Aggregation of a Pseudoisocyanine Chloride in Aqueous NaCl Solution

Hoff's law on a postulated equilibrium nPIC S (PIC)n, he estimated an ..... 4π(n dn/dc)2/λ4NA, with NA Avogadro's number, n the refractive index of ...
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Aggregation of a Pseudoisocyanine Chloride in Aqueous NaCl Solution Bernd Herzog,† Klaus Huber,* and Horst Stegemeyer‡ Fakulta¨ t fu¨ r Naturwissenschaften, Department Chemie, Universita¨ t Paderborn, Warburger Strasse 100, D-33098 Paderborn, FRG Received December 20, 2002. In Final Form: April 3, 2003 Since the pioneering work of Jelley and Scheibe, it has become a widely accepted fact that the cationic dyestuff pseudoisocyanine chloride (PIC) forms large, chainlike aggregates in aqueous solutions. In the present investigation, the onset of this aggregate formation was investigated by means of time-resolved static light scattering. Water with 0.01 N NaCl was used as the solvent. Aggregation was induced by a temperature drop below the aggregation threshold or by increasing the PIC concentration at constant temperature under equilibrium conditions. In all cases, linear particles with a radius of gyration of 180 nm < Rg < 210 nm have been observed. Results could successfully be interpreted in terms of the wormlike chain model from Kratky and Porod. The Kuhn segment length was lk ∼ 500 nm being close to the overall contour length of the aggregate chains. A significant growth was observed only for the averaged molar mass and linear mass density of the aggregates. The results are related to an adequate pattern of particle formation and evidence is provided that these particles are the major constituents of PIC gels.

Introduction In 1937, Jelley published a paper1 where he reported on resonance radiation for the first time. This effect was particularly striking for the cationic dye 1,1′-diethyl-2,2′cyanine chloride, also denoted as pseudoisocyanine chloride (PIC). Dissolved in aqueous NaCl, the system showed an extremely sharp absorption band (J-band) at 574 nm and a fluorescence band which was shifted to longer wavelength by only 3 nm. Whereas Jelley still regarded the systems as being molecularly dispersed, Scheibe added further insight only one year later.2 By means of viscosimetry, conductivity, and spectroscopy, he was able to reveal the main parameters which influenced the resonance radiation. Using water as a solvent, he could show that the sharp absorption band became visible above a PIC concentration of 5 mM. Also, the molar conductivity significantly dropped and further addition of PIC increased the viscosity leading to a gel at 10 mM. An increase in temperature reversed all these effects. In a straightforward manner, he postulated a “reversible polymerization” via physical bonding between the monomers. Applying the law of mass action and van’t Hoff’s law on a postulated equilibrium nPIC S (PIC)n, he estimated an aggregation number to lie between 150 and 500 at the onset of particle formation. At the same time, he claimed that gel formation which occurs at negligibly higher PIC concentration, indicated already much larger aggregation numbers. These pioneering discoveries not only initiated an investigation of the fundamental properties of PIC aggregates but also launched the development of its applicability as photographic sensitzers. Basic research focused on the size and shape of PIC aggregates and the * To whom correspondence may be addressed. E-mail: huber@ chemie.uni-paderborn.de. † Present address: Ciba, Consumer Care Chemicals Division, BS-Grenzach, D-79630 Grenzach-Wyhlen, FRG. ‡ Present address: Erwin Pfeffferle Weg 10, D-79244 Mu ¨ nstertal, FRG. (1) Jelley, E. E. Nature 1936, 138, 1009; 1937, 139, 631. (2) Scheibe, G. Kolloid-Z. 1938, 82, 1. Scheibe, G. Ber. Bunsen-Ges. 1948, 52, 283.

gelation and aggregation mechanism. Rehage et al.3 performed rheological investigations on PIC gels. Their results support the model of an entanglement network formed with stable chains rather than with loosely formed aggregates such as surfactant micelles. Koch4 carried out concentration-dependent dynamic light scattering in the gel phase and found an increase of the mesh size with decreasing PIC concentration. Unfortunately, he was not able to extend his experiments to the pregel state where isolated aggregates predominantly occur in solution. Three further publications5-7 determined aggregation numbers on the basis of the concept of the law of mass action. Whereas two groups,5,6 like Scheibe,2 used temperature-dependent measurements of the extinction at the maximum of the J-band, the third group measured the pressure-dependent extinction at the maximum of the J-band.7 Daltrozzo et al.5 observed an increase of the aggregation number N from 7 to 25 within the PIC concentration regime of 4 mM e cm e10 mM in water. Neumann and Pollmann7 found 5 < N < 29 within the PIC concentration regime of 1.264 mM e cm e 5.5 mM in water. Stegemeyer and Sto¨ckel6 extended this concentration regime to 38 mM, extracting an average value of N ) 40 which was compatible with the findings of Daltrozzo et al.5 However, the aggregation process may equally well be modeled by a process comparable to a phase transition. In such a case, the law of mass action, if at all, would only be applicable to the initial formation of aggregate nuclei. Aside from aggregation numbers, Daltrozzo et al.5 gave an interesting hint on the formation process by means of measuring colligative properties. The authors showed that above a PIC concentration of cm ) 4 mM closely following initiation of aggregation, the number of particles did not change anymore with an increase in the PIC concentration. (3) Rehage, H.; Platz, G.; Struller, B.; Thunig, C. Tenside, Surfactants, Deterg. 1996, 33, 3. (4) Koch, O. Dissertation Shaker Verlag, Aachen, 2001. (5) Daltrozzo, E.; Scheibe, G.; Gschwind, K.; Haimerl, F. Photogr. Sci. Eng. 1974, 18, 441. (6) Stegemeyer, H.; Sto¨ckel, F. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 9. (7) Neumann, B.; Pollmann, P. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 15.

