in cis-decalin are worth analyzing further by considering a gel with cross-section polydisperse fibrils. Using a distribution function of the type w(r) ≈ r-λ (0 < λ < 3) with two cutoff radii, rmin and rmax, a transitional q-range can be defined where the product qr can take any value.24 The intensity reads
q4IA(q) )
[
4Fπ2Cpol 1 A(λ)qλ W λπrλ
max
]
(5)
where F is the fibril density, and W and A(λ) are given through
W)
∫rr
max
w(r)dr
(6)
min
3-λ ( 2 ) A(λ) ) λ+1 λ+3 λ+1 2 Γ( Γ Γ 2 ) ( 2 ) ( 2 ) Γ(λ)Γ
(7)
λ
where Γ is the Gamma-function. The present scattering curves suggest that λ > 1 and also that rmax is very large. Under these conditions, 5 reduces to λ q4IA(q) ) 4Fπ2CpolA(λ)λrλ-1 min q
(8)
which is convenient to plot in a logarithmic scale (see Figure 9). As is apparent from Figure 9 the same behavior is observed for fCu ) 0 and fCu ) 2f /Cu that both yield λ ) 1.8 ( 0.05 (for fCu ) f /Cu relation 8 is not fulfilled so that any direct comparison is worthless). Assuming that everything else remains constant in relation 8, it is observed that rmin increases by about 3-fold. In no case does the fibrils cross-section decay upon addition of bicopper complex in iPS/CuS8/cis-decalin ternary systems. This again suggests that a heterogeneous nucleation process has to be discarded.
2164 J. Phys. Chem. B, Vol. 106, No. 9, 2002
Lo´pez and Guenet
Figure 9. Scattering curve in log q4IA(q) vs log q for systems in cisdecalin. Only the low-angle data are plotted (q < 1 nm-1). Cpol ) 0.04 g/cm3 in all cases: the binary system (b); the ternary system for fCu ) 2f /Cu (O).
Figure 10. Scattering curves for the bicopper complex in cis-decalin systems plotted by means of a Kratky representation (q2IA(q) vs q). Cpol ) 0.02 g/cm3; nascent ternary system for fCu ) f /Cu (O), the aged ternary system for fCu ) f /Cu (b); and for fCu ) 2f /Cu (9).
Bicopper Complex in the Ternary System. As has been shown and discussed in a previous paper,7 the bicopper complex filaments are encapsulated in the gel fibrils prepared from transdecalin for fCu ) f /Cu. The scattering intensity is then written
q2I(q) ∝ CCuµL ×
4J21(qrc) q2r2c
[
× πq -
2
]
(9)
in which µL and rc are the mass per unit length, the crosssectional radius, and 〈L〉 the mean-length of the bicopper complex filaments, respectively. Conversely for fCu ) 2f /Cu the scattered intensity has been accounted for by considering a two-population system: encapsulated monomolecular filaments and three-dimensional objects. The intensity is then written
4J21(qrc) S 2 × πq q I(q) ∝ X 2 + (1 - X)CCuµL × 2 2 Vq q rc (10) 2
[
]
in which X is the fraction of 3-D objects, S and V their surface, and their volume. The three-dimensional objects are CuS8 crystals grown from the complex-rich phase. Typical scattering curves obtained for the bicopper complex in the ternary system iPS/CuS8/cis-decalin are drawn in Figure 10 (here Cpol ) 0.02 g/cm3). For fCu ) f /Cu the result depends on the aging time of the sample. In a nascent sample, a curve corresponding to monomolecular filaments is observed (relation 9), whereas aging for a few hours gives rise a prominent upturn
at low-q values together with a significant decrease of the signal at high-q values (relation 10). Applying relation 10 suggests that 2/3 of the filaments have turned into 3-D crystals. This clearly means that most of the filaments are unstable, which precludes the occurrence of an efficient encapsulation. This outcome is in agreement with the DSC findings. For fCu ) 2f /Cu, the upturn is seen independent of the aging time, and again the scattered intensity can be fitted with relation 10. More than 2/3 of the bicopper complex do not form filaments, and are therefore not encapsulated. As was surmised in the section devoted to thermal properties, the increase of the gelation threshold does not originate in a heterogeneous process iPS/CuS8/cis-decalin. Discussion Although there are now a series of strong arguments for postulating the occurrence of a heterogeneous nucleation effect in ternary systems prepared with trans-decalin, this phenomenon does not take place in ternary systems consisting of cis-decalin. In particular, the increase of the fibrils cross-section in ternary cis-decalin systems is in conflict with this mechanism. The origin of the increase of the gelation point in iPS/CuS8/cisdecalin systems should be sought in another effect. Possibly, the two different types of behavior are determined by the piling process in either isomer. As was stressed above, long filaments are formed in trans-decalin for concentration as low as Cfil ) 0.5% as opposed to what is observed in cis-decalin where this concentration is much larger (Cfil ) 5-7%). Accordingly, the ternary system in trans-decalin is reminiscent of a mixture of homopolymers in a solvent, whereas in cis-decalin, it can be schematically viewed as a polymer in a mixture of solvents. In trans-decalin, the two polymers can be miscible up to a certain composition23 above which phase separation is to occur. Conversely in a mixture of solvents the behavior of the polymer is highly dependent upon the interaction between both solvents. In this respect, it is known that a gelation/melting point will be significantly affected as can be can be illustrated on a qualitative basis by considering Flory’s theory.24 For ternary systems, polymer crystals/solVent 1/solVent 2, the melting point variation as a function of solvent composition at constant polymer volume fraction is written25,26
