Degree of Response to Homeopathic Potencies Correlates with Dipole Moment Size in Molecular Detectors: Implications for Understanding the Fundamental Nature of Serially Diluted and Succussed Solutions
DiagnOx Laboratory, Cherwell Innovation Centre, Upper Heyford, Oxon, United Kingdom
CC-BY-NC-ND 4.0 · Homeopathy 2018; 107(01): 019-031
Original Research Article
The Faculty of Homeopathy
Background The use of solvatochromic dyes to investigate homeopathic potencies holds out the promise of understanding the nature of serially succussed and diluted solutions at a fundamental physicochemical level. Recent studies have shown that a range of different dyes interact with potencies and, moreover, the nature of the interaction is beginning to allow certain specific characteristics of potencies to be delineated.
Aims and Methods The study reported in this article takes previous investigations further and aims to understand more about the nature of the interaction between potencies and solvatochromic dyes. To this end, the UV-visible spectra of a wide range of potential detectors of potencies have been examined using methodologies previously described.
Results Results presented demonstrate that solvatochromic dyes are a sub-group of a larger class of compounds capable of demonstrating interactions with potencies. In particular, amino acids containing an aromatic bridge also show marked optical changes in the presence of potencies. Several specific features of molecular detectors can now be shown to be necessary for significant interactions with homeopathic potencies. These include systems with a large dipole moment, electron delocalisation, polarizability and molecular rigidity.
Conclusions Analysis of the optical changes occurring on interaction with potencies suggests that in all cases potencies increase the polarity of molecular detectors to a degree that correlates with the size of the compound’s permanent or ground dipole moment. These results can be explained by inferring that potencies themselves have polarity. Possible candidates for the identity of potencies, based on these and previously reported results, are discussed.
solvatochromic dyes – aromatic bridged amino acids – molecular detectors – dipole moments – homeopathic potencies
Previous studies have demonstrated that solvatochromic dyes show significant changes in their UV-visible (US-vis) spectra under a range of conditions in the presence of homeopathic potencies.  The approach taken in the current article has been to extend those investigations to include compounds that are not strictly solvatochromic but embody some crucial components of solvatochromic compounds in an attempt to further understand the molecular features necessary for dye–potency interaction. The methodology employed has been one in which a substantial number of aromatic compounds have been screened, the only requirements of the compounds tested being water solubility and an electron delocalised bridge between two polar groups. Surprisingly, it has been found that π-conjugated zwitterions respond to serially-diluted and succussed solutions. This discovery has revealed the existence of a large class of molecular detectors, which are in some ways superior to solvatochromic dyes for investigating potencies. For instance, π-conjugated zwitterions exhibit responses to potencies which, in one case, is the largest so far seen, and together with their relatively easy availability and potential for endless variations of structure, means specific aspects of the potency–dye interaction can be teased apart in some detail. As a consequence, several structural features necessary in order for compounds to be molecular detectors can now be delineated, and in turn several inferences can be made about the fundamental physicochemical nature of potencies.
Materials and Methods
Experimental protocol is essentially as described previously.  However, some minor improvements have been made and these are shown in [Fig. 1]. On obtaining potency and control solutions in 90% ethanol from the pharmacy, a 100-fold dilution was performed into reverse osmosis water (ROW) using standard amber moulded glass bottles from the same manufacturing batch. Exact material compatibility in terms of any leachates was established by inductively coupled plasma optical emission spectrometry (ICP-OES) at this stage. A further 100-fold dilution of each solution was then made into high density polyethylene (HDPE) bottles. These bottles were then stored separated by a minimum of at least 1.5 m.
Fig. 1 Experimental protocol employed in this study (see text and Materials and Methods for details). HDPE, high density polyethylene.
Assays involved taking 50 μL of each solution and adding these aliquots to 2.95 mL of pre-prepared dye solution. Both control–dye and potency–dye solutions were then placed in black film canisters as described previously. Difference spectra were run at intervals up to a maximum of 20 days. A total dilution of (100 × 100 × 60), or 600,000-fold, therefore occurs between solutions obtained from the pharmacy and solutions used for assays. Furthermore, as control and potency solutions approached depletion, ROW was added to both HDPE containers to replenish stocks. Over the course of the current studies both solutions have been replenished several times, resulting in a further c.100-fold dilution of the potency solution without any diminution of its effectiveness.
