Cooperativity of the Assembly Process in a Low Concentration

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Cooperativity of the Assembly Process in a Low Concentration Chromonic Liquid Crystal Benjamin R. Mercado,† Kenneth J. Nieser,† and Peter J. Collings*,†,‡ †

Department of Physics & Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081, United States Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19105, United States

‡

S Supporting Information *

ABSTRACT: IR-806 is a near-infrared cyanine dye that undergoes a twostep assembly process in aqueous solutions. The final assemblies orientationally order into a liquid crystal at a very low concentration (∼0.6 wt % at room temperature). While the first step of the assembly process is continuous as the dye concentration or temperature is varied (isodesmic), the second step is more abrupt (cooperative). Because the absorption spectrum of IR-806 changes dramatically during the assembly process, careful equilibrium and kinetic absorption experiments are utilized to examine the details of the cooperative second step. These experiments involve changes in both concentration and temperature, allowing a close thermodynamic analysis of the assembly process. Both equilibrium and kinetic investigations reveal that the assembly process is highly cooperative and can be described by multiple models (for example, nucleation and growth) in the highly cooperative limit. The enthalpy associated with the growth process and the activation energy of the rate-limiting step during disassembly are determined. These findings have significant implications for the structure of the assemblies that form the liquid crystal phase in IR-806.

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INTRODUCTION The process of molecular assembly is ubiquitous in nature and underlies a huge range of phenomena in fields such as biology and material science. One area in which molecular assembly is crucial but poorly understood involves chromonic liquid crystals. These are materials in which molecules in a solvent spontaneously form long, thin assemblies, which at high concentration and low temperature order orientationally, and sometimes positionally, to form a liquid crystal phase. Such systems are not rare, as significant numbers of dyes, drugs, nucleotides, and short DNA strands are known to form chromonic liquid crystal phases. These aqueous liquid crystals are also the subject of interesting applications, including specialized materials such as optical films and biosensors, along with various uses in organic electronics. While chromonic liquid crystals have been known and understood to some degree for many decades, only recently have theoretical, computational, and experimental investigations started to reveal details of their fundamental properties and behavior. Several recent reviews nicely summarize the current state of research into these materials.1−3 There has also been recent work to image the assemblies using cryo-transmission electron microscopy.4,5 Most of the scientific work on chromonic liquid crystals has emphasized phase behavior, structure, and properties. Much less attention has been paid to the assembly process itself, which occurs both in liquid crystal phases and at concentrations and temperatures at which no liquid crystal phase exists. In some systems, experimental6−10 and computational11,12 work © 2014 American Chemical Society

has provided strong evidence that the assembly process is nearly isodesmic (i.e., the free energy change in adding a molecule to an assembly is relatively independent of the size of the assembly). This makes the assembly process continuous, that is, assemblies form at all concentrations with the number and size of the assemblies increasing as the concentration is increased or the temperature is decreased. The distribution of assembly size is extremely broad, and there is no critical concentration or temperature that defines a limit for the presence of assemblies. At room temperature, the liquid crystal phase formed by these types of assemblies is stable starting at a concentration that can vary from 10 to 30 wt %, depending on the compound. However, there is also evidence that the assembly process is more complicated in some cases. The absorption spectrum of pseudoisocyanine chloride (PIC) changes continuously with increasing concentration at low concentrations but then changes abruptly at a higher concentration.13 The liquid crystal phase becomes stable at concentrations just above the abrupt change in the spectrum. The dye benzopurpurin 4B forms a liquid crystal phase at concentrations as low as 0.4 wt %, forming assemblies of micrometer size.14,15 It has also been shown that the near-infrared cyanine dye IR-806 undergoes isodesmic assembly at low concentrations, but a second assembly step occurs at higher concentration, which leads to Received: October 3, 2014 Revised: November 1, 2014 Published: November 3, 2014 13312