[
RVp φ2 1 1 - 1 ) φ1 + + χ12φ1φ2 1,2 ∆H V x2 Tm Tm p 1 φ2 χ1pφ1 + χ2p + 1 (1 - φp) + χ1p(1 - φp)2 (11) x2
(
)
]
1 in which T1,2 m and Tm are the melting temperature in the binary solvent and in solvent 1 (namely Decalin) at a given polymer volume fraction, V1 and Vp the molar volumes of solvent 1 and of the polymer, ∆Hp the melting enthalpy of the polymer crystals, R the gas constant, χij the different interaction parameters, x2 the ratio of the molar volume of solvent 2 to solvent 1, and φi the different volumes fractions related through φ1 + φ2 + φp ) 1. For the sake of simplicity, we shall use the following approximations: φ1 ≈ 1, and 1 - φp ≈ 1. Relation 11 reduces to
RVp φ2 1 1 ) × [1 + x2χ12 - χ2p] T1,2 T1m ∆HmV1 x2 m
(12)
Effect of the Solvent Isomer
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2165
From relation 12, it is clear that increasing φ2 will remain constant or increase T1,2 m if
1 + x2χ12 - χ2p e 0
(13)
As x2 ≈ 5, it suffices that χ12 be slightly negative (i.e., strong interaction between cis-decalin and the bicopper complex) to fulfill 13. This means that a mixture of solvents can be a poorer solvent than each of its constitutents provided these constitutents display strong affinity for one another.26 To be sure, the system iPS/CuS8/cis-decalin cannot be strictly described by relation 8 because the bicopper complex molecules are not individually dispersed as is expected from the derivation of the theory but form short filaments. The above theory is therefore only useful for a qualitative approach of the problem. Concluding Remarks The results presented herein show the decisive role of the solvent isomer in the encapsulation process. Although this process occurs in systems prepared from trans-decalin solution through heterogeneous nucleation, it is hampered in those prepared from cis-decalin. These outcomes arise most probably from the differing intercations between the bicopper complex and either Decalin isomer. As with iPS chains in the gel state, this effect is likely to be due to some molecular recognition process. Additional efforts should be accomplished in this way in order to account for the discrepancies observed. Acknowledgment. D. Lo´pez is indebted to the European Union for a postdoctoral grant in aid (TMR Program). The authors are grateful to Dr. A. Bruˆlet (CEN Saclay) for experimental support on PAXE camera and to Odile GAVAT for the synthesis of the bicopper complex.
References and Notes (1) Terech, P.; Maldivi, P.; Guenet, J. M. Europhys. Lett. 1992, 17, 515. (2) Dammer, C.; Terech, P.; Maldivi, P.; Guenet, J. M. Langmuir 1995, 11, 1500. (3) Cates, M. E. Macromolecules 1987, 20, 2289. (4) Cates, M. E. J. Phys. France 1988, 49, 1593. (5) Lopez, D.; Guenet, J. M. Macromolecules 2001, 34, 1076. (6) Sagi, J.; Affleck, I. Phys. ReV. B 1996, 53, 9188. (7) Lopez, D.; Guenet, J. M. Eur. Phys. J. B 1999, B12, 405. (8) Guenet, J. M. ThermoreVersible Gelation of Polymers and Biopolymers; Academic Press: London, 1992. (9) Atkins, E. D. T.; Hill, M. J.; Jarvis, D. A.; Keller, A.; Sarhene, E.; Shapiro, J. S. Coll. Polym. Sci. 1984, 262, 22. (10) Sugiyama, J.; Rochas, C.; Turquois, T.; Taravel, F.; Chanzy, H. Carbohydr. Polym. 1994, 23, 261. (11) Reidy, M. P.; Green, M. M. Macromolecules 1990, 29, 175. (12) Yue, S.; Berry, G. C., Green, M. M. Macromolecules 1996, 23, 4225. (13) Natta, G. J. Polym. Sci. 1955, 16, 143. (14) Martin, R. L.; Waterman, H. J. Chem. Soc. 1957, 2545. (15) Fazel, N.; Bruˆlet, A.; Guenet, J. M. Macromolecules 1994, 27, 3836. (16) Cotton, J. P. In Neutron, X-ray and Light Scattering; Lindner, P., Zemb, T., Eds.; Elsevier: New York, 1991. (17) Nakaoki, T.; Kobayashi, M. J. Mol. Struct. 1991, 242, 315. (18) Itagaki, H.; Takahashi, I. Macromolecules 1995, 28, 5477. (19) Itagaki, H.; Nakatani, Y. Macromolecules 1997, 30, 7793. (20) Carl, P. DEA report, 1995 Louis Pasteur UniVersity, Strasbourg. (21) Fillon, B.; Wittmann, J.-C.; Lotz, B.; Thierry, A. J. Polym. Sci. Polym. Phys. 1993, 31, 1383. (22) Fillon, B.; Lotz, B.; Thierry, A.; Wittmann, J.-C J. Polym. Sci. Polym. Phys. 1993, 31, 1395. (23) See, for instance: Hsu, C. C.; Prausnitz, J. M. Macromolecules 1974, 7, 320; Zeeman, L.; Patterson, D. Macromolecules 1972, 5, 513; HSu, C. C.; Patterson, D. Macromolecules 1977, 10, 708. (24) Guenet, J. M. J. Phys. II (Paris) 1994, 4, 1077. (25) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953. (26) Ramzi, M.; Rochas, C.; Guenet, J. M. Macromolecules 1996, 27, 4668.
