Structural Investigation of Carbosilane Liquid Crystalline Dendrimers

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J. Phys. Chem. B 2008, 112, 16346–16356

Structural Investigation of Carbosilane Liquid Crystalline Dendrimers R. M. Richardson* H. H. Wills Physics Laboratory, UniVersity of Bristol, Bristol, BS8 1TL. U.K.

E. V. Agina, N. I. Boiko, and V. P. Shibaev Chemistry Department, Moscow State UniVersity, Moscow, 119992, Russia

I. Grillo Institut Laue LangeVin, 6 Rue Jules Horowitz, BP 156, 38042 Grenoble, Cedex 9, France ReceiVed: July 1, 2008; ReVised Manuscript ReceiVed: October 29, 2008

X-ray and neutron scattering investigations have been made on two series of liquid crystal dendrimers. The low generations (first to fourth) predominantly show smectic phases. The fifth generation shows a tendency to form columnar phases and two different types have been observed. The transition from smectic to columnar has been explained in terms of the distance between the dendritic core and the mesogenic units. As the generation number is increased, the distance increases until it becomes greater than the maximum length of the flexible spacers causing a change in molecular shape and the formation of columnar phases. Although the materials are nearly monodisperse, the small variation in the number of mesogens per molecule gives rise to some subtle structural effects. Two coexisting structures have been observed over large temperature ranges in some materials and small angle neutron scattering indicates that there is some microphase segregation which is a reversible function of temperature. Introduction Recently, liquid crystalline (LC) dendrimers have attracted the attention of researchers working on the chemistry and physics of liquid crystals, polymers, and self-assembly. This interest arises from the search for new materials for nanotechnology. Molecular particles with dimensions of a few nanometers whose ordering and properties may be changed by the action of external forces are required. LC dendrimers which combine structural units capable of LC phase formation (mesogenic groups) with a regular dendritic superbranched structure and monodispersity could fulfill these requirements. Carbosilane LC dendrimers are of particular interest because of their kinetic and thermodynamic stability and the wide range of possible molecular architectures due to a specific chemical reaction of silicon.1-7 The unusual structure of dendrimers with terminal mesogenic groups can lead to a hierarchy of LC dendritic structures that is not typical of other LC systems. For example, LC dendrimers can form both lamellar smectic mesophases and different types of columnar mesophases. X-ray investigations of these LC dendrimers have revealed complicated nanostructural organization. It has been shown that the dendrimers of the low generations (1-3) form only lamellar phases while the dendrimers of the high generations (4-5) can form both lamellar and columnar mesophases.8-10 The different structures shown by some LC dendrimers imply that the overall shape of the molecule changes. Unfortunately, this information cannot be obtained directly from the X-ray diffraction results and so we decided to undertake a new investigation using the small angle neutron scattering (SANS) technique in order to determine the shape of LC dendrimer molecules in different mesophases. * To whom correspondence should be addressed.

This technique has given single molecule quantities such as orientational order parameters in calamitic phases11,12 and the backbone dimensions in side chain liquid crystal polymers.13 Thus the original aim of this work is to study shapes, sizes, and packing of carbosilane LC dendrimers in different mesophases depending on their generation number and the chemical nature of the terminal mesogenic groups using X-ray and neutron scattering techniques. In fact, the determination of the shape of single molecules was not achieved because of an unexpected segregation effect. Instead, a new insight into the susceptibility of nearly monodisperse dendrimer systems to segregate has been gained and this is discussed fully in later sections. Synthesis and Phase Behavior of Liquid Crystal Dendrimers Because of the SANS requirement for scattering length density contrast, carbosilane LC dendrimers of generations 1-5 were synthesized with protonated and deuterated terminal mesogenic groups based on p-methoxybenzoic and p-butoxybenzoic acids. We refer to these as the “Anis series” and the “But series”, respectively. In both cases, only the outer phenyl ring was deuterated giving four deuterium atoms per mesogenic unit. Synthesis. All carbosilane LC dendrimers in question were synthesized using standard techniques elaborated earlier.14 The chemical structures of all the dendrimers synthesized are presented in Figure 1. They consist of a carbosilane dendritic core with mesogenic units attached at the periphery via flexible spacers. Deuterated samples were synthesized by the same method but using completely deuterated hydroquinone as a precursor.14 The synthesized dendrimers were purified using semipreparative GPC. To prevent further cross-linking of the dendritic molecules, the final stage was evaporation from

10.1021/jp805769w CCC: $40.75  2008 American Chemical Society Published on Web 12/02/2008

Carbosilane Liquid Crystalline Dendrimers

J. Phys. Chem. B, Vol. 112, No. 51, 2008 16347

Figure 1. The chemical structure of the LC dendrimers of the 1-5th generation.

toluene. The structure and purity of all dendrimers synthesized for this work were checked by NMR 1H-spectroscopy and GPCanalysis. The polydispersity index (Mw/Mn) deduced from GPC was typically 1.03, suggesting that the materials should be regarded as pure compounds rather than polydisperse polymers. In regard to deuterated dendrimers, the absence of the back deuteroexchange during modification of the mesogenic groups was confirmed by NMR spectroscopy. For this purpose, the ratio of signals corresponding to the protons of the phenol ring and the protons of butoxybenzoic acid was quantified. For the final dendrimers, the degree of replacement of corresponding protons with deuterium was 97%. Phase Behavior. The phase behavior and thermodynamic properties of the synthesized dendrimers were studied by differential scanning calorimetry (DSC), polarizing optical microscopy (POM), and X-ray diffraction. It should be noted that phase transition temperatures and enthalpies were found to be the same for protonated and deuterated dendrimers within the precision of DSC and POM measurements (Figure 2, Table 1). Phase Structure. The diffraction from all the LC dendrimers samples was recorded using small-angle X-ray diffraction apparatus at Bristol University. This uses copper KR radiation from a 2 kW sealed tube with a pyrolytic graphite monochromator and a nickel filter. The radiation is detected by an area detector.15 In addition, the diffraction patterns of some materials were recorded using the D22 small angle neutron scattering apparatus16 at ILL, Grenoble, and the LOQ apparatus17,18 at ISIS. Aligned monodomain samples were prepared by cooling the material in a 9.4 T magnetic field from the isotropic phase. For both series, the lower generations (1-4) showed the equally spaced layer reflections expected from a smectic phase. Figure 3 shows small-angle scattering from the g3-But dendrimer where it can be seen that the layers have aligned perpendicular to the field. The in-plane scattering occurred at higher angles, corresponding to a distance of about 4.5 Å-1.

