**2.1. Controversial experimental evidence**

The aggregation of single CDs and CD-guest complexes, in water, has been described in a number of recent studies [2, 3, 13, 31, 37, 40, 41]. Despite the efforts for understanding the factors that govern inclusion/binding with guest molecules, the precise manner in which CD molecules aggregate and the cooperative effects underlying this phenomenon are much less studied and still far from consensual.

light scattering (DLS) data of α-, β-, and γ-CD aqueous solutions, with mean hydrodynamic radii of less than 1 nm and higher than 60 nm for the fast and slow components (attributed to monomer and aggregated CDs, respectively). This has been revisited by Puskás et al. [49] by using the same technique. However, contrarily to previous work, only γ-CD aggregates have been confirmed. In other studies [50, 51], the formation of CD aggregates of globular shape, at [β-CD] = 3 mM, with a minimum hydration radius of ca. 90 nm, was reported, based on data from different techniques, including DLS, cryo-TEM, and electron spin resonance (ESR) probe spectroscopy. However, at higher CD concentrations, these particles coexist with other structures as large as a few micrometers. These aggregates tend to increase with CD concentration, suggesting cooperative aggregate-aggregate interactions. In addition, Rao and Geckeler [52] have concluded that the formation of β-CD supramolecules can also occur in aqueous solutions at room temperature. By increasing the stirring time and the concentration from 4 to 10 mM, it was possible to follow the formation of cage-like structures (with an average size of 7.5 nm), after 5 h stirring, evolving to channeled structures (with 260 nm length) after 72 h stirring.

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The thermodynamic parameters of β-CD self-assembly have been studied, assuming that CDs behave as colloids [36]. For that, the scattering intensity of a set of β-CD solutions of different concentrations has been measured; by plotting the scattering intensity as a function of β-CD concentration, two different regimes were observed below and above the critical aggregation concentration (cac = 1.6 mM): at c < cac, and only monomers (the occurrence of small aggregates cannot be also neglected) exist in solution. However, at c > cac, the scattering intensity increases linearly with β-CD concentration, indicating the presence of two different set of aggregates of 60.0 nm and 120 nm in size. Using the pseudo-phase model, the free energy of aggregation was calculated to be −15.95 kJ mol−1 at 298.15 K. From the dependence of the cac value on the temperature, the variation of the aggregation enthalpy and, consequently, the aggregation entropy (at 298.15 K) were estimated to be −26.48 kJ mol−1 and −35.32 J K−1 mol−1, respectively. These values for thermodynamic parameters suggest that (a) aggregation is enthalpy driven, and (b) aggregates are formed by noncovalent interactions [53]. Following the same approach, the cac values of α-, β-, and γ-CDs were also measured by using a permeability technique, based on dialysis membranes with molecular weight cut off higher than 2 kDa [3, 54]. Inspecting the flux of CDs as a function of concentration, two different regimes have been found which were attributed to the formation of aggregates. The calculated values for the cac of α-, β-, and γ-CDs are 12.2, 6.1, and 7.2 mM,

Recently, a thermodynamic study [55] using isodesmic and K2-K self-assembly models was performed on CD derivatives (HP-β-CD, HP-γ-CD, and sulfobutylether(SBE)-β-CD). The isodesmic model assumes that the Gibbs energy and equilibrium constant (K) are equal in each addition of a monomer to an aggregate (for details see Ref. [55]). The K2-K model is a modified version of the former, in which the K value of the first step of the self-assembly is different from those of the remaining steps. The respective cac values and aggregate sizes were also

cac values of ca. 2% (m/v). Three different groups of particle sizes were also identified based on correlation functions: (i) a group with ca. 1 nm corresponds to a single CD molecule, (ii) a group with size values ranging from ca. 30 nm to 60 nm for HP-γ-CD and from ca. 10–70 nm for SBE-β-CD and from ca. 100 nm to 200 nm for HP-β-CD, and (iii) a small group with larger

H NMR and TEM, respectively. These CDs displayed similar

respectively.

determined, using DLS and 1

The classical assumption states that inclusion complexes between CDs and guest molecules are always formed in "ideal" solutions, with individual complexes, independent of each other. However, the treatment of the interaction between system components is oversimplified, since CDs can form both inclusion and noninclusion complexes and water-soluble aggregates. In some cases, the aggregation results in the opalescence of aqueous CD solutions. However, the reduced diameter of the aggregates is smaller than the wavelength of visible light, and more often, the formation of clear solutions is promoted.