10.1021/la020980w CCC: $25.00 © 2003 American Chemical Society Published on Web 05/17/2003

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Additional monomers were then incorporated into growing aggregates only. Although occasionally mentioned, the measure of the number of monomers forming a delocalized exciton may not directly be related to particle size. By a line shape analysis of the J-band, Knapp8 as well as Fidder and Wiersma9 agreed on a monomer number with a lower limit close to 100. As clearly stated by Fidder and Wiersma,9 the size of the aggregates may be much larger. In fact, time-resolved experiments as those performed by Sundstro¨m et al.10 may form a bridge between the coherence length of the exciton and the aggregate size. They investigated the annihilation of singlet excitons by picoand subpicosecond spectroscopy. By assuming an excitonexciton annihilation of highly mobile singlet excitons and treating the energy migration as a hopping mechanism, the authors estimated aggregation numbers to be in the range of 2 × 104 < N < 5 × 104. Finally, light scattering is a highly promising method to determine the size of dyestuff aggregates.11-15 First static light scattering experiments on PIC, both in pure water and in aqueous 0.01n NaCl, were published by Neumann.16 In agreement with the findings of Daltrozzo et al.,5 he found a shift of the critical aggregation concentration toward lower values if NaCl is added to the aqueous PIC solution. He also provided further evidence for the rodlike shape of the aggregates which meanwhile became the widely accepted shape for PIC aggregates.5,17,18 At this point we have to refer to a recent publication by von Berlepsch and Bo¨ttcher.19 The authors investigated the aggregation of PIC in 0.2 N NaCl by means of cryotransmission electron microscopy which is supplementary to LS. Their results revealed an interesting insight in the process of fiber formation and the morphology of the fibers in the pregel state. Two distinct species, i.e., strands with a cross section of 2.3 nm in agreement with small-angle neutron scattering (SANS) results by Eiser and Berret20 and bundles of those strands, could be established. Still, the method hardly allows a guess of the averaged fiber length and the stiffness. von Berlepsch and Bo¨ttcher19 suggested a fiber length larger than 350 nm and a persistence length (half the Kuhn segment length) larger than 100 nm. No indication was found for a concentrationdependent fiber length. Contrary to electron microscopy, light scattering provides a much better averaging within an observed sample. This leads to high-quality data on the average size and geometry of the aggregates, i.e., the z-averaged radius of gyration Rg, the weight averaged fiber length Lw, and the Kuhn segment length lk. Moreover, light scattering allows many more measurements as a function of temperature and concentration than would ever be possible with electron microscopy. If these light scattering experiments (8) Knapp, E. W. Chem. Phys. 1984, 85, 73. (9) Fidder, H.; Wiersma, D. A. Phys. Rev. Lett. 1991, 66, 1501. (10) Sundstro¨m, V.; Gillbro, T.; Gadonas, R. A.; Piskarskas, A. J. Chem. Phys. 1988, 89, 2754. (11) Datyner, A.; Flowers, A. G.; Pailthorpe, M. T. J. Colloid Interface Sci. 1980, 74, 71. (12) Datyner, A.; Pailthorpe, M. T. J. Colloid Interface Sci. 1980, 76, 557. (13) Datyner, A.; Pailthorpe, M. T. Dyes Pigm. 1987, 8, 253. (14) Escudero Ingle´s, S.; Katzenstein, A.; Schlenker, W.; Huber, K. Langmuir 2000, 16, 3010. (15) Katzenstein, A.; Huber, K. Langmuir 2002, 18, 7049. (16) Neumann, B. J. Phys. Chem. B 2001, 105, 8268. (17) von Berlepsch, H.; Bo¨ttcher, C.; Da¨hne, L. J. Phys. Chem. B 2000, 104, 8792. (18) Scheibe, G.; Hartwig, St.; Mu¨ller-Mu¨nchen, R. Z. Elektrochem. 1943, 49, 50. (19) v.Berlepsch, H.; Bo¨ttcher, Ch. J. Phys. Chem. B 2002, 106, 3146. (20) Eiser, E.; Berret, J.-F. Personal communication, 1999.

Herzog et al.

can be performed time resolved, kinetic experiments could even become accessible, which would not be possible at all with electron microscopy. Motivated by these capabilities, we decided to shed further light on the mechanism of PIC aggregation by means of static light scattering. Our main focus aimed at the capture of intermediate structures when passing the aggregation threshold. This should be achieved either by varying the temperature at constant PIC concentration or increasing the PIC concentration at constant temperature. Information on such intermediates may provide further insight in the formation mechanism of primary PIC aggregates and at the same time could help to better understand succeeding gelation of PIC. However, we soon had to realize that the system is highly sensitive to temperature and the time required for the aggregating particles to reach equilibrium in the index matching bath of the goniometer was much longer than expected. Fortunately, time-resolved experiments were possible through availability of a multiangle light scattering instrument. Therefore, the following action was chosen: Timeresolved experiments on aggregation induced by small temperature jumps will be performed to determine the equilibration time of the scattering sample in the index matching bath as well as to learn more about aggregate formation with time (i). Equilibrium values for the mass and the size of the particles shall be measured as a function of PIC concentration (ii) and temperature (iii). Finally, particle scattering curves shall provide additional information on the shape of the aggregates, if the size of the particles will be large enough. As solvent, we used 0.01 N NaCl in water. The reason for this is as follows: Electrostatic interactions among scattering particles may impair a proper evaluation of the scattering data in terms of single particle behavior. Such interactions might occur between the PIC aggregates if not all cationic charges along the rodlike aggregates are neutralized by counterions, in analogy to regular polyelectrolyte behavior.21 Addition of the inert salt NaCl is able to screen electrostatic interactions between charged particles and may thus improve the quality of the evaluated data. Experiments and Data Treatment Materials. PIC was obtained from 1,1′-diethyl-2,2′-cyanine iodide by chromatography with a LAB III, Merck GmbH, Darmstadt. To protect the dyestuff from light, the whole procedure was carried out under red light. The molar mass of PIC is 362.9 g/mol. For all measurements on aqueous PIC solutions, either bidistilled water or bidistilled water with 0.01 N NaCl was used as solvent. The NaCl was of pa grade from Fluka. Preparation of Solutions for Light Scattering Experiments. All light scattering experiments were performed with dilute PIC solutions. In pure water, a concentration regime of 1.27 g/L e c e 3.27 g/L corresponding to 3.5 mM e cm e 9.0 mM was used. In aqueous 0.01 N NaCl, the concentration regime was 0.27 g/L e c < 1.02 g/L corresponding to 0.75 mM e cm e 2.82 mM. Solutions of PIC in pure water were prepared by weighing the dye directly into volumetric flasks of 25 mL and adding the appropriate amount of bidistilled water. For solutions containing a constant concentration of 0.01 N NaC1, stock solutions of the dye as well as of 0.1 N NaC1 were prepared first. Concentrations of the PIC stock solutions were between 3.43 and 9.0 mM. To generate the desired PIC concentrations, an (21) Molecular conformation and dynamics of macromolecules in condensed systems: a collection of contributions based on lectures presented at the 1st Toyota Conference, Inuyama City, Japan, 28 September-1 October 1987; Nagasawa, M., Ed.; Studies in Polymer Science Series; Elsevier Science Publishers B.V.: Amsterdam, 1988; Vol. 2, p 49.