Figure 2. DSC curves of LC dendrimers gn -Anis (a) and gn-But (b).The number near the curve corresponds generation number.

This scattering was diffuse, indicating disordered packing of the mesogenic units as in a low molar mass Sm A or Sm C. The macroscopic alignment appears to be greater at higher temperatures. Figure 4 shows the layer reflections from the g1-

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Richardson et al.

TABLE 1: Phase Transition Temperatures and Enthalpies of LC Dendrimers from DSC and Polarizing Optical Microscopy Data phase transition temperatures, °C and enthalpies, J/g (in parentheses) compound

protonated mesogenic groups

deuterated mesogenic groups

H-Si-Und-But G-1(Und-But)8 G-2(Und-But)16 G-3(Und-But)32 G-4(Und-But)64 G-5(Und-But)128 H-Si-Und-Anis G-1(Und-Anis)8 G-2(Und-Anis)16 G-3(Und-Anis)32 G-4(Und-Anis)64 G-5(Und-Anis)128

Cr 29.7 (19.6) SmA 64 N 69.0 (9,4) I Cr 35.3 (16.5) SmA 101.6 (11.3) I Cr 19.3 (8.2) SmA 103.5 (9.6) I Cr 20.0 (8.2) SmA 108.3 (7.7) I Cr 22.6(6.7) SmA 117,0 (6.6) I Cr 22.7 (5.8) Drec 90 Dhex 140 (6.3) I Cr1 36(8.8) Cr2 48.6 (37.0) SmA 59(9.1) I g 10 Cr1 22(0.8) Cr2 30(13.1) SmC 52 SmA 58(6.1) I g 8 CrK 25(9.3) SmC 64 SmA 70 (5.3) I g -13 Cr2 10(5.4) SmC 65 SmA 79.5 (5.0) I Cr2 8(5.1) SmC 69(2.0) SmA 77.5(2.2) I g -18 Cr2 0(2.4) SmC 50 Drec 95 (3.6) I

Cr 27.7 (19.1) SmA 64 N 67.6 (9,2) I Cr 34.1 (15.9) SmA 102.9 (11.1) I Cr 21.0 (8.0) SmA 102.5 (9.5) I Cr 21.1 (8.5) SmA 108.6 (7.8) I Cr 21.2(6.0) SmA 118,4 (6.4) I Cr 24.4 (5.5) Drec 90 Dhex 141 (6.2) I Cr1 34(8.2) Cr2 47 (38.0) SmA 58.4(9/0) g 10 Cr1 24(0.9) Cr2 29(12.0) SmC 52 SmA 59(6.7) I g 10 Cr 27(8.7) SmC 63.5 SmA 70.8 (4.9) I g -11 Cr2 8 (4.7) SmC 65.5 SmA 79.8 (5.0) I Cr2 9.5(5.8) SmC 67.9(2.0) SmA 78.1(2.2) I g -15 Cr2 2(2.7) SmC 50 Drec 96.2 (3.7) I

Anis dendrimer. It is the exception in that the layers have formed with their normals tilted by 37° with respect to the aligning field. This is a positive indication of a tilted smectic phase such as a Sm C, where the mesogenic units rather than the layer normals may align with the field and it supports the assignment of Sm C to some of the lamellar phases of the Anis series of dendrimers on the basis of microscopy studies. To determine the layer spacing accurately, the scattered intensity was regrouped into a profile of intensity versus scattering vector, Q. The layer spacings have been calculated from the center of gravity of the first order reflection using d ) 2π/Q001. The resulting spacings in Figure 5 show an increase of ∼2 to 3 Å for each generation, which is consistent with the increased volume of the dendritic core. The layer spacings of the But series are slightly less than for the Anis series. This is surprising since the mesogenic units of the But series are larger but it could result from stronger orientational order of the Anis series mesogenic units or a greater degree of interdigitation between the But mesogenic units. The smectic layer spacing is generally less at lower temperatures. This probably accounts for the poor alignment seen in Figure 3 at low temperatures. An aligned

Figure 3. SAXS from g3-But LC dendrimer cooled from isotropic phase in a 9.4 T magnetic field then reheated to (a) 25 °C, (b) 50 °C, (c) 75 °C, and (d) 100 °C.

monodomain is formed at the isotropic to smectic transition and at lower temperatures the reduction in the smectic layer spacing causes the layers to undulate in order to fill the volume. The layer spacings for the But series showed a small increase with temperature which is a very weak suggestion that they might be SmC. However, since the “four spot” pattern was not observed and there was no microscopic evidence to suggest a tilted phase, the lamellar phases of the But series of dendrimers have been assigned as SmA. For the g3-But dendrimer, there are additional peaks corresponding to hkl of 001/2. They appear most strongly at higher temperatures (for example, Figure 3d) and persist into the isotropic phase when the 001 peaks have disappeared. Thus they are caused by a separate minor phase with approximately double the layer spacing coexisting with either the normal smectic phase or the isotropic phase. This unusual phenomenon suggests a stable bilayer structure has formed in this dendrimer, but its structure has not been elucidated in more detail. The fifth generation of both series showed a different diffraction pattern at some temperatures. In addition to the row of equally spaced layer reflections along the meridian, there were additional reflections. For the g5-Anis dendrimer, at temperatures between 60 and 90 °C, the Bragg peaks (indexed in Figure 6) were consistent with a simple two-dimensional rectangular lattice with dimensions a ∼ 40 Å and c ∼ 52 Å, which is similar to that observed for a cyanobiphenyl LC dendrimers of the fifth generation.7 For the cyanobiphenyl LC dendrimers, no peaks associated with periodicity in the third dimension were found despite an extensive search using synchrotron radiation, and this

Figure 4. Neutron diffraction from the g1-Anis LC dendrimer at 20 °C after cooling from the isotropic phase in a magnetic field.