Assays have also been performed in which samples from the preceding amber molded glass bottles have been used, and no difference has been observed from results obtained from taking samples from the following HDPE bottles ([Fig. 1]). This indicates that leachates from amber molded glass bottles have no effect on results. The protocol outlined in [Fig. 1] has, therefore, been used as a precaution rather than as a necessity.
Unless otherwise stated Glycerol 50M has been used throughout this study. This has allowed comparisons to be made between all dyes, both in this study and in previous studies. At infrequent intervals, different potencies of Glycerol and potencies of other homeopathic medicines have been tested on the molecular detectors described in this article to ensure the methodology is not somehow specific to Glycerol 50M.
6-amino-2-naphthoic acid (ANA), 4-aminobenzoic acid (ABA), 4′-amino-[1,1′-biphenyl]-4-carboxylic acid (ABPA), methylene violet (Bernthsen) (MV), coumarin 343 (C343), β-cyclodextrin (β-CD), cucurbituril (CB7), citric acid/sodium citrate, sodium dihydrogen phosphate/disodium hydrogen phosphate, boric acid/sodium borate and sodium N-cyclohexyl-3-aminopropanesulfonate (CAPS) were obtained from Sigma Aldrich UK and were of the highest purity available.
5, 6-diamino-naphthalene-1, 3-disulfonic acid (DANDSA) was obtained from Molekula, UK.
4-pyridinium phenolate (4PP) was synthesised and provided by WuXi App Tec (Hong Kong) Ltd. Structure and purity were confirmed by NMR.
The provenances of Brooker’s merocyanine (BM), bis-dimethylaminofuchsone (BDF), phenol blue (PB), and 2, 6-dichloro-4-(2, 4, 6-triphenyl-pyridinium-1-yl)-phenolate (ET33) are as stated previously. 
ROW was used throughout this study and had a resistivity of 15MΩcm (checked daily).
Disposable high purity UV-transparent cuvettes (Brand GmbH) with stoppers were used throughout and are described previously. Disposable four-sided optically transparent fluorescence cuvettes (Brand GmbH) made of the same material as the UV cuvettes, with stoppers, were used to record fluorescence spectra.
As in previous studies   dye solutions were made and stored in HDPE bottles and allowed to equilibrate overnight before use. All dye solutions were stored in the dark as a precaution against light-induced degradation. This was deemed unnecessary but continued as a practice to ensure compatibility with previous studies.
Dyes were made up in buffers at concentrations sufficient to give an absorbance of between 0.5 and 1.5. Buffer solutions in which dye was dissolved were at a concentration of 20 mM throughout.
Homeopathic Potencies and Control Solutions
Glycerol 50M along with other potencies of glycerol were obtained from Helios Homeopathy Ltd, Tunbridge Wells, UK. All the results presented in this study were performed with Glycerol 50M.
Thirty microlitres of potency (in 90% ethanol) was diluted into 3.0 mL of ROW in an amber moulded glass bottle provided by the Homeopathic Supply Company Ltd, Bodham, UK. This ‘diluted’ aqueous potency was then further ‘diluted’ by transferring 30 μL into 3 mL of ROW in a 5 mL HDPE bottle. This final ‘HDPE’ potency solution was then used in assays ([Fig. 1]).
Control solutions were either un-medicated and un-succussed 90% ethanol obtained from Helios Homeopathy Ltd and diluted 100-fold as above into amber moulded glass bottles from the same batch as that used for potency dilutions, or control solutions consisted simply of ROW added to amber molded glass bottles from the same batch. As with potency solutions, a further 100-fold ‘dilution’ was performed into ROW in a 5 mL HDPE bottle, and this solution was used in assays ([Fig. 1]).
Final control and potency solutions in HDPE bottles were stored separated by a minimum of at least 1.5 m at room temperature in black plastic film canisters (Geo-Versand, GmbH, Germany).
Leachates from both potency and control bottles prior to dilution in HDPE bottles were analyzed by ICP-OES (Oxford-Analytical Ltd, Bicester, UK) and found to be at the same (<3μM) level for all elements tested (Ca, Mg, Si, K, Na, B, Fe). Dilution into ROW in HDPE bottles would then be expected to dilute those leachates to a < 0.03 μM level. A further 60-fold dilution occurs on addition of potency or controls to assay solutions.