Aggregation of Pseudoisocyanine Chloride appropriate amount of the PIC stock solution was given into a volumetric flask of 25 mL together with 2.5 mL of the 0.1 N NaC1. Finally, water was added up to the calibration mark. All the solutions were stirred with a magnetic stirrer for at least 1 h. Scattering intensities have to be measured both from PIC solutions and the respective solvents. Cylindrical quarz cuvettes (Helma, Mu¨llheim, FRG) with a diameter of 20 mm were used as scattering cells. All scattering cells were cleaned from dust by continuously injecting freshly distilled acetone from below for 15 min. In all cases, 5 mL of the corresponding liquid was filtered into dust-free cuvettes through MILLEX-GV filters with a pore width of 0.22 µm from Millipore (USA). Prior to any filtration, the filters were conditioned with 10 mL of the corresponding liquid. Above a certain PIC concentration, solutions showed an increased viscosity at ambient temperature making filtration impossible. In distilled water this occurred for PIC concentrations higher than 6 mM and in the presence of 0.01 N NaC1 for PIC concentrations higher than 2 mM. Therefore, solutions, syringes, and filters were tempered at 50 °C prior to filtration. At this temperature all investigated solutions exhibited a low viscosity and filtration through 0.22 µm filters became possible. Static Light Scattering Experiments (SLS). If the storage temperature of the scattering cells was different from the measurement temperature, changes in scattering intensity had been observed for a time period which started with insertion of the cells into the index matching bath of the scattering instrument. This time period may even exceed the time required for the thermal equilibration. Therefore, in a first series of experiments the time required by the system to approach equilibrium was determined. The respective samples were stored at 25 °C for 60 min prior to insertion into the index matching bath with T ) 18 °C. Insertion defined the starting time, t ) 0, of the timeresolved experiments. As outlined in a later section, the results clearly suggested an equilibration time of 30 min in the index matching bath. Consequently, the following procedure was applied for all succeeding measurements at equilibrium. Before any measurement, the sample cells were stored for at least 60 min in the same thermostate bath as was used for thermostating the index matching bath. After the cell was inserted into the index matching bath, the scattering cells were equilibrated for 30 min prior to the actual recording of the intensities. All scattering experiments were done with a model 1800 static light scattering instrument from ALV-Laser Vertriebsgesellschaft (FRG). A krypton ion laser, model 2016 STABILITE, from Spectra Physics (USA) with a wavelength of λ ) 647.1 nm was used as a light source. The laser power was adjusted to 200 mW except for the oligomers, where a power of 400 mW was applied. For further details of the SLS instrument the reader is referred to a preceding paper.14 In addition, a prototype of this light scattering instrument, which differs only slightly from the one used in the present work, was described recently by Becker and Schmidt.22 The applied wavelength lay outside the absorption regime of PIC. Yet, a residual extinction of 0.0016 was observed at 647 nm in a cuvette with an optical path length of 1 cm for the highest dyestuff concentration investigated in 0.01 N NaCl. Although this lowers the transmission by a negligible 0.4% at the most, additional care was taken to avoid heating of the sample due to absorption: The beam shutter was opened only during actual sets of measurement runs, exposing solutions to the primary beam no longer than 60 s. Under these conditions, no significant change of the normalized scattering signals could be observed with the laser power if it was kept below 400 mW. Prior to any measurement of a dyestuff solution, the scattering intensity of the standard toluene and of the solvent was performed subsequentially at all 18 scattering angles in an angular range of 32° < θ < 143°. Either distilled water or a solution of 0.01 mol/L NaCl in distilled water was used as the solvent. The solvent measurement enabled subtraction of the background scattering from the solution scattering. Scattering data were evaluated in terms of ∆Rθ, which is the difference between the Rayleigh ratio of the dyestuff solution and the solvent background, respectively. Data are represented as a function of the square of the scattering (22) Becker, A.; Schmidt, M. Makromol. Chem., Macromol. Symp. 1991, 50, 249.

Langmuir, Vol. 19, No. 13, 2003 5225 vector, q ) (4πn/λ) sin(θ/2), with n the refractive index of the solvent, λ the laser wavelength in vacuo (647.1 nm), and θ the scattering angle.

P(q) ) ∆Rθ/(Kc)/∆RΟ/(Kc)

(1)

In eq 1, K is the contrast factor and c the concentration in grams per milliliter of the dyestuff. The contrast factor K equals 4π(n dn/dc)2/λ4NA, with NA Avogadro’s number, n the refractive index of the solvent, and dn/dc the refractive index increment of PIC in water. For the latter two parameters 1.3332 and 0.615 cm3/g was used respectively.16 The particle scattering factor P(q) in general corresponds to ∆Rθ/(Kc) which is normalized by its limit at q f 0 and c f 0, ∆RΟ/(Kc). As in other investigations on concentration-dependent aggregation phenomena, we had to abstain from extrapolating scattering data to c f 0. Due to this incomplete extrapolation, all evaluated mass data are apparent in nature. But the use of PIC concentrations not exceeding 0.8 g/L in 0.01 N NaCl for quantitative analysis may justify this approximation anyhow. Spectroscopic Experiments. UV-vis spectroscopic measurements were carried out with the same PIC solutions as those used for the scattering experiments. A Perkin-Elmer Lambda 16 UV/Vis spectrometer operating at a slit width of 0.25 mm was employed. Constant measuring temperature was achieved by connecting the cuvette holder to a thermostate bath. All measurements were performed with the same pair of optical cells comprising a sample and a reference cell. The optical cells (137-QS, Hellma, Mu¨llheim, FRG) had a path length of 0.002 cm, allowing measurements in the relevant range of PIC concentrations. Exinctions at the absorption maximum of the dye at 483 nm were between 0.1 and 1.8. In this concentration range, Lambert-Beer’s law was valid and the spectrometer was sensitive enough. The cells were fused and had inlet and outlet tubes which allowed carefull filling of the solutions into the cells. The tubes were sealed with Parafilm in order to prevent solvent evaporation during the measurement. Aggregate formation was followed by recording extinction at λ ) 573 nm in the J-band. Evaluation of Scattering Data and Interpretation in Terms of the Wormlike Chain Model. Scattering experiments with PIC solutions in distilled water were only used to extract the onset of intense scattering while reaching the aggregation threshold. This allowed the evaluation of the corresponding part of a phase diagram. Scattering measurements in 0.01 N NaCl were evaluated in detail. The applied procedure was introduced in two earlier publications14,15 and is composed of four successive steps: (1) For our experimentally found aggregates, a series expansion turned out to be more accurate in determining apparent weight averaged molar mass Mw and z-mean square radii of gyration Rg2 than the conventional Zimm or even Guinier approximation. The applied expansion reads as follows