Figure 7. SANS from magnetically aligned g5-But at (a) 100 °C and (b) 140 °C measured on the LOQ instrument. The peaks appear broad because of the relaxed resolution (5%) of the instrument. The lattice parameters have been calculated from SAXS data.

Figure 8. Schematic views of the columnar phase for the fifth generations: (a) simple rectangular network formed by the g5-Anis dendrimer and (b) the face-centered rectangular network formed by the g5-But dendrimer. The columns are perpendicular to the page.

Figure 5. The d-spacings corresponding to the main peaks for (a) the Anis series and (b) the But series of dendrimers. The rectangular lattice parameters a and c for the fifth generation dendrimers are shown in (c).

Figure 6. The SAXS from magnetically aligned g5-Anis LC dendrimer at about 80 °C.

confirmed the columnar structure of the phase. For the g5-But dendrimers at temperatures up to 90 °C, there are also additional peaks (indexed in Figure 7a) which are also consistent with a two-dimensional rectangular lattice but in this case, alternate peaks are absent indicating a face-centered lattice. At higher

temperatures, these became six equal reflections on a hexagon as shown in Figure 7b. The diffraction from the low temperature phase corresponds to a face-centered rectangular cell (a ∼ 45 Å, c ∼ 110 Å) while the upper phase is clearly hexagonal (c ) 3a ) 88 Å at 140 °C). The structures formed by both g5 dendrimers are believed continuous in the third dimension (since no hkl peaks with k > 0 are seen) so the symmetry is rectangular columnar. They are illustrated schematically in Figure 8 and the temperature-dependent cell dimensions are shown in Figure 5c. One sample of the g5-But dendrimer showed both these structures coexisting at temperatures of 50 °C and below. This suggests that the free energies of the two structures are similar and that small differences in the molecular structure (for instance incomplete and complete addition of the mesogenic units) might influence the system to form one or other of them. Explanation of Smectic to Columnar Transition. Smectic phases with disordered layers are often formed by liquid crystal dendrimers19,20 butend-groupinteractionsandmesogenpacking21-23 may favor other structures. The length of the flexible chains in a complex molecule may be a sensitive parameter.24 For liquid crystal dendrimers, it has been recognized that the formation of smectic phases becomes less likely for higher generations because the flexible spacers becomes overstretched.25 This may cause different structures to occur for higher generation numbers.7,26 The X-ray results from the Anis and But series do indeed suggest that the molecules for generations 1-4 may be accommodated in a simple smectic structure because each molecule can adopt a roughly cylindrical shape as illustrated in Figure 9a to fit into a layer. However, as the diameter of the


Richardson et al. TABLE 3: Values Used to Calculate of the Zero Q Intensity, I(0), for Dendrimers in Solution in d-Toluenea g

M/(g mole-1)

Bnormal/ fm

Blabeled/ fm

Icalc(0)calc/ cm-1

Iexp(0)/ cm-1

Rg/Å

3 4 5

23019 46350 93013

3231 6446 12876

4563 9111 18206

1.5 3.0 6.1

1.8 3.8 8.2

19 22 29

a M is the molar mass of a normal dendrimer. B is the neutron scattering length of a normal or labeled dendrimer molecule. The experimental values of the intensity and radius of gyration, obtained by fitting to the data, are also shown.

Figure 9. (a) Cross section and (b) top view of LC dendrimer molecule with dimensional parameters that determine whether the flexible spacers can accommodate cylindrical molecular shape which would favor a lamellar phase. The range of the hexagonal order has been exaggerated to clarify the meaning of the parameters.

TABLE 2: Estimates of the Maximum Distance (in Ångstrom) from the Molecular Axis to an Outer Mesogen, L1, and the Corresponding Distance from the Molecular Center to the Inner End of the Mesogenic Unit, L2 g

L1/Å

Rcore/Å

(d/2-Lmeso)/Å

L2/Å

(Lspacer + Rcore)/Å

1 2 3 4 5

1.6 8.5 14.5 22.1 32.3

6 8 10 13 16

9 10 11 13 17

9 13 18 26 36

24 26 28 31 34

cylinder becomes greater for larger generations, it becomes impossible to achieve this shape because mesogenic units on the outside of the cylinder stretch the spacer too much. It is possible to estimate the critical generation number by considering the dimensions of the liquid crystal dendrimer. Figure 9a shows the key distances that are the smectic layer spacing, d, the length of the mesogenic unit, Lmeso, the maximum distance from the molecular axis to the outermost mesogenic unit, L1, and the radius of the dendritic core, Rcore. The dendritic core is assumed to be spherical because distortion will not change the average radius. The distance from the molecular axis to the outer dendrimer, L1, is also an average value. The local packing of the mesogenic units in a smectic A structure is hexagonal although this order decays within one or two mesogen diameters. To explain the calculation of L1, the range of hexagonal order has been exaggerated in Figure 9b so that the relationship between the number of mesogenic units and the diameter of the group may be seen. The diameter of a mesogenic unit is estimated from the diffuse peak at Q ∼ 1.4 Å-1 (d110 ∼ 4.5 A), which is assumed to correspond to the separation of close packed lines of mesogens as illustrated in Figure 9b. Since only special numbers of mesogens (1, 7, 19, 37, etc.) can form hexagons, the typical value L1 for the real numbers of mesogens (4, 8, 16, 32, etc.) has been derived by interpolation and the values are shown in Table 2. The value of Rcore has been derived from the volume of the core (Rcore ) (3Vcore/4π)1/3). The volume of the core was estimated from the volume of one LC dendrimer molecule, Vm, scaled by the ratio of the mass of the dendritic core to the total molecular mass. The molecular volumes are derived from the measured density (Vm ) M/(NADLC Dendrimer) where M is the molar mass, D is the density, and NA is the Avogadro number). The density of the g5 dendrimer was found to be 1.01 g cm-3 (by a floatation method) and some of the molar masses are shown in Table 3. The resulting values of Rcore are shown in Table 2. Since the total smectic layer thickness, d, is known from the diffraction results, it is now