The first reference to the occurrence of self-aggregation dates back to 1983, when Koichiro and co-workers [42], based on viscosity and activity coefficient data of aqueous solutions of αand γ-cyclodextrins, suggested the occurrence of dimers or larger aggregates. These authors have also pointed out that such aggregates are acting as "structure making" [43] by tightening water-water hydrogen bonding. Ten years later, Häusler and Müller-Goymann [44] have observed that at concentrations above 50% (w/w), hydroxypropyl (HP)-β-CD self-aggregates, leading to an increase in the solution viscosity. They also found that the addition of chaotropic solutes (e.g., urea and NaCl) tends to decrease the viscosity of solutions as a consequence of CD disaggregation. A similar observation was found for γ-CD (10% m/v) solutions [45], at physiological pH. In both works, the self-aggregation of CD monomers is justified by intermolecular H-bonding interactions promoted by the hydrophilic rims [44, 45].

Coleman et al. [46] extended their studies to β-CD, the less soluble of all native CDs, and found that the addition of water structure-breaking solutes or an increase of the solution pH (at values higher than 12.5) in order to ionize the ─OH groups leads to an increase in solubility. This evidence led them to hypothesize that the solubility of CDs is related with interactions between CD aggregates and the water through the formation of two chains of hydrated β-CD molecules forming a rod-like aggregate. These authors also argue that the structure of water has an important role on the aggregation/disaggregation of CDs.

The quantification of size and mass percentage of aggregates was only made possible, in a systematic manner, during the last decade. It has been concluded, by using photon correlation spectroscopy (PCS), that in a 12 mM CD aqueous solution, large polydisperse aggregates of 200–300 nm in size were formed [29]; however, the respective mass percentage is quite small when compared to that of free CD. For example, the mass contribution of α-CD aggregates is ca. 0.8% (0.096 mM) assuming coils or 0.001% (0.12 μM) considering spheres [29]. For other CDs, the mass contribution of aggregates is also residual, i.e., 0.0011% (0.13 μM) for β-CD [47] and 0.02% (0.154 mM) for γ-CD solutions [45]. He et al. [48] found a bimodal distribution in dynamic light scattering (DLS) data of α-, β-, and γ-CD aqueous solutions, with mean hydrodynamic radii of less than 1 nm and higher than 60 nm for the fast and slow components (attributed to monomer and aggregated CDs, respectively). This has been revisited by Puskás et al. [49] by using the same technique. However, contrarily to previous work, only γ-CD aggregates have been confirmed. In other studies [50, 51], the formation of CD aggregates of globular shape, at [β-CD] = 3 mM, with a minimum hydration radius of ca. 90 nm, was reported, based on data from different techniques, including DLS, cryo-TEM, and electron spin resonance (ESR) probe spectroscopy. However, at higher CD concentrations, these particles coexist with other structures as large as a few micrometers. These aggregates tend to increase with CD concentration, suggesting cooperative aggregate-aggregate interactions. In addition, Rao and Geckeler [52] have concluded that the formation of β-CD supramolecules can also occur in aqueous solutions at room temperature. By increasing the stirring time and the concentration from 4 to 10 mM, it was possible to follow the formation of cage-like structures (with an average size of 7.5 nm), after 5 h stirring, evolving to channeled structures (with 260 nm length) after 72 h stirring.

**2. General aspects**

48 Cyclodextrin - A Versatile Ingredient

**2.1. Controversial experimental evidence**

studied and still far from consensual.

The aggregation of single CDs and CD-guest complexes, in water, has been described in a number of recent studies [2, 3, 13, 31, 37, 40, 41]. Despite the efforts for understanding the factors that govern inclusion/binding with guest molecules, the precise manner in which CD molecules aggregate and the cooperative effects underlying this phenomenon are much less

The classical assumption states that inclusion complexes between CDs and guest molecules are always formed in "ideal" solutions, with individual complexes, independent of each other. However, the treatment of the interaction between system components is oversimplified, since CDs can form both inclusion and noninclusion complexes and water-soluble aggregates. In some cases, the aggregation results in the opalescence of aqueous CD solutions. However, the reduced diameter of the aggregates is smaller than the wavelength of visible