Kc/∆Rθ ) a1 + a2q2 - a3q4

(2a)

Kc/∆Rθ ) 1/Mw[1 + (〈S2〉z/3!)q2 - (〈S4〉z/5! - (〈S2〉z/3!)2)q4] (2b) In eq 2b, 〈S2〉z and 〈S4〉z are the z-averaged second and fourth moment of the distribution of mass within the particles with 〈S2〉z/2 ) Rg2. Evaluation of all values of Mw ) ∆RΟ/(Kc) and Rg2 according to eq 2 were based on the initial part of the scattering curves, covering a q2-range of 0 < q2 < 2.5 × 10-4 nm-2. (2) Further interpretation of the scattering curves is largely simplified if a model can be used as an input. We assumed the model of wormlike chains23 with the contour length of the chain proportional to its mass. Polydispersity of the contour length can be characterized by a Schulz-Zimm distribution24 of the length, determined by the so-called polydispersity index U

U ) Lw/Ln - 1 ) 1/z

(3)

In eq 3, Lw is the weight averaged contour length of the wormlike (23) Kratky, O.; Porod, G. Recl. Trav. Chim. Pays-Bas 1949, 68, 1106. (24) Zimm, B. J. Chem. Phys. 1948, 16, 1099.

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aggregates and Ln is its number average, respectively. In accordance with other systems,14 a value of z equal to 1 was assumed. (3) The particle scattering functions of wormlike chains follow a power law of P(q) ∼ q-1 for large enough q, resulting in a plateau of (∆Rθ/Kc)q. In almost all cases such plateau values were actually recovered. The plateau values can be transformed to the linear mass densities of the wormlike aggregate ML according to

q ∆Rθ/(Kc) ) π ML ) π Mw/Lw

(4)

and by using the weight averaged molar mass, allow calculation of the weight averaged contour length Lw ) Mw/ML. (4) The persistence length a as the second wormlike chain parameter could be extracted by means of the analytical expression for the mean square radius of gyration Rg,th2 for polydisperse wormlike chains obeying a Schulz-Zimm24 distribution of the contour length.25

Rg,th2 ) (z + 2)aLw (z + 1)3

- a2 +

[ (

4 2 (z + 1)a 2a3 2a (z + 1) - 2 1Lw Lw z(z + 1) (z + 1)a + Lw

)] z

(5) The value of a which minimizes the square of the deviation ∆ from experimental Rg2

∆ ) Rg2 - Rg,th2

(6)

was taken as the proper persistence length of the chain. The Influence of Residual Monomers. In principle, every aggregation process leaves a fraction of “unpolymerized” monomers in solution, the amount of which depends on the equilibrium constant of the aggregation process. This residual amount of monomers bears two problems for a light scattering analysis of aggregate solutions. The first problem refers to the extraction of aggregate mass data from eqs 1 and 2, and the second problem deals with a proper evaluation of the aggregate size parameters from the angular-dependent scattering curves. Both problems shall be addressed in the following paragraphs, together with their implication on the data evaluation applied in the present work. The mass-dependent results rely on the contrast factor, the concentration of the scattering particles, and the experimentally accessible excess scattering signal ∆Rθ thereof. The contrast factor K is assumed to be equal for monomers and aggregates. Data analysis aims at the characterization of the aggregates. Unfortunately, the concentration c as well as the signal ∆Rθ refers to all scattering particles including monomers. To account for this problem, a rather simple correction procedure was suggested recently by Neumann16 who investigated the same system as in the present work. At first sight, it seems as if we could apply the suggested procedure16 also to our results. However, as shall be briefly outlined, it is only a crude approximation, which is of no use in the present context. The procedure16 is as follows: A residual monomer content co was estimated by means of a dimerization ()aggregation) constant for PIC in pure water at T ) 20 °C. The estimated monomer fraction was subtracted numerically from the overall dyestuff concentration. This subtraction was performed without subtracting a respective monomer scattering contribution from the overall scattering intensity. In other words, a corrected dye concentration referring to aggregates was used together with an overall scattering intensity from all particles including monomers. This inconsistency is acceptable in the case of aggregates much larger than the coexisting monomers. However, it becomes incorrect as soon as it will be applied to oligomers as was done in ref 16 for oligomers with an average aggregation number of 3-5. In such a case, just another error was introduced which is at least as large as the one which was to be eliminated. The same is true for another source of uncertainty. This stems from applying an aggregation constant determined in distilled water to ag(25) Oberthu¨r, R. C. Makromol. Chem. 1978, 179, 2693.