Figure 10. Cross sections of g5 dendrimer showing possible distortions from cylindrical shape. These more disklike shapes would favor a columnar phase.

possible to calculate the distance from the tip of an outer mesogenic unit to the molecular center (L2 ) ((d/2 - Lmeso)2 + L12)1/2) and taking Lmeso ) 10 Å the values of L2 in Table 3 are obtained. These are compared with the maximum length of the flexible spacer plus the radius of the core, Lspacer + Rcore, where Lspacer ) 18 Å has been estimated from C-C bond lengths and angles. It can be seen in Table 2 that for g ) 1 to g ) 4, the spacer plus core length is greater than the distance from the mesogen to the center (i.e., Lspacer + Rcore > L2) so the cylinderlike conformation of the dendrimer molecule is possible. However for g ) 5 or more, Lspacer + Rcore < L2 so the cylindrical conformation becomes distorted and the free energy increases via entropic and energetic effects. Figure 10 illustrates some possible distortions. It is therefore suggested that for g ) 5 or more, a distorted cylinder or a disklike rather than cylinderlike conformation may be preferred, and either of these possibilities would drive the formation of columnar phases, rather than lamellar phases. The original motivation for the SANS part this work was to measure this difference in molecular shape between g e 4 and g g 5 LC dendrimers. Small Angle Neutron Scattering Studies Background. Neutron scattering with isotopic substitution is established as a powerful method to separate the scattering from different organic components in a complex material. For instance, it has been used in polymer science to determine the dimensions of single polymer chains in the melt (see ref 27 and references therein). This results from the fact that hydrogen and deuterium have very different scattering lengths for neutrons (bH ) -3.74 fm and bD ) +6.67 fm) but are chemically similar so the substitution of H atoms by D atoms is unlikely to perturb the system. It has been found that the chemical differences between H and D influence the mixing for high molar mass polymers (for instance, ref 28 reports phase separation of



polystyrene), but for low molar mass liquid crystals, the differences are usually negligible. Thus, it has been demonstrated that a mixture of normal hydrogenous and deuterated versions of calamitic liquid crystals gives an easily identifiable component in the neutron scattering that effectively results from single “difference” molecules. This single molecule scattering is free from intermolecular interference effects and its intensity distribution as a function of scattering vector, I(Q), may be calculated in detail using the formulas given in ref 12. However, the approximate shape of the scattering may be anticipated by the following argument. The only atoms that scatter neutrons in a difference molecule are those that have been deuterium substituted. Thus for a rodshaped molecule of length, L, and radius, R, the single molecule scattering consists of a disk shaped region in reciprocal space with its short axis parallel to the long axis of the molecule. If the long molecular axis is vertical as shown in Figure 10, the scattering will appear on an area detector as a horizontal streak with thickness, ∆Q// ∼ 2π/L and length, ∆Q⊥∼ 2π/R. The intensity (per unit volume of sample) from such a mixture at a scattering vector of zero is given by the formula

I(0) ) (N/V)φ(1 - φ)∆B2

(1)

where N/V is the number density of the dendrimer molecules, φ is the volume fraction of the deuterium labeled molecules, and ∆B is the difference in scattering length between a normal hydrogenous molecule and a deuterium labeled molecule. The value of ∆B is calculated from ∆B ) z∆b where z is the number of labeled atoms per molecule and ∆b is the difference between the scattering length of a hydrogen atom and a deuterium atom. For an LC dendrimer with labeling in the phenyl rings of the mesogenic units (about 20 Å from the center of the dendritic core), the single molecule scattering would be spread out to at least Q ∼ 0. 3 Å-1 and its zero Q intensity would be given by the above formula. If the mesogenic units were distributed isotropically, then the scattering would appear isotropic and if the mesogenic units were strongly confined to a vertical axis, the scattering would spread much further in the horizontal direction. It turned out to be impossible to measure the single molecule scattering because unexpectedly strong microphase segregation occurred so the single molecule scattering could not be separated. However, it was possible to measure the dimensions of single dendrimer molecules in solution and to study the segregation in the LC phases in detail. These results are presented in the following sections. SANS from But Series of Liquid Crystal Dendrimers in Toluene Solution. Most of the SANS measurements were made on equimolar mixtures of normal and deuterium labeled of LC dendrimers in their mesophases and the results are presented in the next section. However, the measurements of SANS from solutions of these mixtures in d-toluene were also made to confirm the molecular weight of the dendrimers and to eliminate the possibility that the molecules had become covalently crosslinked. For a dilute solution, the intensity (per unit volume of sample) at Q ) 0 is independent of the conformation of the solute molecules and can be used as a measure of the molecular weight. The intensity at Q ) 0 depends only on contrast between solute molecules and the solvent, the volume of a solute molecule and the concentration. Thus I(0) may be calculated from the formula

I(0) ) ∆F2Vpφ

(2)

Figure 11. SANS from But LC dendrimer in d-toluene solution. The points are data and the lines are fits of eq 6.

where φ is the volume fraction of solute, Vp is the volume of one solute particle, and ∆F is the scattering length density contrast between the solute and the solvent. It can be seen that I(0) is very sensitive to cross-linking of the solute molecules. A hypothetical n-mer would have a volume of n times a single particle and so the scattering would be increased by a factor of n. For liquid crystal dendrimers in toluene, these three factors can all be calculated from known quantities. If the solute is not cross-linked, the solute exists as single molecules and so Vp ) Vm, the volume of one molecule.