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a liquid crystal phase.16 This second step appears to begin upon reaching a certain threshold concentration. An X-ray investigation of pinacyanol acetate concluded that, upon reaching a concentration of 2 wt %, the measurements were consistent with a multiwall tube as the assembly structure.17 Careful measurements with pinacyanol chloride demonstrate the formation of a single type of assembly over a range of concentrations; however, if the concentration is high enough, these assemblies transform into another type of assembly over the course of a few weeks.4 In all of these systems, the liquid crystal phase becomes stable at much lower concentrations, typically less than 1 wt %. Because it is difficult to imagine an ordered phase at such low concentrations, it has been hypothesized that these assemblies include a significant amount of water in their structure.16,17 To gain a better understanding of more complicated assembly processes, very detailed equilibrium experiments and new kinetics experiments were performed on IR-806 solutions. These include varying the temperature and the concentration, allowing the second step of the assembly process to be examined much more thoroughly.18 According to equilibrium absorption investigations, only two types of assemblies are involved, the process is highly cooperative, and an enthalpy of ∼65 kJ/mol is involved as the assemblies grow. Although kinetic experiments have been extremely useful in revealing the details of many assembly processes, for example, protein aggregation,19,20 amyloid formation,21 actin polymerization,22 and microtubule assembly,23 very few kinetic experiments have been performed on liquid crystal-forming systems.24 The kinetics experiments reported here allow the threshold behavior to be revealed without any doubt and show that the second step of the assembly process has a rate-limiting reaction during disassembly with an activation energy of ∼48 kJ/mol. The picture that emerges from this work is that linear assemblies previously formed by isodesmic assembly come together through a very cooperative process to form a more complicated structure that is most likely closed and incorporates a significant amount of water.

likely that the structure of the assemblies that forms during the second step includes a good deal of solvent, some type of closed structure appears to be required. Thus, the nucleation and growth model was chosen because the formation of a nucleus is one way to form a closed structure that can increase in size upon the addition of more molecules. The nucleation and growth model as applied to the second step of IR-806 assembly assumes an initial reaction of N small assemblies coming together to form a single large assembly with an equilibrium constant KN. The nucleus, and all assemblies larger than the nucleus, then add a single small assembly with a growth equilibrium constant K. If Ci is the concentration of large assemblies made from i small assemblies, A1 is a small assembly, and Ai is a large assembly of i small assemblies, then the reactions and equilibrium constants can be written as follows. NA1 → AN

CN = KN C1N

AN + A1 → AN + 1

CN + 1 = KCN C1 = KKN C1N + 1

AN + 1 + A1 → AN + 2

CN + 2 = KCN + 1C1 = K 2KN C1N + 2

AN + 2 + A1 → AN + 3 ···

CN + 3 = KCN + 2C1 = K3KN C1N + 3 ···

AN + n − 1 + A1 → AN + n CN + n = KCN + n − 1C1 = K nKN C1N + n (1)

If CT is the total concentration of small assemblies, and σ is defined by KN = σKN−1, then ∞

CT = C1 +

∑ (N + n)CN + n n=0 ∞

=

C1KN C1N

∑ (N + n)K nC1N n=0

(2)

which, after performing the summation yields

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CT = C1 + σ

THEORY Many theoretical models may be appropriate for the assembly of chromonic liquid crystals. Some are quite simple, like the isodesmic model for example, which is defined by a series of reactions, each adding one molecule. Another example is a single reaction forming an assembly of fixed size, which is appropriate for micelle formation. However, to describe the second step in the IR-806 assembly process, a more sophisticated model is necessary. Because this step seems to have a threshold, and because the assemblies most likely have a linear structure of some kind, a model with an initial ratelimiting step followed by continued growth is most appropriate.18 The nucleation and growth, and the activation and growth, models both fit this mold. The initial reaction in the nucleation and growth model is the formation of a nucleus with a fixed number of molecules. Then, a series of reactions occurs in which one molecule is added to an assembly with a size equal to or larger than a nucleus. In the activation and growth model, the initial reaction is a change involving one molecule from an “inactivated” to an “activated” form. Activated molecules can then form assemblies through an isodesmic process. In fact, these two models predict very similar behavior, especially if the parameters in each of the models make the assembly process highly cooperative. Because it is

(KC1)N N − (N − 1)KC1 K (1 − KC1)2

(3)