UV-vis spectra were recorded on a Shimadzu UV-2600 double-beam spectrophotometer.
Fluorescence spectra were recorded on a Shimadzu RF-6000 spectrofluorophotometer. Buffers were prepared using a Hanna pH210 microprocessor pH meter.
Difference spectra were performed as follows. A total of 2.95 mL of buffered dye solution were pipetted into each of two Brand UV cuvettes with stoppers and the spectrophotometer set to zero across the wavelength range used for scanning (typically c.300–800 nm for solvatochromic dyes and 220/230–600 nm for aromatic bridged amino acids). Fifty microlitres of control solution was then added to the reference cuvette and 50 μL of potency solution added to the sample cuvette ([Fig. 1]). Cuvettes were inverted three times to mix and then scanned (t = 0). After the initial scan, both cuvettes were placed in separate black plastic film canisters (Geo-Versand, GmbH) to exclude all light and kept under these conditions between any subsequent scans. Scans were normally performed at t = 0 minutes, 10 minutes, 40 minutes, 100 minutes, c.200 minutes, c.6 hours, and c.12 hours after mixing. Subsequent scans were performed at intervals of days after mixing up to a maximum of 20 days.
Normal (non-difference) scans of dye solutions with potency or control solutions added were against ROW, which had been zeroed beforehand.
All assays were performed in 20 mM buffered solutions. Buffers used were citrate (pH 3–7), phosphate (pH 6–8), borate (pH 8–10), and CAPS (pH 10–11).
Fluorescence spectra were performed using Brand disposable four-sided optically transparent fluorescence cuvettes (Brand GmbH) made of the same material as Brand UV cuvettes. Separate fluorescence spectra were recorded of dye–control and dye–potency solutions transferred from assays in Brand UV cuvettes so spectra could be directly compared with UV-vis spectra at a set time.
Compounds Used in the Current Study
All of the compounds used in the current study are water soluble and this was one of the main criteria in selecting chromophoric reagents for their suitability. Structures of all compounds are given in [Fig. 2]. Six of the compounds— Methylene Violet (Bernthsen) (MV), Coumarin 343 (C343), Bis-dimethylaminofuchsone (BDF), 4-pyridinium phenolate (4PP), 2, 6-Dichloro-4-(2, 4, 6-triphenyl-pyridinium-1-yl)-phenolate (ET33) and Brooker’s merocyanine (BM) are solvatochromic (see Appendix for definition); the first three being positively solvatochromic and the last three negatively solvatochromic. The other four compounds shown are essentially non-solvatochromic: that is their transition dipole moments are minimal. They are members of a class of compounds comprising amino acids with an aromatic bridge. There exists very little in the literature on this type of compound. What is available pertains to 4-aminobenzoic acid.   Aromatic bridged amino acids consist of amino and carboxylic or sulfonic acid groups attached at opposite ends of a delocalised core of electrons. As with solvatochromic dyes, an electron or electron density is free to move between the two ends of the molecule under the influence of an appropriate stimulus. Unlike solvatochromic dyes, however, solvent polarity has little effect on the relative stability of the compounds’ ground and exited electronic states, and light does not cause a spatial movement of electrons. In principle, proton transfer can also occur with certain aromatic bridged amino acids, and this feature along with the other properties of this class of compound will be discussed in relation to the results obtained with potencies.
Fig. 2 Structures of molecular detectors used in this study. From top left: Methylene violet (Bernthsen) (MV), coumarin 343 (C343), Brooker’s merocyanine (BM), 4-pyridinium phenolate (4PP), 2, 6-dichloro-4-(2, 4, 6-triphenyl-pyridinium-1-yl)-phenolate (ET33), Bis-dimethylaminofuchsone (BDF), 6-amino-2-naphthoic acid (ANA), 4-aminobenzoic acid (ABA), 4′-amino-[1,1′-biphenyl]-4-carboxylic acid (ABPA), 5, 6-diaminonaphthalene-1,3-disulfonic acid (DANDSA).