w/DDendrimer w/DDendrimer + (1 - w)/Dtoluene

φ)

Vp ) Vm )

(

∆F ) NA

(3)

MDendrimer NADDendrimer

DtolueneBtoluene DDendrimerBDendrimer MDendrimer Mtoluene

(4)

)

(5)

where M is the molar mass, D is the density of a pure material, B is the total scattering length of a dendrimer or toluene molecule, and NA is the Avogadro number. The molar masses and scattering lengths are shown in Table 3. Small angle neutron scattering measurements were made on 2% by weight solutions of the g3, g4 and g5-But LC dendrimers mixtures using the D22 instrument16 at ILL (wavelength, 8 Å; sample detector distance, 8 m). Since the normal hydrogenous and the deuterium-labeled dendrimers contain predominantly hydrogen, there is a strong contrast between the solute and the solvent. The Figure 11 shows the results after standard corrections for transmission, solvent background, and normalization to an absolute scale.29 The fitted lines have been calculated using the Debye scattering formula for a Gaussian polymer chain shown below:

I(Q) ) I(0)

2(exp(-x) + x - 1) x2

(6)

where x ) Q2Rg2 with the radius of gyration being a measure of the dimension of the molecules in solution. The fits are satisfactory and since the details of the model are not important below Q ∼ 1/Rg, they serve to determine I(0) by extrapolation and estimate the size of the molecules in solution.


Richardson et al.

Figure 12. Scattering from the H/D mixture of the g3 dendrimer taken with (a) neutrons with sample temperature of 75 °C and (b) X-rays with sample temperature of 100 °C. Both diffraction patterns show the 001 smectic layer reflections but only the neutron scattering shows the anisotropic scattering at low Q around the beam stop. In (b) there is a weak peak at half the scattering vector of the layer reflection. It remains visible even when the 001 peak has disappeared in the isotropic phase. This suggests that it arises from a coexisting region of the sample with a different structure.

It can be seen in Table 3 that the calculated values of I(0) are quite similar to those derived from the experimental results. The discrepancies probably arise from the difficulty of weighing milligram quantities of dendrimers to make up 200 mm3 of solution. The results support the assumption that cross-linking has not occurred and that the dendrimer species in solution are single molecules. The values of the radius, Rg, also support this assumption. SANS Results from But and Anis Series of Liquid Crystal Dendrimers in Their Mesophases. The equimolar mixtures of normal and deuterium-labeled LC dendrimers were prepared by mixing in a common solvent and evaporation to achieve complete intermixing. They were contained in standard fused silica cells, and the sample volume was 2 × 10 × 10 mm3. These samples and the control samples (i.e., the pure unlabeled dendrimers and labeled/unlabeled codendrimers) were aligned by cooling in a 9.4 T magnetic field before the scattering experiment. The SANS measurements were made with the D22 apparatus and the raw data were reduced to an absolute intensity using standard methods.29 Different sample to detector distances were used to observe the layer reflections or to measure the signal from the segregated regions. Figure 12a shows the neutron scattering from a mixture of normal and d-labeled g3-But dendrimer with a sample detector distances of only 2 m. It shows that good alignment has been achieved since the layer reflections are very well aligned and a hint of a low Q scattering signal can be seen near the beam stop. Figures 13a and 13c are from exactly the same sample with a greater sample detector distance of 8 m so that the low Q scattering signal is clearly seen. Figure 13b is from a normal (all hydrogenous) sample of the same compound (g3-But) in a similar Q range. It appears that there are two components to the low Q scattering. There is a roughly isotropic component that can be seen at very low Q in the H/D mixtures and the all-H sample. It appears to be temperature independent. There is a second component whose intensity increases with temperature, and at 75 °C it dominates the first component. It is weak in the all-H sample but is clearly visible as a horizontal streak of scattering from the H/D mixtures and the H/D codendrimer. No scattering similar to the anisotropic component was observed in the same region of scattering vector using X-rays as shown in Figure 12b. This anisotropic component would be well in the accessible Q range (i.e., Q > 0.03Å-1). The isotropic component would be very close to the X-ray beam

Figure 13. Neutron scattering from the g3 dendrimer. The aligning magnetic field was in the Q// direction. The color scaling and the Q scaling for each data set is the same so the contours may be compared: (a) is from the H/D mixture at 20 °C; (b) is from the all-hydrogenous sample at 20 °C; (c) is from the H/D mixture at 75 °C; and (d) is a fit of the anisotropic Debye formula to the data in panel c.

Figure 14. The intensity as a function of Q⊥ along a narrow horizontal band for the g3 dendrimer. The continuous lines are from the mixture of H and D molecules, and the short dashed lines are from the H/D codendrimer. In both cases, the intensity increases with sample temperature. The long dashed line is from the all-H sample. A straight line with slope of -2 indicates that the final slope of the data is approximately -2.

stop but there is only a very weak signal in the corresponding region. The Anis series of dendrimers gave similar scattering (which will not be presented in detail) which suggests that this may be a widespread phenomenon. Figure 14 shows the temperature dependence of the intensity along a narrow horizontal band running from the center of the scattering pattern for the different g3-But samples. It can be seen that the intensity from the H/D mixture is a reversible function of the sample temperature. The intensity of the anisotropic component increases with temperature then returns to its original level on cooling. The intensity from the all-H sample is much weaker. The Figure 14 also shows the intensity from a random codendrimer that was prepared by the reaction of an equimolar mixture of normal and d-labeled mesogenic units with


J. Phys. Chem. B, Vol. 112, No. 51, 2008 16353 TABLE 4: Results from Fitting Anisotropic Debye Function to SANS Data from Mixture of H and D g3 Dendrimers and to the g3 H/D Codendrimer H/D H/D H/D H/D CoCoCoCo-

Figure 15. The intensity as a function of Q⊥ along a narrow horizontal band for the mixtures of H and D-labeled versions of the g3, g4 and g5 dendrimers. The continuous lines are from the g3, the short dashed lines are from g4, and the dots are from the g5 dendrimer. In all cases, the intensity increases with sample temperature but there is no simple trend with generation number.