Given values for the parameters CT, N, K, and σ, the concentration of single small assemblies C1 can be calculated. The concentrations of assemblies of all other sizes can then be calculated using eq 1. However, solving eq 3 involves an equation of the Nth order. A more simple way to perform the calculation is to multiply both sides of eq 3 by K KCT = KC1 + σ(KC1)N

N − (N − 1)KC1 (1 − KC1)2

(4)

First, a value for KC1 is chosen. Then, eq 4 is used to calculate KCT. Finally, the fraction of small assemblies in all of the large assemblies is given by (CT − C1)/CT = (KCT − KC1)/KCT. In this way, a plot of the fraction of small assemblies in large assemblies versus KCT can be made. Because K is a constant, this plot has the same shape as if the KCT axis was the total concentration of small assemblies CT axis. This has been done in Figure 1 with a fixed value for σ and a wide range of nucleus sizes N. Notice that as the nucleus size increases (i.e., the cooperativity of the process increases), the onset of large assembly formation gets more abrupt. In the limit of infinite nucleus size (infinite cooperativity), the plot would have a discontinuous slope at KCT = 1. The same progression toward a 13313

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of each size of large assembly plus an equation for the total concentration of small assemblies. In the following set of equations, all of the Ci are time dependent, and NN is the largest number of small assemblies in a large assembly considered in the calculation. The forward and reverse rate constants for the formation/breakup of the nucleus are given by kN+ and kN−, respectively, and the forward and reverse rate constants for adding/subtracting a small assembly to/from a large assembly are given by k+ and k−, respectively. dCi =0 2≤i≤N−1 dt dCN = kN +C1N − kN −CN − k+C1CN + k −CN + 1 dt dCi = k+C1Ci − 1 − k+C1Ci + k −Ci + 1 − k −Ci N + 1 ≤ i ≤ NN − 1 dt dCNN = k+C1CN − 1 − k −CN dt NN

dC dC1 = −∑ i i dt dt i=N

Figure 1. Assembly fraction vs concentration. N is the number of small assemblies in a nucleus, and σ is equal to 0.01. The horizontal axis is the total concentration multiplied by the growth equilibrium constant, the latter of which can be considered constant.

(5)

These coupled differential equations can be solved numerically when given initial conditions for (1) the total concentration of small assemblies, (2) the concentration of each size of large assembly, (3) the size of the nucleus, and (4) the values of the four rate constants. Of course, the value of NN must be large enough to include all of the sizes of large assemblies that form. As a check, the concentration of each size of large assembly after sufficient time should equal the value predicted by the equilibrium calculation using eq 3. The results of the kinetics calculations using eq 5 are shown later where they are compared to experimental data. Briefly, experiments that involve a significant dilution of a solution with large assemblies reveal that two reactions with very different rate constants occur. Experiments that involve the growth of large assemblies due to an increase in salt have a sigmoidal shape. Both of these observations are consistent with calculations involving the nucleation and growth model if the parameters in the model are appropriately chosen.

more abrupt threshold results if N remains constant and σ is decreased. If one assumes that the logarithm of the growth equilibrium constant times the absolute temperature T is equal to a Gibbs free energy change divided by the gas constant, then theoretical plots showing how the fraction of small assemblies in large assemblies depends on temperature can be generated. These plots are shown in Figure 2, where the various parameters have

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EXPERIMENTAL METHODS Equilibrium Experiments. Absorption measurements were taken with an Agilent Technologies Cary 60 UV−vis spectrophotometer equipped with a Quantum Northwest TC 125 Temperature Controller. The wavelength range was typically 550−950 nm. The absorption of the samples was so high that very thin cells were required. These were prepared using microscope slide glass and 10−20 μm thick glass spacers. The glass was held together and the sample sealed using Uhu Plus 2 min or 5 min two-part epoxy. The path length was measured by interference effects that were present during an absorption scan of an empty cell. The IR-806 concentrations ranged from 0.2 to 0.6 wt %. The range of temperatures for each concentration was selected such that the absorption coefficient spectra at the lowest and highest temperatures indicated either a significant number of large assemblies were present (low temperature) or no large assemblies were present (high temperature). The full range of the absorption measurements was from 5 to 53 °C. Kinetics Experiments. Kinetics experiments were performed with two instruments. The first was an Applied Photophysics RX2000 Rapid Kinetics Spectrometer Accessory