The first reference to the occurrence of self-aggregation dates back to 1983, when Koichiro and co-workers [42], based on viscosity and activity coefficient data of aqueous solutions of αand γ-cyclodextrins, suggested the occurrence of dimers or larger aggregates. These authors have also pointed out that such aggregates are acting as "structure making" [43] by tightening water-water hydrogen bonding. Ten years later, Häusler and Müller-Goymann [44] have observed that at concentrations above 50% (w/w), hydroxypropyl (HP)-β-CD self-aggregates, leading to an increase in the solution viscosity. They also found that the addition of chaotropic solutes (e.g., urea and NaCl) tends to decrease the viscosity of solutions as a consequence of CD disaggregation. A similar observation was found for γ-CD (10% m/v) solutions [45], at physiological pH. In both works, the self-aggregation of CD monomers is justified by inter-

Coleman et al. [46] extended their studies to β-CD, the less soluble of all native CDs, and found that the addition of water structure-breaking solutes or an increase of the solution pH (at values higher than 12.5) in order to ionize the ─OH groups leads to an increase in solubility. This evidence led them to hypothesize that the solubility of CDs is related with interactions between CD aggregates and the water through the formation of two chains of hydrated β-CD molecules forming a rod-like aggregate. These authors also argue that the structure of

The quantification of size and mass percentage of aggregates was only made possible, in a systematic manner, during the last decade. It has been concluded, by using photon correlation spectroscopy (PCS), that in a 12 mM CD aqueous solution, large polydisperse aggregates of 200–300 nm in size were formed [29]; however, the respective mass percentage is quite small when compared to that of free CD. For example, the mass contribution of α-CD aggregates is ca. 0.8% (0.096 mM) assuming coils or 0.001% (0.12 μM) considering spheres [29]. For other CDs, the mass contribution of aggregates is also residual, i.e., 0.0011% (0.13 μM) for β-CD [47] and 0.02% (0.154 mM) for γ-CD solutions [45]. He et al. [48] found a bimodal distribution in dynamic

light, and more often, the formation of clear solutions is promoted.

molecular H-bonding interactions promoted by the hydrophilic rims [44, 45].

water has an important role on the aggregation/disaggregation of CDs.

The thermodynamic parameters of β-CD self-assembly have been studied, assuming that CDs behave as colloids [36]. For that, the scattering intensity of a set of β-CD solutions of different concentrations has been measured; by plotting the scattering intensity as a function of β-CD concentration, two different regimes were observed below and above the critical aggregation concentration (cac = 1.6 mM): at c < cac, and only monomers (the occurrence of small aggregates cannot be also neglected) exist in solution. However, at c > cac, the scattering intensity increases linearly with β-CD concentration, indicating the presence of two different set of aggregates of 60.0 nm and 120 nm in size. Using the pseudo-phase model, the free energy of aggregation was calculated to be −15.95 kJ mol−1 at 298.15 K. From the dependence of the cac value on the temperature, the variation of the aggregation enthalpy and, consequently, the aggregation entropy (at 298.15 K) were estimated to be −26.48 kJ mol−1 and −35.32 J K−1 mol−1, respectively. These values for thermodynamic parameters suggest that (a) aggregation is enthalpy driven, and (b) aggregates are formed by noncovalent interactions [53]. Following the same approach, the cac values of α-, β-, and γ-CDs were also measured by using a permeability technique, based on dialysis membranes with molecular weight cut off higher than 2 kDa [3, 54]. Inspecting the flux of CDs as a function of concentration, two different regimes have been found which were attributed to the formation of aggregates. The calculated values for the cac of α-, β-, and γ-CDs are 12.2, 6.1, and 7.2 mM, respectively.