Figure 16. The intensity as a function of Q// along a narrow vertical bands for H/D mixture of the g3 dendrimer at 75 °C. A constant incoherent background has been subtracted. The different data sets correspond to different values of Q⊥ that are shown in the key. Comparison with a straight line with slope of -2 indicates that the final slope of the data is approximately -2.

the same dendritic cores. The random codendrimer is only slightly weaker than the H/D mixture. Figure 15 shows a comparison between the third, fourth, and fifth generations that all show similar temperature dependence. However, it is clear that the intensity from the fourth generation is weaker than from the other two. It appears that the anisotropic component of the scattering is most well developed in the third generation dendrimer at 75 °C, and it dominates the isotropic component. It also turned out that the scattering from this material is more spread out so the data loss due to the beam stop is not important. Attention has therefore been focused on analyzing the shape of the scattering from at the highest temperature measurement on this sample. It can be seen in Figure 14 that the intensity from the g3 dendrimer at 75 °C appears to have a Guinier region at Q⊥ < 0.01Å-1 followed by a ∼Q-2 decay. This suggests an open structure (with fractal dimension of ∼2) and characteristic size of about 100Å perpendicular to the aligning field. Figure 16 shows the intensity from some narrow vertical bands from the same data. The profiles appear to be sharper with higher maxima for lower values of Q⊥. Applying Guinier’s law to the lowest Q// points of the profiles at Q⊥/ Å-1 ) 0.010, 0.025, 0.040, gives dimension of 460, 290, 110 Å respectively. At lower Q⊥, the beam stop obscured the data but the trend is clearly to larger dimensions. Extrapolation back to Q ) 0 to determine the intensity, I(0), is not accurate because of the sharply peaked

T/°C

I(0)/cm-1

R⊥/Å

R///Å

20 50 75 20 20 50 75 20

12 ( 2 19 ( 4 61 ( 12 17 ( 3 12 ( 2 16 ( 3 86 ( 17 10 ( 2

130 110 180 160 170 160 300 160

490 ( 100 600 ( 120 1200 ( 240 590 ( 120 790 ( 160 910 ( 180 1900 ( 400 770 ( 150

nature of the data but inspection of the trend in ln(I) versus ln Q// suggests that I(0) > 50 cm-1. In order to characterize the data more accurately than is possible by selecting out linear profiles, the whole two-dimensional data sets were fitted with a single function. The Debye formula simply adapted for anisotropy was considered suitable because it has a Guinier region at low Q and a Q-2 decay at larger Q. The formula is the same as eq 6 but with x ) Q⊥2 R⊥2 + Q2//R2//, where Q⊥ ) Q sin β, Q// ) Q cos β and β is the angle between the scattering vector and the direction of the magnetic field. This choice of function was found to give better quality of fits that Gaussian or Lorentzian profiles. An example of a fit is shown in Figure 13d and the best values of the fit parameters, R⊥, R//, and I(0) are shown in Table 4. It can be seen that the fit is satisfactory and the parameters for g ) 3, T ) 75 °C are in the range expected from the preliminary analysis using linear sections through the data. We estimate that the values of I(0) and R// have errors of about 20% which result from the missing data, behind the beam-stop. Discussion of SANS Results from Liquid Crystal Dendrimers in Their Mesophases. The origin of the anisotropic component of the small angle neutron scattering is now considered. Such a signal must arise from variations in the scattering length density of the material. Several possible origins of these scattering length density variations are considered below. (i) The values of I(0) expected from a random mixture of normal hydrogenous and d-labeled molecules has been calculated to be 0.07 cm-1 using eq 1. It can be seen that the observed intensities in Table 4 are many times greater than expected and they are temperature sensitive. The values of R⊥ and R// are also several times greater than expected for a completely random mixture which would give the similar values to those found in solution (i.e., 19 Å). The scattering appears to originate from “objects” with dimensions of the order ∼1000 Å parallel to the aligning direction and ∼200 Å perpendicular to it. It is not single molecule scattering. (ii) The variations in scattering length density may be due to the inclusion of adventitious impurity particles or bubbles. However these which would be expected to contrast with the surrounding LC dendrimer in the SANS and the SAXS cases so the absence of signal in the SAXS suggests adventitious particles are not the cause. It is also very unlikely that adventitious particles would give the strongly temperature dependent scattering so this possibility is dismissed. (iii) The variations in scattering length density may be due to the segregation of H and D labeled components. Such segregation occurs in high molecular weight polymers28 but it too can be ruled out in the present work because the intensity should not be observed from the H/D random codendrimers. Figure 14 shows that the intensity from the H/D codendrimer and the mixed H and D dendrimers are comparable. Detailed


Richardson et al.

calculations (see Appendix) have shown that if the anisotropic scattering resulted from segregation of the H and D labeled molecules, the codendrimer scattering should be ∼3% of the mixture scattering. In fact, it is nearly 100% so this possibility is dismissed. (iv) The variations in scattering length density may be due to variations in the mass density. Variations of the number of molecules per unit volume would give a low Q signal. A rough estimate of the dimensions of the regions of different density is available from Table 4. This can be used to estimate the fractional density variation that would be needed to give the observed I(0) using the equation

( ∆D D )

I(0) ) φ(1 - φ)VRegionF¯ 2

2

NADBmolecule NAD(Bcore + nmesoBmeso) ) Mmolecule (Mcore + nmesoMmeso)

(8)

where Bcore and Bmeso are respectively the total scattering lengths of the dendritic core and one mesogenic unit, including the spacer. Similarly Mcore and Mmeso are the molar masses of the core and mesogenic unit. The number of mesogenic units per core, nmeso, is nominally 32 for a perfect g3 molecule. However, the measured polydispersity index suggests a variation of nmeso For a Gaussian molar mass distribution, the polydispersity index is related to the width of the mass distribution, ∆M:

Mw /Mn ) 1 +

( ) ∆M j M

2

)1+

(

nmeso ) 32 nmeso ) 28 nmeso ) 24 I(0)calc/cm-1

107FH/Å-2

107FHD/Å-2

107FX/Å-2

5.02 4.87 4.47 33

6.78 6.58 6.34 50

94.61 94.66 94.72 2

a The value of I(0) assumes VRegion ) 1.1 × 109 Å3 and the regions have nmeso ) 24 or 32.