Figure 2. Assembly fraction vs temperature. N is the number of molecules in the nucleus, and σ is equal to 0.01. The cooperative limit is approached as the number of molecules in the nucleus gets extremely large.

been chosen such that the process occurs over a suitable range of temperatures near room temperature. Again, notice that the assembly process ends more and more abruptly as the size of the nucleus increases. To calculate the kinetics from a theoretical model such as nucleation and growth, a set of master equations must be solved.25 These equations are expressions for the rate of change 13314

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concentration and temperature. This ratio was chosen because it is sensitive to changes that take place in the absorption spectrum and does not change simply because the IR-806 concentration changes. The effectiveness of this ratio in characterizing the absorption coefficient spectra is revealed in Figure S1 of the Supporting Information, in which spectra at various concentrations and temperatures have been plotted for three different values of the ratio. The goal is to use this ratio as an index for describing the assembly process. That is, if spectra at two different concentration−temperature combinations have the same ratio, then they have the same absorption coefficient spectrum and presumably have the same distribution of small and large assemblies. This procedure allows a “phase diagram” to be constructed, in which different points in the concentration−temperature plane with the same distribution of small and large assemblies can be connected with a curve. This has been done in Figure 4, where curves with roughly the same slope connect similar points in the assembly process.

to the Cary 60 spectrophotometer. The dead time of this instrument was measured to be 20 ms using the DCIP− ascorbic acid reaction.26 This instrument was used to probe for a threshold concentration for the formation of large assemblies in dilution and NaCl-addition experiments. The second instrument was an Applied Photophysics SX20 Stopped-Flow Spectrometer with a dead time measured to be slightly less than 1 ms using the same reaction.27 This instrument was used for all dilution and NaCl-addition experiments in which the data are compared to theoretical models. In the 10:1 dilution experiments, the same range of IR-806 concentrations was used (0.2−0.6 wt %), but in each case the temperature was varied so that the absorption coefficient spectra before dilution were the same. A similar protocol was used for the 1:10 addition of NaCl solutions. The concentration of IR-806 again ranged from 0.2 to 0.6 wt %, and the NaCl concentration was varied between 0.2 and 0.6 M. The temperature was adjusted for each sample so that the absorption coefficient spectra before the addition of NaCl were the same. Likewise, the concentrations of NaCl solutions were selected so that the absorption coefficient spectra after the addition of NaCl were the same.

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EXPERIMENTAL RESULTS The results of measuring the absorption coefficient of a 0.2 wt % IR-806 sample between 5 and 30 °C are shown in Figure 3 along with the IR-806 molecular structure. As pointed out in

Figure 4. IR-806 “phase diagram”. The data indicate which combinations of concentration and temperature produce the same absorption coefficient spectrum, which is determined by the ratio of the absorption coefficients at 830 and 665 nm. The lines are quadratic fits to the data.

Although the existence of a threshold IR-806 concentration for large assemblies to form was somewhat evident from the equilibrium data in ref 16, kinetics experiments with the slower stopped-flow accessory firmly establish its existence. With a 10:1 dilution of samples with different IR-806 concentrations and monitoring the absorption at 850 nm where the large assembly absorbs, it is observed that for concentrations of less than 0.35 wt % there are no absorption changes and therefore no large assemblies present. This is clearly demonstrated in Figure 5, where the absorbance for each concentration has been normalized to begin at one and end at zero. This is exactly where the existence of a threshold is somewhat evident in ref 16. Notice also that kinetic curves are roughly exponential, and the time frame of the disassembly process is on the order of a second. The reaction rate decreases as the IR-806 concentration increases. Similarly, kinetics experiments with the slower stopped-flow accessory reveal that in a 0.2 wt % IR-806 sample, there are no large assemblies, but the addition of an NaCl solution (1:10

Figure 3. Absorption coefficient spectrum of a 0.2 wt % sample of IR806 at the following temperatures: 5.0, 7.5, 10.0, 12.5, 15.0, 17.5, 20.0, 22.5, 25.0, 27.5, and 30.0 °C. The molecular structure of IR-806 is shown.