Recently, a thermodynamic study [55] using isodesmic and K2-K self-assembly models was performed on CD derivatives (HP-β-CD, HP-γ-CD, and sulfobutylether(SBE)-β-CD). The isodesmic model assumes that the Gibbs energy and equilibrium constant (K) are equal in each addition of a monomer to an aggregate (for details see Ref. [55]). The K2-K model is a modified version of the former, in which the K value of the first step of the self-assembly is different from those of the remaining steps. The respective cac values and aggregate sizes were also determined, using DLS and 1 H NMR and TEM, respectively. These CDs displayed similar cac values of ca. 2% (m/v). Three different groups of particle sizes were also identified based on correlation functions: (i) a group with ca. 1 nm corresponds to a single CD molecule, (ii) a group with size values ranging from ca. 30 nm to 60 nm for HP-γ-CD and from ca. 10–70 nm for SBE-β-CD and from ca. 100 nm to 200 nm for HP-β-CD, and (iii) a small group with larger aggregates attaining 1 μm, for β-CD derivatives, and from ca. 140 nm to 1 μm for HP-γ-CD. It was shown that aggregation results from some cooperative contributions, with the first step of the aggregation being less favorable than the subsequent ones. A thermodynamic analysis indicated that the aggregation process was spontaneous, exothermic, and associated to an entropy loss. The calculated standard free energies range from −7.1 kJ mol−1 for SBE-β-CD to −10.6 for HP-γ-CD, and the enthalpy values were −20.6, −27.5, and −46.3 kJ mol−1 for HP-β-CD, SBE-β-CD, and HP-γ-CD, respectively [55].

type of aggregation occurred for a CD concentration of ca. 10% (wt/vol) [32]. The selfassociation of CD complexes can explain the observed decrease in the activity coefficient with increasing CD concentration and the dependence of the complex stoichiometry on

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Several model compounds [32] have been recently used to investigate the effect of the physicochemical properties of the guest molecules on the CD aggregation behavior. For instance, the impact of a set of esters of para-hydroxybenzoic acid, differing in the side chain length, on HP-β-CD aggregation was recently evaluated resorting to permeation experiments, DLS and MS. The number and size of CD aggregates (<200 nm) increased in the presence of longer guests. However, no clear relation was found between the extent of aggregate formation and

The premicellar association of inclusion complexes of cationic surfactants and β-CD followed by micellar association of the inclusion complexes has also been suggested based on NMR studies. In addition, micelle-like assemblies with diameters exceeding 200 nm have been

The structure and size of these CD aggregates are clearly affected by water molecules and hydration shells [2]. Although the ability of CDs to self-assemble to form aggregates is well documented, it has also been shown that the aggregates are very unstable. Attempts to stabilize nanosize self-assembled CD aggregates of the native CDs, and their hydrophilic and

There are two typical crystal structures for native CDs: cages and channels (see **Figure 1**) [22, 66]. The cage arrangement occurs when CDs are grouped crosswise, displaying a herringbone pattern (**Figure 1a**), or are aligned in adjacent layers leading to a brick-like pattern (**Figure 1b**). In both cases, the formation of inclusion complexes is prevented, as the CD cavities are

**Figure 1.** Schematic representation of packing structures of (a) cage-type; (b) layer-type CD; and (c) head-to-tail channel-

observed in aqueous solutions containing trans-β-carotene and β-CD and γ-CD [2].

monomeric derivatives have not been successful so far.

**2.2. Common arrangements in CD aggregates**

blocked on both portals by neighboring CDs.

type CD crystals. Adapted from Ref. [66].

the method applied.

the CD concentration.

The dynamics of CDs in aqueous solution has been fully assessed using different NMR techniques by Valente et al. [56, 57]. The analysis of 1 H NMR self-diffusion of deuterium solutions of CDs shows that, for all three natural CDs, diffusion coefficients depend linearly on the CD volume fraction, suggesting that these molecules are behaving as nonaggregate hard spheres. A similar conclusion was reached from the analysis of the dependence of mutual diffusion coefficients on CDs concentration [58–60].

A more sensitive parameter, related to the volume of the diffusing particle, is the transverse magnetization relaxation time *T*<sup>2</sup> or the spin–spin relaxation rate *R*<sup>2</sup> (=1/*T*<sup>2</sup> ). In a perfectly homogeneous magnetic field, the *R*<sup>2</sup> relaxation rate can be measured directly from the free induction decay in the time domain or the full width at half height of the resonance in the frequency domain. The dependence of *R*<sup>2</sup> as a function of CD volume showed that no aggregation occurs. However, the presence of more transient aggregates cannot be excluded for cases in which the lifetime of the aggregate is short compared to the respective tumbling time. The presence of very large aggregates, not visible in the NMR spectra on account of their slow rotational tumbling, cannot also be ruled out. A different but complementary aspect is related to the mechanism of interaction. For further insight, the aggregation of α-, β-, and γ-CDs in aqueous solutions was addressed by focusing on the CD-CD interactions using deuterium relaxation rates (*R*<sup>1</sup> ) for deuterium-labeled CDs. In this particular case, the dependence of *T*1 (=1/*R*<sup>1</sup> ) on the CD concentration, for all CDs, was explained by the equilibrium between monomeric and dimeric CDs and, again, no evidence in favor of large aggregates of CDs involving a nonnegligible fraction was found [57].