gregation in saline solutions. Although it was emphasized by Neumann16 that this may be an approximation leading to a lower limit of a monomer concentration, the use of the correction is very low if aimed at an improved accuracy of mass data of the aggregates. As we will show in Figure 4, the threshold concentration of precipitation is lowered by some 60% if the salt content was increased from 0 to 0.01 M. Our experiments were performed in 0.01 M NaCl at different temperatures where no adequate aggregation constants are available at present. Above this, in the case of our kinetic experiments, we investigated intermediate states along the way to equilibrium, which forbid the use of an aggregation constant for the estimation of the respective intermediate monomer concentrations. Thus the above-mentioned correction procedure16 cannot be used for our data evaluation. We just have to emphasize that we measure an overall scattering intensity which was not corrected indeed. Therefore, the mass data do not correspond to the aggregates alone but are average values over all coexisting species including the monomers. However, as will be shown in the next chapter, this does by no means effect the assignment of the observed trends in molar mass data to the process of aggregate formation. Moreover, the correction suggested in ref 16 corresponds to a mere multiplication of a scattering curve with a constant factor. This cannot account for a possible influence of a scattering monomer fraction on the angular dependence of the scattering curve. If such an influence becomes effective, this modifies all geometric data extracted from the scattering curves, i.e., radii of gyration, persistence length, and contour length. An instructive example for this type of influence was given by Schmidt et al.26 who calculated particle scattering factors in the Koyama approximation for extremely polydisperse wormlike chains. The polydispersity was generated by combining two fractions of wormlike particles differing strongly in its contour length. Inspired by their findings,26 we performed similar model calculations in order to estimate the maximum amount of monomers which still may coexist with the aggregates without significantly influencing the evaluation of the wormlike chain parameters according to eqs 1-6. We simply constructed model scattering curves of samples with a bimodal mixture at variable composition. The mixture consisted of a fraction, co, of monomers corresponding to the fraction with the short contour length and a fraction, c - co, of aggregates with an averaged contour length of Lw ) 600 nm. As will be outlined in the next chapter, no significant influence is exerted by the monomers on the normalized scattering curves of aggregates with Mw ∼ 105 g/mol if we do not increase the monomer fraction above 90 wt %.

Theoretical Considerations on Monomer-Aggregate Mixtures To model the scattering behavior of a mixture of monomeric units and their wormlike aggregates, a bimodal distribution is generated. One fraction is made of very small particles, having the molar mass of PIC with Mo ) 362.9 g/mol. The normalized particle scattering function of the monomers is assumed to be

Po(q) = 1

(7)

independent of the scattering angle in the range of 0.0 nm-1 < q < 0.025 nm-1. The second fraction is composed of a distribution of wormlike chains with a polydispersity index U ) 1 (z ) 1). Its weight averaged molar mass was set to Mw(agg) ) 105 g/mol, which follows the Mw data measured for our PIC aggregates. The corresponding normalized particle scattering factor is approximated by the z-average of Koyama’s calculation27 and is denoted as Pz(q,Koyama). The geometric parameters characterizing (26) Gerle, M.; Fischer, K.; Roos, S.; Mu¨ller, A. H. E.; Schmidt, M.; Sheiko, S.; Prokhorova, S.; Mo¨ller, M. Macromolecules 1999, 32, 2629. (27) Koyama, R. J. Phys. Soc. Jpn. 1973, 34, 1029.

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Figure 2. Bent rod plot28 of normalized model scattering curves from binary mixtures of PIC monomers and aggregates at two different compositions: curve for the pure aggregate with (c co)/c ) 1 (s); curve with the highest monomer content (c - co)/c ) 0.1 (- - -). Figure 1. Evaluation of model scattering curves by means of eqs 1-6: (a) radius of gyration Rg (b), Kuhn segment length lk (2), and contour length Lw (() versus the weight fraction of the aggregate component (c - co)/c; (b) linear mass density ML of aggregates versus the weight fraction of the aggregate component (c - co)/c. The straight line in (b) is calculated according to eq 11. The model scattering curves represent binary mixtures of PIC monomers and aggregates with a weight averaged molar mass of Mw(agg) ) 105 g/mol. They were generated with eq 9 as a function of the composition in the mixture.

the wormlike chain were chosen to be Lw ) 600 nm for the weight averaged contour length and lk ) 500 nm for the Kuhn segment length. The bimodal mixture is characterized by the weight fraction of monomer co/c and the weight fraction of the aggregate (c - co)/c. Appropriate weighing leads to an overall scattering signal of

∆R/Kc ) [∆R(monomer) + ∆R(aggregate)]/Kc

(8)

∆R/Kc ) [Po(q) Moco/c + Pz(q,Koyama) Mw(agg) (c - co)/c] (9) In the limit of q ) 0, eq 9 corresponds to the averaged molar mass of the mixture Mw

Mw ) coMo/c - (c - co)Mw(agg)/c

(10)

To investigate the influence of the composition on the scattering behavior of the mixture, a set of scattering curves were generated in the range of 0.9 e co/c e 0.0 at increments of ∆(co/c) ) 0.1. All curves being established according to eq 9 were subjected to the same data evaluation procedure as applied to the experimental curves. As a result, fitted values for Rg2, Lw, and lk were received as a function of co/c. The fitted parameters describe averages of the bimodal distributions. Results are summarized in Figure 1. Small trends are noticeable for all three parameters. However, if co/c e 0.8, these trends are smaller than the corresponding experimental uncertainties.15 This means that the overall averages do not deviate significantly from the corresponding average values of the aggregate fraction. Even a further increase of the monomer fraction to 90% does not change this picture significantly, although the change in the contour length Lw is about to cross the uncertainty range. As a consequence, the geometric size parameters Rg2, Lw, and lk extracted from scattering curves of mixtures still char-

acterize the aggregate if the monomer weight fraction does not exceed 90%. This range of monomer weight fraction is getting narrower if the average molar mass of the aggregates decreases. It widens up in the case of an increasing average molar mass of the aggregate. As will be shown below, the latter case is the one to be expected for the underlying growth process. For example, an averaged fiber length of 600 nm would result in an aggregate mass of 1.8 × 106 g/mol if a mass per unit length of 3160 g/(mol‚nm) was assumed.17 In addition, Figure 1 clearly demonstrates that the values for ML evaluated according to eqs 1-6 agree well with eq 11

ML(th) ) {coMo/c - (c - co)Mw(agg)/c}/600 nm

(11)

The numerator of eq 11 is the overall average molar mass Mw from eq 10. Although eq 11 relates the averaged overall mass to the contour length of only the aggregates, it represents the experimentally accessible values. In other words, the molar mass data extracted from scattering curves of mixtures yield reliable trends without the need to be corrected for a monomer content if the mass data have been assigned correctly to the ensemble of aggregates and monomers. Once the scattering curves of eq 9 are normalized by eq 10, they can be hardly distinguished from the respective curve of the pure aggregates. This is illustrated in Figure 2 where two examples are compared. Although they represent the curves for co/c ) 0.9 and co/c ) 0.0, which have the largest difference among our model curves, this difference hardly exceeds the experimental uncertainty. Even at co/c ) 0.9, the normalized scattering curve is almost exclusively determined by the aggregates. Results Influence of Inert Salt on the Phase Behavior. To establish experimental conditions appropriate for SLS experiments, the relevant part of the phase diagram was evaluated first. The phase diagram represents the aggregation temperature T as a function of the PIC concentration c in two media, distilled water and aqueous 0.01 N NaCl. Criterion for aggregation was the appearance of a drastic increase in the scattering power. As a measure, we used the molar mass from the angular-dependent scattering intensity, extrapolated to zero scattering angle.