ref 18, varying the temperature while keeping the concentration constant is a more powerful way to investigate assembling systems. The most striking finding apparent in Figure 3 is the isosbestic point of 723 nm. Clearly, only two absorbing species are present, namely, the small assemblies and the large assemblies. Similar isosbestic points were present in the spectra at the other IR-806 concentrations. To compare the spectra to one another, the ratio of the absorbances at 830 and 665 nm was computed for each IR-806 13315

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ensure that plenty of large assemblies were present. A volume of water equal to 10 times the IR-806 solution volume was added, and the absorbance at 870 nm was monitored. This wavelength was selected because the absorbance depends almost entirely on the concentration of large assemblies present and is within the range of the spectrophotometer. Because of the smaller dead time of this instrument, it is clear that there are two reactions going on: one fast with a reaction time of less than 0.1 s and one slow with a reaction time on the order of seconds. The data for four of the five concentrations are shown in Figure 7. After about one second, the data follow an

Figure 5. Concentration dependence of the dilution kinetics. No large assemblies are present in the 0.20 and 0.30 wt % IR-806 solutions. For concentrations of 0.35 wt % and higher, large assemblies are present, and they disassemble when diluted with 10 times the volume of water. The temperature is 24 °C, the path length is 2 mm, and the absorption is measured at 850 nm.

proportion) induces the formation of large assemblies once the NaCl concentration is high enough. Here, the absorbance at 550 nm is monitored because this is the range of wavelengths in which the small assemblies absorb. These results are shown in Figure 6, in which the absorbance has once again been normalized between one and zero.

Figure 7. Kinetics due to a 10:1 (water/IR-806 solution) dilution using absorption at 870 nm and a path length of 1 mm. The temperature used for each concentration is selected such that the starting absorption coefficient spectrum is the same. (inset) Arrhenius plot using the kinetic parameters from the slow portion of the experimental data, which gives an activation energy for the ratelimiting disassembly step of (48 ± 2) kJ/mol.

exponential function, and the logarithm of the rate constant for the slower reaction has been plotted versus the inverse temperature (Figure 7, inset). Fitting of a straight line to these data yields an activation energy of (48 ± 2) kJ/mol. When the kinetics experiments were designed with the addition of NaCl, different temperatures were again used depending on the IR-806 concentration. This time a low value of the 830/665 nm ratio (∼0.5) was used to ensure that the same low concentration of large assemblies was present initially. To produce similar reactions between IR-806 and NaCl, the concentration of the added NaCl solution was proportional to the IR-806 concentration. To verify that the desired outcome was produced, the absorption coefficient spectra were measured tens of minutes after the NaCl solution was added. As can be seen from Figure S2 in the Supporting Information, the absorption coefficient spectra of all five concentrations are very similar. The results for IR-806 concentrations between 0.2 and 0.6 wt % and NaCl concentrations between 0.2 and 0.6 M are shown in Figure 8. The volume of NaCl solution added was one-tenth the volume of the initial IR-806 solution. The small concentration of large assemblies initially produces a non-zero slope at very short times, and the general shape of the kinetic

Figure 6. NaCl concentration dependence of the assembly kinetics. A 1:10 mixture of a 0.02 M NaCl solution and a 0.2 wt % IR-806 solution produces no large assemblies, but they are produced at higher salt concentrations. The temperature is 24 °C, the path length is 2 mm, and the absorption is measured at 550 nm.

More detailed kinetics measurements were done with the faster stopped-flow instrument. The initial IR-806 concentration was again varied from 0.2 to 0.6 wt %, but the temperatures were selected such that the 830/665 nm absorption ratio was the same. This was done with the aid of the absorption measurements that were used to generate Figure 4, and a very high value of the ratio (∼3.9) was chosen to 13316