The formation of aggregates in aqueous solutions containing CDs can be promoted by the presence of guest compounds, which upon inclusion can also contribute to understand and predict the CD aggregation behavior. The structure and nature of the guest molecule can thus affect the CD aggregation process. CD-guest complexes are, most often, simply formed by one guest molecule and one CD molecule. However, ternary complexes are also frequently described [61], where water-soluble polymers [62, 63], metal ions, or organic salts [64] are used to potentiate some CD effect.

The coexistence of inclusion and noninclusion complexes in aqueous solutions containing CDs has been documented and associated with the formation of aggregates based on these complexes. The first evidence for aggregation with complexes involving CDs and lipophilic guests was reported by Mele and co-workers [65] in 1998. Later studies [32], with contradictory or ambiguous results, fostered further investigation on this phenomenon.

The formation of CD-guest-based aggregates in the nanosize range has been confirmed by DLS and TEM analyses and associated to a negative deviation from linearity. This type of aggregation occurred for a CD concentration of ca. 10% (wt/vol) [32]. The selfassociation of CD complexes can explain the observed decrease in the activity coefficient with increasing CD concentration and the dependence of the complex stoichiometry on the method applied.

Several model compounds [32] have been recently used to investigate the effect of the physicochemical properties of the guest molecules on the CD aggregation behavior. For instance, the impact of a set of esters of para-hydroxybenzoic acid, differing in the side chain length, on HP-β-CD aggregation was recently evaluated resorting to permeation experiments, DLS and MS. The number and size of CD aggregates (<200 nm) increased in the presence of longer guests. However, no clear relation was found between the extent of aggregate formation and the CD concentration.

The premicellar association of inclusion complexes of cationic surfactants and β-CD followed by micellar association of the inclusion complexes has also been suggested based on NMR studies. In addition, micelle-like assemblies with diameters exceeding 200 nm have been observed in aqueous solutions containing trans-β-carotene and β-CD and γ-CD [2].

The structure and size of these CD aggregates are clearly affected by water molecules and hydration shells [2]. Although the ability of CDs to self-assemble to form aggregates is well documented, it has also been shown that the aggregates are very unstable. Attempts to stabilize nanosize self-assembled CD aggregates of the native CDs, and their hydrophilic and monomeric derivatives have not been successful so far.

#### **2.2. Common arrangements in CD aggregates**

aggregates attaining 1 μm, for β-CD derivatives, and from ca. 140 nm to 1 μm for HP-γ-CD. It was shown that aggregation results from some cooperative contributions, with the first step of the aggregation being less favorable than the subsequent ones. A thermodynamic analysis indicated that the aggregation process was spontaneous, exothermic, and associated to an entropy loss. The calculated standard free energies range from −7.1 kJ mol−1 for SBE-β-CD to −10.6 for HP-γ-CD, and the enthalpy values were −20.6, −27.5, and −46.3 kJ mol−1 for HP-β-CD,

The dynamics of CDs in aqueous solution has been fully assessed using different NMR tech-

of CDs shows that, for all three natural CDs, diffusion coefficients depend linearly on the CD volume fraction, suggesting that these molecules are behaving as nonaggregate hard spheres. A similar conclusion was reached from the analysis of the dependence of mutual diffusion

A more sensitive parameter, related to the volume of the diffusing particle, is the transverse

induction decay in the time domain or the full width at half height of the resonance in the

gation occurs. However, the presence of more transient aggregates cannot be excluded for cases in which the lifetime of the aggregate is short compared to the respective tumbling time. The presence of very large aggregates, not visible in the NMR spectra on account of their slow rotational tumbling, cannot also be ruled out. A different but complementary aspect is related to the mechanism of interaction. For further insight, the aggregation of α-, β-, and γ-CDs in aqueous solutions was addressed by focusing on the CD-CD interactions using deuterium

monomeric and dimeric CDs and, again, no evidence in favor of large aggregates of CDs