The amino acids with an aromatic bridge used in this study include 6-amino-2-naphthoic acid (ANA), 4-aminobenzoic acid (ABA), 5,6-diamino-naphthalene-1,3-disulfonic acid (DANDSA) and 4-amino-[1,1′-biphenyl]-4′-carboxylic acid (ABPA). While all four compounds respond to potencies with significant changes in their UV-vis spectra, results with DANDSA are of particular interest, as they provide the largest and most unusual spectral changes so far seen with any compounds, and provide insights into the potency–dye interaction which complement and add to those seen with the six solvatochromic dyes MV, C343, BM, 4PP, ET33 and BDF.
N ≥ 5 for all spectra discussed below. Where spectra are shown, error bars have been omitted for clarity. [Table 1] provides pKa and dipole moment data for all the dyes tested along with their degree of response to Glycerol 50M and summarises the more detailed information given below.
Abbreviations: ABA, 4-aminobenzoic acid; ABPA, 4′-amino-[1,1′-biphenyl]-4-carboxylic acid; ANA, 6-amino-2-naphthoic acid; BDF, bis-dimethylaminofuchsone; BM, Brooker’s merocyanine; C343, coumarin C343; ET33, 2, 6-dichloro-4-(2, 4, 6-triphenyl-pyridinium-1-yl)-phenolate; DANDSA, 5, 6-diamino-naphthalene-1,3-disulfonic acid; MV, methylene violet (Bernthsen); 4PP, 4-pyridinium phenolate; PB, phenol blue.
a pKa values determined spectroscopically (this study).
b Dipole moment values estimated according to established principles.
c Percentage change in dye spectra under the influence of potency is a combination of steps one, two and three (see text for explanation).
Assays at pH Values ≈ dye pKas
Methylene Violet (Bernthsen)[Fig. 3] shows a typical series of difference spectra of MV ± potency at intervals up to 11 days (50 μM dye, 20 mM citrate buffer pH 4.0). What is striking is the size of the spectral changes, constituting c. 7% of the total absorbance of the dye (OD = 1.0 at 614 nm). As with previous studies  the difference spectrum is slow to appear but is then relatively stable over long time periods. The decrease at 614 nm is consistent with potency promoted protonation and loss of monomer. MV is conformationally inflexible ([Fig. 2]) and this may be a factor along with its high dipole moment (≥18D) in conferring a high degree of response to potencies. Fluorescence studies have confirmed that potency promotes MV aggregation (fluorescence spectra show a decrease in fluorescence intensity in the presence of potency). 
Fig. 3 Difference spectrum of 50 μM MV in 20 mM citrate buffer pH 4.0 with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 0, t = 10 minutes, t = 100 minutes, t = 260 minutes, t = 4 days and t = 11 days after mixing (see text for details). MV, methylene violet (Bernthsen).
Coumarin 343 is a structural analogue of MV and shows spectral differences very similar to the latter dye but with a decrease at 427 nm ([Fig. 4]). The difference spectra shown are of 50 μM dye in 20 mM phosphate buffer pH 7.0 ± potency. The changes observed are 4 to 5% of the total absorbance of the dye (1.6 at 427 nm). The inclusion of C343 in this study is important because of its smaller dipole moment relative to that of MV, although like MV, it is structurally inflexible. Difference spectra again are slow to develop and fluorescence studies show that potency promotes C343 aggregation.
Fig. 4 Difference spectrum of 50 μM C343 in 20 mM phosphate buffer pH 7.0 with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 17 minutes, t = 150 minutes, t = 12 hours and t = 7 days after mixing (see text for details). C343, coumarin C343.
Fig. 5 Difference spectrum of 90 μM BM in 20 mM borate buffer pH 8.5 containing 10 mM β- cyclodextrin with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 0, t = 100 minutes, t = 200 minutes, t = 385 minutes, t = 12 hours and t = 14 days after mixing (see text for details). BM, Brooker’s merocyanine.
This negatively solvatochromic dye is the simplest example of the pyridinium phenolates, of which ET30 and ET33 have already been examined. [Fig. 6] shows a series of difference spectra of 100 μM 4PP at pH 8.5 in 20 mM borate buffer ± potency over time. Changes are again slow to appear and constitute c.3% of the total absorbance of the dye (OD = 0.5 at 375 nm) at their maximum. As with MV and BM, the spectral changes seen are consistent with potency-induced protonation. 