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If the data shown in Figure 4 are used to find locations where this relationship should apply, the enthalpy value associated with assembly growth is on the order of −50 kJ/mol. Although the absorption spectrum of IR-806 is not simple, prior analysis has shown that it can be decomposed into six absorption peaks with fixed center wavelengths and fixed widths.16 Three of these peaks do not evolve systematically as the IR-806 concentration is increased, but the other three appear to originate from the monomer, the small assembly, and the large assembly. The amplitudes of these peaks change significantly as the IR-806 concentration increases and the two types of assemblies form. Specifically, the peak at 830 nm is not present at very low concentrations, appearing abruptly around 0.3 wt % at room temperature. Making the assumption that the amplitude of this peak is proportional to the number of IR-806 molecules in large assemblies allows the assembly process to be investigated extremely carefully. For example, recording the absorption spectra of a 0.3 wt % solution at intervals of 1 °C, and decomposing each one to find the amplitude of the 830 nm peak, produces a detailed picture of the second step in the assembly of IR-806 under equilibrium conditions. These data are shown in Figure 9 and clearly resemble the expected pattern

Figure 8. Kinetics due to the addition of NaCl in a 1:10 ratio of NaCl/ IR-806 solution from absorption measurements at 560 nm and a path length of 1 mm. The concentrations of the NaCl solutions were proportional to the IR-806 concentrations: 0.2 M for the 0.2 wt % sample, 0.3 M for the 0.3 wt % sample, etc. The parameters used for the theoretical prediction were selected to give a curve similar to the experimental data for the 0.2 wt % solution: N = 8, kN+ = 0.1 wt %−1, k+ = 5000 wt %−1, kN− = 50 wt %−1, and k− = 5000 wt %−1 initially, with kN+ and k+ jumping by a factor of 2.5 to simulate salt addition.

data is sigmoidal. The process gets faster and faster as the IR806 concentration and temperature increase.

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DISCUSSION A typical slope of the data in the “phase diagram” representing similar points in the assembly process (Figure 4) is about 40 °C/wt %. Most of the data for the liquid crystal phase diagram reported in ref 16 were taken at much higher IR-806 concentrations, but the data at lower concentrations have a slope around 20 °C/wt %. The fact that these slopes are on the same order of magnitude is a strong indication that the assemblies formed by the second step in the assembly process are in fact the assemblies responsible for the liquid crystal phase at slightly higher concentrations or slightly lower temperatures. The integrated form of the van’t Hoff equation is ln

K2 ΔH ⎛ 1 1⎞ =− ⎜ − ⎟ K1 R ⎝ T2 T1 ⎠

Figure 9. Absorption coefficient of the 830 nm peak vs temperature for a 0.3 wt % solution of IR-806. The solid line is the theoretical prediction for the nucleation and growth model in the highly cooperative limit. The fit gives a value for the enthalpy during growth of (−65.4 ± 0.9) kJ/mol.

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from a nucleation and growth model with a very large nucleus size (high cooperativity). In fact, in the limit of very high cooperativity, the nucleation and growth model collapses to a function introduced previously for this model28

where K1 and K2 are the equilibrium constants at absolute temperatures T1 and T2, respectively, ΔH is the enthalpy of the reaction, and R is the gas constant. In the nucleation and growth model, the degree of assembly depends on KCT. Therefore, at two points in the temperature−concentration plane where the absorption spectra are the same (indicating that both represent the same point in the assembly process), then KCT must also be the same. If these two locations are labeled 1 and 2, then K2/K1 = CT1/CT2, and the van’t Hoff equation can be rewritten as ln

CT1 CT2

=−

ΔH ⎛ 1 1⎞ ⎜ − ⎟ R ⎝ T2 T1 ⎠

ϕn =

⎛ ⎡ −ΔH ⎛ 1 CT − C1 1 ⎞⎤⎞ ⎜ = ϕsat⎜1 − exp⎢ − ⎟⎥⎟ ⎝ ⎣ ⎝ CT R T* T ⎠⎦⎠

(8)

where ϕn is the fraction of small assemblies in large assemblies, ϕsat is a parameter introduced to ensure that ϕn/ϕsat is less than one, ΔH is the enthalpy change during growth, and T* is the temperature above which there are no large assemblies. Fitting the amplitude of the 830 nm peak to this function, while allowing for a constant absorption coefficient above T* as shown in Figure 9, yields a value for the enthalpy of the growth