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Figure 5. Excess Rayleigh ratios ∆Rθ of a PIC solution in 0.01 N NaCl. The PIC concentration is c ) 0.762 g/L. The two curves are the first two recordings from an aggregation run induced by a temperature jump from T ) 25 °C (above aggregation threshold) to T ) 18 °C (below aggregation threshold). Measuring times are 90 s (∆) and 150 s ()). Both curves correspond to small oligomers.

Figure 3. Molar mass (a) and extinction at λ ) 573 nm (b) of PIC as a function of PIC concentration in distilled H2O at T ) 20 °C.

Figure 4. Phase diagram represented as aggregation temperature versus PIC concentration. Aggregation was detected by the appearance of a strong scattering signal: PIC in distilled H2O ()) and in aqueous 0.01 N NaCl solution (4). Lines serve as a guide for the eye. Areas to the left of the lines correspond to the one-phase regime.

This zero angle scattering was recorded as a function of temperature at a fixed concentration or as a function of PIC concentration at a fixed temperature. Figure 3 shows an example where the molar mass is plotted versus PIC concentration in distilled water at T ) 20 °C. A jump in intensity occurs between 2.18 g/L < c < 2.72 g/L. It is obvious, that the finite width of concentration (or temperature) steps causes a certain uncertainty. Within this uncertainty, the J-band appears in the same concentration regime as does the onset of a large excess scattering. The coincidental appearance of the J-band and the strong scattering intensity were observed under all investigated conditions. The effects can therefore be regarded as stemming from the same origin. The results are summarized in Figure 4 as T versus c. Data in distilled H2O extend the phase behavior published by Stegemeyer and Sto¨ckel6 to lower temperatures. The present data are completely in line with those from Stegemeyer and Sto¨ckel6 who used the disappearance of the J-band as an indicator for the phase boundary. As revealed earlier,5 addition of an inert salt like NaCl lowers the critical PIC concentration at which aggregation sets in. To suppress interparticle interferences in scattering experiments and to save material, we decided to perform a detailed investigation

Figure 6. Scattering curves represented as ∆Rθ/Kc versus q2 from an aggregation run induced by a temperature jump from T ) 25 °C (above aggregation threshold) to T ) 18 °C (below aggregation threshold). The two lowest curves correspond to the data represented in Figure 5.

in 0.01 N NaCl. A concentration and temperature range of 0.591 g/L < c < 0.762 g/L (1.63 mM e cm e 2.10 mM) and 15 °C < T < 20 °C, respectively, was selected for the corresponding SLS experiments. Approach to Equilibrium following a Temperature Jump. To reveal the time required to reach equilibrium structures, a solution with a PIC concentration of c ) 0.762 g/L (cm ) 2.1 mM) being equilibrated at 25 °C was inserted into the index matching bath of the scattering instrument. Preceding characterization of this sample at 25 °C did not show noticeable aggregation. The index matching bath had a temperature of 18 °C which caused a temperature jump of 7 °C. Immediately after insertion of the sample, SLS measurements were started. To confirm reproducibility of the experiment, two such time-resolved aggregation runs were performed. The power of time-resolved SLS is illuminated by representing angular-dependent Rayleigh ratios from one of the two runs in Figures 5 and 6. The results of both runs are summarized in Figures 7 and 8. During the first minutes, the molar mass kept constant at Mw ) 1300 g/mol still corresponding to small oligomers with a weight averaged aggregation number of 4 (Figures 5 and 7). Rayleigh ratios of the two first runs are shown in Figure 5 as an example. Although the scattering intensity ∆Rθ of the oligomers is comparable to the

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Figure 7. Approach to aggregation equilibrium after a temperature jump from T ) 25 °C (above aggregation threshold) to T ) 18 °C (below aggregation threshold) at a PIC concentration of c ) 0.762 g/L: molar mass of aggregates Mw versus time t at T ) 18 °C after the temperature drop. Closed and open symbols denote two different runs. Closed symbols stem from the aggregation run shown in Figure 6.

Figure 9. Influence of PIC concentration on aggregation behavior at T ) 18 °C. Molar mass Mw (a); linear mass density ML (b); geometric parameters Rg (O), lk (4), and Lw ()) versus PIC concentration (c).

Figure 8. Approach to aggregation equilibrium after a temperature jump from T ) 25 °C (above aggregation threshold) to T ) 18 °C (below aggregation threshold) at a PIC concentration of c ) 0.762 g/L: linear mass density ML of aggregates versus time t after the temperature drop (a); radius of gyration Rg (O, b), lk (4,2), and Lw (], [) versus time t after the temperature drop (b). Closed and open symbols denote two different runs. Closed symbols stem from the aggregation run shown in Figure 6.

Rayleigh ratio of the background (i.e., 0.01 N NaCl), we succeeded to estimate molar masses of the oligomers to within an uncertainty of (25%. This became possible only due to the large scattering contrast of PIC and the high sensitivity of the instrument. The uncertainty of 25% results from a comparison of data from different sample cells which may differ slightly in their optical properties. However, the main use of oligomer scattering was to locate and distinguish aggregation. The quantitative interpretation of data was focused on samples with higher aggregates. First significant changes became observable only 5 min after the start of the aggregation runs. Along with an increase of the molar mass, by an order of magnitude, a significant angular dependence of the scattering data became detectable. After 30 min, the scattering signal leveled off, yielding a molar mass of Mw ) 140000 g/mol (Figure 7). The most striking result, however, was the instantaneous adoption of the final aggregate size, which is represented as the radius of gyration Rg in Figure 8b. Values for Rg kept close to 200 nm during the whole aggregation run. Evaluation of the wormlike chain parameters revealed additional insight into the process