(7)

where φ is the volume fraction of the regions of reduced density, ∆D/D is their fractional reduction of mass density and VRegion is their typical volume. Taking φ ) 0.5, and VRegion ) 2πR⊥2 R// ) 2π × 3002 × 1900 ) 1.1 × 109 Å3 as for the g3 codendrimer and a value of ∆D/D ) 0.08 gives I(0) ) 79 cm-1 for the H/D mixtures or copolymer and I(0) ) 43 cm-1 for the all-H dendrimer using SANS. These are in reasonable agreement with the observed magnitudes but this model does not explain why no signal is observed with X-rays. Also, the magnitude of the fractional density variations needed to explain the observed SANS is unreasonably large. So this hypothesis is not accepted. (v) The variations in scattering length density may be due to variations in the composition if we accept that there is some variation in the number of mesogenic units joined to the dendritic core. The scattering length density is determined by the total scattering length of a molecule multiplied by the number density of molecules. This is determined by the density of the material and the molar mass. If the contributions of the different parts of the LC dendrimer molecule are separated, the scattering length density is given by the equation below:

F)

TABLE 5: Calculation of Scattering Length Density and Intensity at Q ) 0 for Neutron and X-ray Scattering with Different Numbers of Mesogenic Groups Attached to the g3 Corea

)

2 ∆nmesoMmeso (9) Mcore + nmesoMmeso

Thus, if it is assumed that the GPC measures the range of molar masses, the measured polydispersity index is consistent with ∆nmeso ≈ 7. The scattering length density for nmeso ) 24, 28, and 32 have therefore been calculated. The neutron scattering length of hydrogen is negative whereas the scattering lengths of most other atoms including deuterium are positive. Thus the mesogenic units contain unsaturated hydrocarbon (and the deuterium in the labeled materials) so will contribute more to the scattering length density than the cores. For X-rays, the scattering lengths are proportional to atomic number (b ) zre,

Figure 17. A highly schematically illustration of the segregated structure for the third generation LC dendrimer. The rectangles represent the side view of the dendrimer molecules in cylindrical conformations. The cylinders are packed into smectic layers that have a thickness of approximately 45 Å consistent with the X-ray results. The in-plane extent of the layers is arbitrary since it has not been determined from the X-ray data. The interplane correlation is very roughly consistent with the sharpness of the layer reflections. There are two types of cylinders: the red represent those with nmeso ) 32 and the blue represent those with nmeso ) 24. They are segregated into highly anisometric regions with diameter perpendicular to the director up to 600 Å and length up to 3800 Å giving volumes up to 1.1 × 109 Å3. These would correspond to ∼10 × 10 × 100 molecules, which are much bigger than illustrated.

where re is the scattering length of an electron for X-rays). The hydrogen content is therefore unimportant and so core and mesogen make similar contributions to the scattering length density for X-rays. To quantify these concepts, the scattering length density for different values of nmeso has been evaluated using eq 8 and I(0) has been evaluated using eq 10 with the value of VRegion given above

I(0) ) φ(1 - φ)VRegion∆F2

(10)

where ∆F is the difference in scattering length density for regions containing molecules with different numbers of mesogens per core. The results are presented in Table 5 that shows that plausible assumptions for the number mesogenic units per core can predict the magnitude of the SANS signal for the H/D mixtures and codendrimers. It also indicates that that the signal from the all-H material will be less and the signal for X-rays will be very much smaller. This hypothesis is therefore consistent with the experimental facts. Figure 17 shows a highly schematic illustration of this model. The compositional inhomogeneity caused by a variation of the number of mesogenic units joined to the dendritic core is the basis of this model. It has recently been supported by MALDI TOF mass spectroscopy experiments on the same


J. Phys. Chem. B, Vol. 112, No. 51, 2008 16355 low generation numbers and columnar phases favored for higher generations because the cylindrical shape of the molecules is not possible. However, there are subtle variations that arise from the fact that the molecules are not identical. Coexisting structures have been observed in the smectic phase of g3-But and the small angle neutron scattering suggests that there is a reversible microphase segregation which probably has the same origin. The new segregation phenomenon that has been observed suggests that in large molar mass materials where the entropy of mixing is relatively unimportant, quite modest compositional heterogeneity may cause microphase segregation. There are implications for the strategy of adjusting material properties by synthesizing codendrimers with different mesogenic units. If the units are not well distributed, segregation is likely to occur. Acknowledgment. We are grateful for the award of an INTAS Young Scientist Fellowship (03-55-706) which supported this work. The collaboration has also been supported by COST action D35-WG0013. We also appreciate the help of Dr. Stephen King at ISIS with LOQ experiments and the help of Dr. Martin Murray and Dr. Craig Butts, University of Bristol, with magnetic alignment. Appendix

Figure 18. (a) Small angle scattering from g5-But codendrimer with (b) a vertical section through the data. The maxima at Q ) 0.012 Å-1 suggest that there is a periodic composition wave with wavelength ∼500 Å-1.