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process of (−65.4 ± 0.9) kJ/mol, which is consistent with the estimation made using the van’t Hoff equation. If the rate-limiting reaction is associated with nucleus disassembly, the nucleation and growth model predicts that the disassembly of the large assemblies into smaller assemblies around the size of the nucleus occurs first, with the disassembly of the nuclei happening second. This is shown in Figure S3 of the Supporting Information, where both the distribution of large assembly size and the fraction of small assemblies in large assemblies are shown at four times during the process. Experimentally, the fast and slow reactions of the dilution kinetics are best observed with the 0.2 wt % IR-806 solution. These data are displayed in Figure 10, where it is clear that the

the model parameters are possible without sacrificing close agreement with the data. It is appropriate to consider the impact of these new results on what is known about the structure of IR-806 large assemblies that form the liquid crystal phase. One must first keep in mind that the IR-806 concentration necessary for liquid crystal formation is considerably lower than the concentrations typical of liquid crystal formation in systems for which there is strong evidence that the assemblies are simple stacks of molecules with a cross section of one or two molecules. This difference in concentration is large, approximately one order of magnitude (e.g., 1 vs 10 wt %).16,29 X-ray evidence is also revealing. Whereas the distance between assemblies in a system for which the assemblies are simple stacks is about 3 times the molecular dimension in the nematic phase near the nematic− isotropic coexistence region,29 the distance between assemblies in IR-806 is approximately 10 times the molecular dimension at a similar point in the phase diagram.16 This is why it was surmised that the assembly structure must contain a significant amount of water, because a structure much larger than a molecular dimension is necessary for the assemblies to be able to interact enough to order orientationally. The X-ray measurements also pointed to a linear structure; thus, a hollow cylindrical model in which the inside of the assembly is water and the outside is IR-806 only a few molecules thick was suggested.16 The results presented here add to the evidence of a water-containing structure for the large assemblies. The highly cooperative nature of the second assembly step is expected if more than a few small assemblies are required to form a large assembly. Moreover, if the structure is one of IR-806 molecules enclosing an interior of water, then a certain number of small assemblies are necessary to form a large assembly. This is why the nucleation and growth model was chosen to describe the assembly process for IR-806, because the nucleation step requires the involvement of a certain number of molecules.

Figure 10. Kinetics due to a 10:1 water/IR-806 solution dilution for a 0.2 wt % IR-806 solution at 5.9 °C using absorption at 870 nm. The absorption change is extremely small, so oscillations due to slight pressure variations or electrical interference are present. The parameters used for the theoretical prediction were selected to give a curve similar to the experimental data: N = 8, kN+ = 0.5 wt %−1, k+ = 250 wt %−1, kN− = 0.46 wt %−1, and k− = 140 wt %−1.

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CONCLUSION The fact that IR-806 molecules assemble in aqueous solution via a two-step process is confirmed through detailed equilibrium and kinetics experiments. In addition, both equilibrium and kinetics investigations reveal that the second step of the process is highly cooperative, with a threshold concentration below which and a threshold temperature above which no large assemblies are present. In addition, all experimental results for the second step of the assembly process are consistent with a nucleation and growth model in which the formation or breakup of nuclei is the rate-limiting reaction. The enthalpy of the growth reaction was measured to be (−65.4 ± 0.9) kJ/mol, and the activation energy for the nucleus breakup reaction was measured to be (48 ± 2) kJ/mol. Three pieces of evidence point to a structure for the large assembly that is long and thin and incorporates a good deal of water: (1) the large assemblies order into a liquid crystal phase, (2) the liquid crystal phase occurs at very low concentrations of IR-806, and (3) the formation of large assemblies is a highly cooperative process. Specific assembly structures that fall into this general class have been proposed for other chromonic liquid crystal systems.17,30,31 They involve a hollow cylindrical structure with a single layer or multiple layers of molecules surrounding a central core of water.