The formation of aggregates in aqueous solutions containing CDs can be promoted by the presence of guest compounds, which upon inclusion can also contribute to understand and predict the CD aggregation behavior. The structure and nature of the guest molecule can thus affect the CD aggregation process. CD-guest complexes are, most often, simply formed by one guest molecule and one CD molecule. However, ternary complexes are also frequently described [61], where water-soluble polymers [62, 63], metal ions, or organic salts [64] are

The coexistence of inclusion and noninclusion complexes in aqueous solutions containing CDs has been documented and associated with the formation of aggregates based on these complexes. The first evidence for aggregation with complexes involving CDs and lipophilic guests was reported by Mele and co-workers [65] in 1998. Later studies [32], with contradic-

The formation of CD-guest-based aggregates in the nanosize range has been confirmed by DLS and TEM analyses and associated to a negative deviation from linearity. This

tory or ambiguous results, fostered further investigation on this phenomenon.

or the spin–spin relaxation rate *R*<sup>2</sup>

) for deuterium-labeled CDs. In this particular case, the dependence of

) on the CD concentration, for all CDs, was explained by the equilibrium between

H NMR self-diffusion of deuterium solutions

(=1/*T*<sup>2</sup>

relaxation rate can be measured directly from the free

as a function of CD volume showed that no aggre-

). In a perfectly

SBE-β-CD, and HP-γ-CD, respectively [55].

50 Cyclodextrin - A Versatile Ingredient

coefficients on CDs concentration [58–60].

magnetization relaxation time *T*<sup>2</sup>

relaxation rates (*R*<sup>1</sup>

*T*1 (=1/*R*<sup>1</sup>

homogeneous magnetic field, the *R*<sup>2</sup>

frequency domain. The dependence of *R*<sup>2</sup>

involving a nonnegligible fraction was found [57].

used to potentiate some CD effect.

niques by Valente et al. [56, 57]. The analysis of 1

There are two typical crystal structures for native CDs: cages and channels (see **Figure 1**) [22, 66]. The cage arrangement occurs when CDs are grouped crosswise, displaying a herringbone pattern (**Figure 1a**), or are aligned in adjacent layers leading to a brick-like pattern (**Figure 1b**). In both cases, the formation of inclusion complexes is prevented, as the CD cavities are blocked on both portals by neighboring CDs.

**Figure 1.** Schematic representation of packing structures of (a) cage-type; (b) layer-type CD; and (c) head-to-tail channeltype CD crystals. Adapted from Ref. [66].

The channel-type assembly is observed if the CDs are stacked in columns so that cavities are aligned to produce channels (**Figure 1c**). While the channel arrangement can be converted into a cage structure by water sorption/desorption cycles, with an intermediated amorphous state, the latter usually results from rapid recrystallization of CDs. After reaching sorption equilibrium, CD molecules undergo a slow rearrangement to the cage structure with defined water content [66]. Similar patterns are generally found in the crystal structures of CD inclusion complexes [66]. When the entire guest molecule is small enough to be included inside a single CD cavity, cage-type structures are formed. On the other hand, a channel-type structure is observed in the presence of long-chain molecules as guests (e.g., polymers). Rusa and co-workers [2, 67] have reported the encapsulation of poly(ε-caprolactone) and poly(l-lactic acid) into α- and γ-CDs. The inclusion of a polymeric structure inside the CD cavity induces the formation of channel-like structures, being those with α-CD more stable due to the increase of hydrophobic CD-polymer interactions. By using an appropriate experimental procedure, the authors were able to produce a solid-state channel packing of CDs containing only water molecules inside the cavities [68]. The same group has also observed the inclusion of poly(vinyl alcohol) (PVA) into CD by taking advantage of the freezing–thawing process for PVA gelation [69]. In this process, the gelation of PVA-containing composites occurs, taking into account two different types of cross-linking: (i) the hydrogel-bonding naturally observed during the freezing-thawing process and (ii) the CD-CD aggregation resulting from channel-type arrangements [69].

also been investigated and explored for preparation of functionalized lipid membranes and improved biomimetic systems [73, 76]. A broader range of potential applications of CD aggre-