of particle formation. Like Rg, the contour length of the worm jumped to its final value close 620 nm almost instantaneously. Chain stiffness could be characterized by a persistence length of ca. 250 nm, corresponding to a Kuhn segment length of lK ) 500 nm. The only parameter, which changed between 10 min < t < 30 min was the molar mass Mw and, along with it, the linear mass density ML of the wormlike chain (Figure 8a). In addition, a selection of three normalized scattering curves corresponding to t ) 10, 20, and 30 min is represented as bent rod plot28 in Figure 11a. The common trend is typical for slightly bent rods where the value of lk is close to Lw. As expected from the constancy of the derived wormlike chain parameters Lw and lK, the particle scattering functions P(q) did not change very much within this period of time. To put it in another way, the scattering curves lie so close together that they clearly support the scheme of a constant shape and size for all intermediates. Concentration Threshold of Aggregation at T ) 18 °C. To pursue evaluation of aggregate particles when surpassing the aggregation threshold, a series of seven samples with varying concentrations were investigated. The applied concentration regime was 0.591 g/L < c < 0.762 g/L (1.63 mM < cm < 2.10 mM). Measuring temperature was 18 °C. All samples were equilibrated for at least half an hour in the index matching bath prior to any SLS measurement. As long as the PIC concentration was kept below c ∼ 0.7 g/L, the molar mass adopts a value of Mw ∼ 1000 g/mol, again close to the mass of an oligomer with a weight-averaged aggregation number of 3. Only at c ) 0.714 g/L, a slight increase of the molar mass to Mw ) 16000 became noticeable. Results are summarized in Figure 9. Again, all geometric parameters seemed to have (28) Denkinger, P.; Burchard, W. J. Polym. Sci., Part B: Polym. Phys. 1991, 29, 589.

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Figure 10. Influence of temperature on aggregation behavior at c ) 0.762 g/L: molar mass Mw (a); linear mass density ML (b); geometric parameters Rg (O), lk (4), and Lw ()) versus equilibrium temperature (c).

reached the final values by then. The only changing quantities were the mass related parameters. The largest molar mass and mass per unit length were observed for the highest PIC concentration. Interpretation of this dependence reveals T ) 18 °C and c ) 0.698 g/L (1.92 mM) as the coordinates of another point in the phase diagram. Form factors from all concentrations lying above the aggregation threshold are shown in Figure 11b. As in the case of the time-resolved measurements, no significant difference is detectable. All curves are compatible with the shape of a highly stiff worm. Temperature Threshold of Aggregation. Finally, the temperature dependence of the aggregation behavior was investigated from a sample with a PIC concentration of c ) 0.762 g/L (cm ) 2.1 mM). Results are summarized in Figure 10. SLS measurements were recorded in temperature increments of 0.5 °C after equilibration for half an hour at each temperature. At 15 °C, mass Mw and mass per unit length ML of the equilibrated aggregates were 489000 g/mol and 1020 g/(mol‚nm), respectively. Increase of the temperature led to a continuous decrease of both Mw and ML, indicating deaggregation while approaching the aggregation threshold from below. This threshold lies at 18.75 (0.3 °C. Above this temperature, the scattering again stems from small oligomers with Mw ∼ 700 g/mol. As with the time- and concentrationdependent experiments, the geometric parameters did not change until the threshold was surpassed. It is only beyond this threshold, when a complete breakdown of the remaining aggregates occurred. As lk and Lw kept constant over the whole regime where large particles exist, the shape of the particles did not change significantly. A selection of scattering curves recorded at 15, 16.5, and 18 °C, respectively, is shown in Figure 11c. The curves exhibit the same shape as in the time- and concentration-dependent measurement series.

Herzog et al.

Figure 11. Particle scattering functions represented as bent rod plots.28 (a) Selection of curves, recorded while approaching the aggregation equilibrium after a temperature jump from T ) 25 °C (above aggregation threshold) to T ) 18 °C (below aggregation threshold): t ) 10 min ()), t ) 20 min (4), and t ) 30 min (O). (b) Concentration dependence at T ) 18 °C: c ) 0.714 g/L (O), c ) 0.744 g/L ()), and c ) 0.762 g/L (4). (c) Temperature dependence at c ) 762 g/L: T ) 15 °C (4), T ) 16.5 °C ()), and T ) 18 °C (O).

Discussion The process of aggregation was induced and observed along three different routes: (i) time-resolved approach to equilibrium after a temperature jump; (ii) change of PIC concentration at constant temperature; (iii) change of temperature at constant PIC concentration. Whereas with route i an equilibrium state was reached only at the end of the time-resolved growth process, routes ii and iii yield aggregate solutions in their equilibrium state. In all three cases, the average mass of the aggregates increased gradually along the varied parameter, i.e., with proceeding time t toward equilibration, with increasing PIC concentration c, and with decreasing temperature T. Except for the sharp onset of aggregation, in none of the observed growth processes could a change of the global dimensions of the aggregates be observed. As a consequence, no shapesensitive relationship between mass Mw and size Rg was accessible. Unlike to the present system, this was possible for an anionic azo dyestuff system14,15 investigated earlier. Fortunately, the aggregates were large enough to yield scattering curves which could be successfully interpreted in terms of the Kratky-Porod model23 of wormlike chains. The characteristic feature of all light scattering measurements was the formation of the same type of wormlike particles, independent of the chosen aggregation conditions. The size of the aggregates in all cases corresponded to a radius of gyration close to 200 nm with an average contour length slightly above 600 nm and a Kuhn segment length of some 500 nm. The latter points to a fairly stiff worm, with the Kuhn segment length not much smaller than the overall fiber length. In all cases, growth is restricted to an increase in the averaged fiber cross section.