fast reaction is over in a tenth of a second, whereas the slow reaction takes many seconds to conclude. To compare these data at a wavelength representing the large assemblies to the model, the nucleation and growth model was calculated with various values of the parameters. As is evident in Figure 10, proper selection of the nucleus size and kinetic parameters yields a plot that follows the data nicely. A similar procedure can be performed with the data for forming assemblies by comparing the absorption data at a wavelength representing the presence of small assemblies. Again, a specific choice of the nucleus size and kinetic parameters yields a curve that closely resembles the data for the 0.2 wt % solution when a 0.2 M NaCl solution is added in the ratio of 1:10 (Figure 8). To simulate the addition of the NaCl solution in the calculation, the equilibrium distribution of assembly sizes is forced to change by increasing the forward rate constants kN+ and k+ by a factor of 2.5. It must be stated explicitly that the comparisons of the data to the nucleation and growth model shown in Figures 8 and 10 are not fits of theory to the experimental data. Rather, they represent a combination of the model parameters that produces a curve that closely follows the experimental data. Because the number of model parameters is large, significant variations in 13318

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ASSOCIATED CONTENT

S Supporting Information *

(1) Absorption coefficient spectra showing how similar spectra can result from different combinations of concentration and temperature, (2) absorption coefficient spectra showing how similar spectra can result from different combinations of IR-806 and NaCl concentrations, and (3) a theoretical calculation using the nucleation and growth model to show how the large assemblies break up into small assemblies when the concentration is suddenly reduced. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (610) 328-7791. Fax: (610) 328-7895. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the donors of the American Chemical Society Petroleum Research Fund for partial support of this research, along with the Howard Hughes Medical Institute, and the Research Experiences for Undergraduates Program at the Laboratory for Research in the Structure of Matter at the University of Pennsylvania. The authors also thank Heinrich Roder and Ming Xu of the Fox Chase Cancer Center (Philadelphia, PA, U.S.A.) for allowing use of the SX20 spectrophotometer.

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REFERENCES

(1) Tam-Chang, S. W.; Huang, L. Chromonic Liquid Crystals: Properties and Applications as Functional Materials. Chem. Commun. 2008, 2008, 1957−1967. (2) Park, H. S.; Lavrentovich, O. D. In Lyotropic Chromonic Liquid Crystals: Emerging Applications; Li, Q., Ed.; John Wiley & Sons, Inc.: Hoboken, NJ, 2012; pp 449−484. (3) Lydon, J. In Chromonic Liquid Crystals; Goodby, J. W., Collings, P. J., Kato, T., Tschierske, C., Gleeson, H. F., Raynes, P., Eds.; WileyVCH: Weinheim, Germany, 2014; pp 439−483. (4) von Berlepsch, H.; Ludwig, K.; Bottcher, C. Pinacyanol Chloride Forms Mesoscopic H- and J-Aggregates in Aqueous Solution - A Spectroscopic and Cryo-Transmission Electron Microscopy Study. Phys. Chem. Chem. Phys. 2014, 16, 10659−10668. (5) Gao, M.; et al. Direct Observation of Liquid Crystals Using CryoTEM: Specimen Preparation and Low-Dose Imaging. Microsc. Res. Tech. 2014, 77, 754−772. (6) Horowitz, V. R.; Janowitz, L. A.; Modic, A. L.; Heiney, P. A.; Collings, P. J. Aggregation Behavior and Chromonic Liquid Crystal Properties of an Anionic Monoazo Dye. Phys. Rev. E 2005, 72, 0417101−041710-10. (7) Tomasik, M. R.; Collings, P. J. Aggregation Behavior and Chromonic Liquid Crystal Phase of a Dye Derived from Naphthalenecarboxylic Acid. J. Phys. Chem. B 2008, 112, 9883−9889. (8) Park, H. S.; Kang, S. W.; Tortora, L.; Nastishin, Y.; Finotello, D.; Kumar, S.; Lavrentovich, O. D. Self-Assembly of Lyotropic Chromonic Liquid Crystal Sunset Yellow and Effects of Ionic Additives. J. Phys. Chem. B 2008, 112, 16037−16319. (9) Dickinson, A. J.; LaRacuente, N. D.; McKitterick, C. B.; Collings, P. J. Aggregate Structure and Free Energy Changes in Chromonic Liquid Crystals. Mol. Cryst. Liq. Cryst. 2009, 509, 751−762. (10) Renshaw, M. P.; Day, I. J. NMR Characterization of the Aggregation State of the Azo Dye Sunset Yellow in the Isotropic Phase. J. Phys. Chem. B 2010, 114, 10032−10038. 13319

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