materials where substantial variations of molar mass were observed.30 The highly anisotropic shape of the segregated regions suggests that intermolecular interactions along the director are strongly influenced by the compositional inhomogeneity but interactions perpendicular to the director are not. It is also consistent with the microphase segregation suggested by the coexisting structures observed in g3-But and g5-But by diffraction. It is possible that the anisotropic scattering is enhanced or reduced to a small degree by density variations considered in (iii) above. However, we do not believe that density variations are a major contribution because no anisotropic signal was observed in the SAXS. The signal from the g4-But dendrimer is lower than for the g3 and g5 dendrimers. This is probably because of its compositional inhomogeneity of g4 happens to be less. It is also possible to explain the temperature dependence of the size of the regions using this model. We postulate that the tendency for molecules with different numbers of mesogens to demix increases with temperature. Thus increasing the temperature increases the size of the regions with different values of nmeso. Since the diffusion of large molecules is very slow, the separation is limited and reverses on cooling. The microphase separation that occurs during spinodal demixing of mixtures of linear polymers is characterized an initial sinusoidal composition variation followed by a slow coarsening of the structure.31 The sinusoidal composition variation would give a peak in the scattering at Q ∼ 2π/ wavelength, and this has been observed in one example of a g5-But co dendrimer and is shown in Figure 18. This is further support for the hypothesis of microphase segregation that is driven by a compositional inhomogeneity of the LC dendrimer molecules rather than incompatibility between H and D. Conclusion The structure and phase behavior of liquid crystal dendrimers initially appears simple with predominantly smectic phases for

The correlation function from any scattering system quantifies the tendency of regions of similar scattering length density to cluster. Since the scattering from the whole sample is physically inaccessible, it is usual to consider the correlation of the quantity, η(r) ) F(r) - Fj and to factorize out the value of the correlation function at zero distance, Γ(0)

Γ(r) ) Γ(0)γ(r) where γ(r) is a normalized correlation function that decays from 1 at r ) 0. The value of Γ(0) is known as the invariant and is related in a model free way to the total scattering and to the mean square value of η

1 (2π)3

∫ I(Q)dQ ) V1 Γ(0) ) 〈η2〉

where V is the volume of the sample. The maximum value of 〈η2〉 may be calculated for complete segregation of an equimolar mixture into two types of region: only normal H molecules and only D-labeled molecules:

〈η2〉max )

( ) ∆B 2Vm

2

where ∆B is the difference in the scattering length between a normal H molecule and a D-labeled molecule. For a random codendrimer where an equal number of normal H and D-labeled mesogenic units are mixed perfectly then reacted with the dendritic cores, the maximum possible value of 〈η2〉 is given by n

〈η2〉max )

( ) ∆B 2Vm

∑ nCi( (i -n/2n/2) ) 2

2

i)o

n

∑ nCi i)o

where Ci are the binomial coefficients (e.g., for g ) 1, n ) 8 n Ci )1, 8, 28, 56, 70, 56, 28, 8, 1). The second factor is 0.031 for a third generation dendrimer indicating that the total scattering from the random codendrimer is expected to be about 3% of that from the mixture of two isotopomers. n

16356 J. Phys. Chem. B, Vol. 112, No. 51, 2008 References and Notes (1) Frey, H.; Mulhaupt, R.; Lorenz, K.; Rapp, V.; Mayer-Posner, F. J. Polym. Mater. Sci. Eng. 1995, 73 (2), 127. (2) Ponomarenko, S. A.; Rebrov, E. A.; Bobrovsky, A. Y.; Boiko, N. I.; Muzafarov, A. M.; Shibaev, V. P. Liq. Cryst. 1996, 21 (1), 1–12. (3) Lorenz, K.; Frey, H.; Stuhn, B.; Mulhaupt, R. Macromolecules 1997, 30 (22), 6860–6868. (4) Terunuma, D.; Kato, T.; Nishio, R.; Matsuoka, K.; Kuzuhara, H.; Aoki, Y.; Nohira, H. Chem. Lett. 1998, (1), 59–60. (5) Richardson, R. M.; Ponomarenko, S. A.; Boiko, N. I.; Shibaev, V. P. Liq. Cryst. 1999, 26 (1), 101–108. (6) Terunuma, D.; Nishio, R.; Aoki, Y.; Nohira, H.; Matsuoka, K.; Kuzuhara, H. Chem. Lett. 1999, (7), 565–566. (7) Ponomarenko, S. A.; Boiko, N. I.; Shibaev, V. P.; Richardson, R. M.; Whitehouse, I. J.; Rebrov, E. A.; Muzafarov, A. M. Macromolecules 2000, 33 (15), (8) Richardson, R. M.; Whitehouse, I. J.; Ponomarenko, S. A.; Boiko, N. I.; Shibaev, V. P. Mol. Crys. Liq. Cryst. 1999, 330, 1411. (9) Ponomarenko, S. A.; Boiko, N. I.; Zhu, X. M.; Agina, E. V.; Shibaev, V. P.; Magonov, S. N. Polym. Sci., Ser. A 2001, 43 (3), 245–257. (10) Zhu, X. M.; Boiko, N. I.; Rebrov, E. A.; Muzafarov, A. M.; Kozlovsky, M. V.; Richardson, R. M.; Shibaev, V. P. Liq.Cryst. 2001, 28 (8), 1259–1268. (11) Richardson, R. M.; Allman, J. M.; McIntyre, G. J. Liq. Cryst. 1990, 7 (5), 701–719. (12) Hamley, I. W.; Luckhurst, G. R.; Richardson, R. M.; Santos, F. J. Chem. Phys. 2002, 116 (9), 3887–3899. (13) Richardson, R. M.; Barmatov, E. B.; Whitehouse, I. J.; Shibaev, V. P.; Yongjie, T.; Godinho, M. H. F. Mol. Cryst. Liq. Cryst. 1999, 330, 1529. (14) Agina, E. V.; Boiko, N. I.; Richardson, R. M.; Ostrovskii, B. I.; Shibaev, V. P.; Rebrov, E. A.; Muzafarov, A. M. Polymer Science Series A 2007, 49 (4), 412–424.

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Structural Investigation of Carbosilane Liquid Crystalline Dendrimers

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