Aggregation of Pseudoisocyanine Chloride

This feature is supported by the normalized scattering factors shown in Figure 11. Normalization was performed according to eq 1 via division by ∆RΟ/(Kc) ) Mw. The latter was evaluated according to eq 2, which does not imply any a priori assumption on the aggregate structure. Yet, all curves lie on top of each other indicating the same shape and size for the respective particles. In principle, two different sequences of particle formation exist: (I) Aggregate formation is simultaneous. Initiation and growth of aggregates proceed for a constant number of aggregates along two separable time intervals. (II) Initiation and growth of aggregates is continuously repeated in the course of the aggregation time leading to a gradual increase of the number of final aggregates. It has to be emphasized that neither of the two sequences must be mixed up with the mechanism of single particle formation. The only growth observed by our light scattering experiments is an increase of the averaged particle mass and, in connection with this, an increase of the averaged linear mass density of the particles. If we underlie sequence I, this increase of molar mass is compatible with a lateral growth of fibers having reached their final length almost instantaneously. It is not compatible with a gradual longitudinal growth of fibers having reached their final cross section from the very beginning. Under the assumption of sequence II, the increase of the aggregate mass reflects an increase of the mass fraction referring to thick fibers. In other words, the number of thick fibers grows on the expense of either thin fibers or monomers/ oligomers. No information on the formation mechanism of the fiber like aggregates is accessible in this case. If we consider both, our light scattering results and the electron micrographs of von Berlepsch et al.,17,19 a lateral growth toward thick fibers via sequence I appears to be rather unlikely. If it would take place, it would be hard to understand why electron microscopy reaveals only two fiber types differing in its cross section at all concentrations investigated. Also, sequence I is not compatible with data from Figures 7 and 8b which include intermediates having Rg ∼ 200 nm and averaged mass values as low as Mw ∼ 104 g/mol. The latter aspect will be adressed in more detail below. As a consequence, aggregate formation most likely proceeds according to sequence II. Several formation mechanisms of the aggregates are compatible with this sequence: Longitudinal growth of fibers with cross sections of 2.3 nm; incorporation of monomers into double strands until a cross section of 2.3 nm is reached; lateral alignment of double strands to form fibers with six double strands and a cross section of 2.3 nm. All mechansims lead to an increase of the number of thick fibers which is synonymous with an increase of the averaged cross section along aggregation time, decreasing temperature or increasing concentration. Finally, the fibers resulting from any of these mechanisms may form bundles and/or gels. Although the development of Mw and ML does not allow discrimination between these mechanisms, a closer look to the linear mass density of the aggregates may be instructive. The largest value observed with our experiments is close to 1000 g/(mol‚nm) under conditions of T ) 15 °C and c ) 0.762 g/L (mM). This value could be compared with the aggregate model suggested by von Berlepsch et al. only recently.17 On the basis of cryo-TEM (transmission electron microscopy) experiments, they suggested fiberlike chains which are composed of six double strands. The thickness of the fibers was 2.3 nm. In coexisting nanocrystal domains they found a repeating period with a length of 1.38 nm. Assuming that the

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repeating period in PIC crystals is close to the one in PIC aggregates, a mass per unit length can be estimated according to 12 × 362.9/1.38 g/(mol‚nm)) 3156 g/(mol‚ nm). Clearly, this value is much larger than the largest value found in our investigation. However, if our values of ML from light scattering are smaller than the one by von Berlepsch and Bo¨ttcher,17 this is then due to our averaging and just means that not all material has been transformed into thick fibers. The larger the dye concentration (or the lower the temperature), the larger is the number of thick fibers. A theoretical example was given in the chapter Theoretical Considerations on MonomerAggregate Mixtures. Interestingly enough, we are able to interpolate a threshold concentration co, below which only monomers and small oligomers exist. This interpolation can be done for T ) 18 °C from Figure 9 or Figure 4, yielding co ) 0.7 g/L. Below this concentration, an average molar mass of Mw ) Mo ∼ 1000 g/mol was established by LS, independent of the PIC concentration. Under the assumption that an increase of c beyond co initiates aggregation without changing the content of monomers/oligomers, we can estimate an averaged aggregate mass Mw(agg) at c ) 0.762 g/L. The concentration c ) 0.762 g/L was the highest PIC concentration investigated by us with LS at T ) 18 °C. Estimation proceeds according to

Mw(agg) ) (Mw - Moco/c)c/(c - co)

(12)

The averaged overall molar mass measured at 0.762 g/L and T ) 18 °C was Mw ) 208400 g/mol (Figure 9a). Inserting this value together with Mo ) 1000 g/mol and c - co ) 0.062 g/L in eq 12, an averaged molar mass of the aggregate fraction can be calculated to Mw(agg) ) 2.55 × 106 g/mol. Underlying an averaged contour length of Lw ) 570 nm from Figure 9c, a linear mass density of ML ) 4500 g/(mol‚nm) can be estimated for the aggregates. This value agrees surprisingly well with the value of 3160 g/(mol‚nm) which can be derived from von Berlepsch et al.17 However, we have to state that an uncertainty of 4% in co increases the uncertainty of c - co (and of ML) to 30%. This forbids a similar estimation of ML for lower PIC concentrations which lie closer to co. As already mentioned, occurrence of averaged molar mass values of Mw ∼ 104 g/mol together with a radius of gyration of Rg ∼ 200 nm is also in support of sequence II. Taking again Mw(agg) ) 2.55 × 106 g/mol, the overall mass average drops to Mw ∼ 104 g/mol if, according to eq 7, c/(c - co) ∼ 0.005. Inserting these parameters in an equation for the z-averaged square radius of gyration which is analoguous to eq 9, the resulting Rg turns out to be still close to 200 nm! Thus, at a stage where Mw ∼ 104 g/mol and Rg ∼ 200 nm, only a very few PIC aggregates have been formed, using up less than 1% of the monomers/ oligomers. Most important, our findings are not compatible with a gelation mechanism induced by ever-growing fibers. Rather would gel formation be caused by an increasing number of fibers, where the increase is induced by either an increase in PIC concentration or a decrease in temperature. Gelation then occurs at a threshold number of fibers. Summary We were able to systematically characterize PIC aggregates in dilute solution as a function of PIC concentration and temperature at equilibrium and as a function of the aggregation time while approaching equilibrium, thus

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supplementing in an excellent way the electron microscopic results by von Berlepsch et al.17,19 The aggregates have a fiberlike or wormlike shape. Their size can be described by an averaged radius of gyration close to 200 nm, a Kuhn segment length of 500 nm, and a contour length of some 600 nm. The experimentally observed growth is due to an increase of the averaged fiber cross section only. This most likely stems from a continuous increase of thick fibers on the expense of monomers/ oligomers or thin strands. The fiberlike aggregates may be regarded as the major constituents forming the network

Herzog et al.

of a PIC gel. Gelation sets in if a critical concentration of these fiberlike constituents are formed. Acknowledgment. Interesting comments from Professor P. Pollmann (Universita¨t Paderborn) and Professor M. Schmidt (Universita¨t Mainz) are much appreciated. The authors thank Mrs. Katja Qass and Mr. Rene´ Baudin for assistance in the laboratory. This work has been supported by the Fonds der Chemischen Industrie. LA020980W