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Irrespective of the disparate observations, the self-aggregation capability must be affected by the type of CD present in the aqueous solution. While the aggregates of α-CD and γ-CD can be completely removed by standard filtering procedures, the formation of β-CD aggregates (at least as dimers or possibly larger aggregates) persists in solution, displaying fast aggregation kinetics. This suggests that the hydrophilic CD portals play a definite role in the aggregation process [29]. The disruption of hydrogen bond networks by ionization (or func-

The presence of aggregates in solutions containing structure-breaking solutes, in which the solubility of β-CD is enhanced, has provided new insights into this unusual behavior. The low solubility of β-CD (see **Table 1**) has been explained by the presence of aggregates and the respective unfavorable interaction with the hydrogen bond network of bulk water [46]. Note that aspects pertaining to the binding energy in the solid state cannot be disregarded. The relevance of understanding the mechanistic details of the CD aggregation phenomena encompasses either controlling/preventing the formation of aggregates (that preclude the development of specific formulations and the product development) or designing novel for-

Computer simulations have been used to rationalize the experimental findings concerning recognition [77], inclusion [36, 77–79], and aggregation [34, 35, 37, 39, 80]. The cooperative binding of at least two CD monomers to a guest molecule has been considered the driving force responsible for self-assembly processes in the construction of CD-based nanoarchitectures [78]. For aggregation processes without using guests, the assembly is usually driven by the hydrophilic portals (in native CDs) and by interactions between substituent chains of CD

The orientational patterns of inter-glucopyranose hydrogen bonds at the secondary portal of β-CD and the respective effect on the CD structure and dimer binding/stability in polar and nonpolar solvents have been explored by van der Spoel et al. [77] in the presence of various guest molecules. It was demonstrated, based on MD simulations and free energy calculations, that polar solvents with stronger hydrogen bond accepting abilities can easily disrupt intermolecular hydrogen bonds, resulting in less stable dimers. Also, the guest models included in the channel-type cavity increase the binding affinity between CD monomers, particularly in polar solvents [77]. Using a similar computational approach, the authors have explored the effect of three different dimerization modes of β-CD molecules and the presence of isoflavone drug analogues in the construction of CD-based nanostructured materials. It was demonstrated that the cooperative binding of CD cavities to guest molecules favors the dimerization process and, consequently, the overall stability and assembly of the CD nanostructures. It

gates are compiled in recent publications such as Refs. [70, 73] and references therein.

tionalization) increases solubility and may suppress aggregation.

derivatives with the neighboring cavities of other CDs [78].

**3. Computational observations**

mulation strategies.

#### **2.3. Applications of CD aggregates**

As already mentioned in previous sections, a variety of CD-based aggregates can be formed under different conditions (e.g., concentration, solvent medium, and temperature). These include native and modified CDs, inclusion complexes and the respective aggregates and also rotaxanes and polyrotaxanes, nanotubes, and other high-order structures, such as nanospheres and network aggregates [70]. The potential uses of these self-assembled nanomaterials have been explored for advanced applications, ranging from drug solubilization and drug delivery [71], selective binding [72], and controlled adsorption [72]. In pharmaceutical and biomedical fields, it is expected that such applications may include (i) the nanoencapsulation of drugs in the hydrophobic interchain volumes and nanocavities of modified CDs, which can be used as drug carriers or pharmaceutical excipients, (ii) anticancer phototherapy, (iii) gene delivery, and (iv) protection of unstable active components through the formation of inclusion complexes [70]. Several interesting examples of these potential applications have been focused on amphiphilic CDs, which allow to easily modulate both hydrophobic/hydrophilic and self-assembly properties, by grafting different substituents on the portals of native CDs [70, 73]. For instance, supramolecular assemblies based on CD/porphyrin nanoassemblies have been studied *in vitro* [74] as potential nanotherapeutics in A375 human melanoma cells. Other micellar structures and spherical vesicles based on CD-perylene conjugates have been designed to be included in fluorescence sensory and photoresponsive materials, photoinduced electron transfer systems, and organic electronic devices [75]. The self-aggregation of amphiphilic CDs has also been explored for drug delivery applications, as they are able to capture selectively drug molecules, displaying enhanced solubilization capacity [71]. The affinity of amphiphilic CDs for incorporation in model and biological membranes has also been investigated and explored for preparation of functionalized lipid membranes and improved biomimetic systems [73, 76]. A broader range of potential applications of CD aggregates are compiled in recent publications such as Refs. [70, 73] and references therein.