Fig. 6 Difference spectrum of 100 μM 4PP in 20 mM borate buffer pH 8.5 with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 0, t = 10 minutes, t = 40 minutes, t = 100 minutes, t = 12 hours and t = 2 days after mixing (see text for details). 4PP, 4-pyridinium phenolate.
Like DANDSA below, 6-Amino-2-Naphthoic Acid (ANA) is a π-conjugated amino acid and not solvatochromic. Nevertheless [Fig. 7] shows a series of spectra of 200 μM ANA in 20 mM citrate buffer pH 3.5 ± potency. The decreases at c.315 nm and 250 nm are consistent with slow protonation induced by potency. Spectral changes constitute c.3 to 4% of the total absorbance of ANA (OD = 0.8 at 315 nm).
Fig. 7 Difference spectrum of 200 μM ANA in 20 mM citrate buffer pH 3.5 with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 0, t = 10minutes, t = 40 minutes, t = 100 minutes, t = 200 minutes and t = 4 days after mixing (see text for details). ANA, 6-amino-2-naphthoic acid.
Fig. 8 Difference spectrum of 70 μM DANDSA in 20 mM citrate buffer pH 4.0 with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 0, t = 100 minutes, t = 220 minutes, t = 7 days and t = 18 days after mixing (see text for details). DANDSA, 5, 6-diamino-naphthalene-1,3-disulfonic acid.
DANDSA demonstrates the first clear evidence that potency is initially acting to change the pKa value of a molecular reporter, which is then followed by changes in aggregation levels, rather than by acting directly on aggregation levels. These results are discussed below in relation to a proposed common mechanism of action of potencies on all molecular reporters so far examined.
4-Aminobenzoic Acid (ABA) is the smallest and simplest molecule examined for the effects of potency. Surprisingly perhaps, despite its size, it also demonstrates changes in its UV spectrum in the presence of potency with a decrease in absorbance at c. 292 nm in 20 mM citrate buffer pH 3.5. This change constitutes c.1% of the total absorbance of ABA and is consistent with potency-induced protonation. It is significant that ANA, a molecule that differs from ABA only in the length of its aromatic bridge ([Fig. 2]), and consequently its dipole moment, should respond more strongly than ABA. The importance of this structural difference between ANA and ABA in relation to their ability to respond to potencies is discussed below.
4′-Amino-[1, 1′-Biphenyl]-4-Carboxylic Acid
4′-Amino-[1, 1′-Biphenyl]-4-Carboxylic Acid (ABPA) is a structural analogue of ANA in which the naphthalene ring is replaced by a biphenyl electron delocalised bridge. Difference spectra, ± potency in 20 mM citrate buffer pH 4.2 show a decrease at c.305 nm and an increase at c.270 nm, consistent with potency-induced protonation. Overall absorbance changes constitute c.2% of total absorbance. This lower number compared with that found for ANA may reflect the conformational mobility of ABPA compared with ANA, an issue already mentioned in relation to BM, and discussed in more detail below.
The above results from eight different molecular reporters demonstrate that potencies interact with a range of structural forms to produce significant spectral changes. Several compounds, and particularly DANDSA, have indicated that there are, however, at least two steps involved in the production of these spectral changes. The first involves potency-induced protonation. As solutions are buffered and it is known that ordinary pH indicators show no response to potencies, together with the slow appearance of spectral changes over hours, this suggests some kind of electron density shift occurs across the molecules resulting in altered pKa values.  This conclusion has already been deduced from results obtained with BDF in a previous study. The current study has provided further evidence that this indeed may be the case. If potencies are producing a pKa change in molecular detectors, then a preceding step involving some kind of electron density movement across the molecules may well be the primary form of the interaction between potencies and molecular detectors.
This possibility can be tested in the following way. If assays are performed at pH values well away from the pKa value of compounds, then protonation/deprotonation is not possible, and the putative step two is silenced. If molecular encapsulators such as β-CD or cucurbiturils are added to solutions to prevent any aggregation of compounds, then step three is also silenced. Any spectral changes in the presence of potencies are then likely to be attributable to an earlier, possibly primary, step.
The following results pertain to assays performed at pH values >> pKa values and in the presence of molecular encapsulators with dyes MV, BDF, BM, 4PP and ET33. It should be noted here that only solvatochromic dyes are capable of showing sufficient spectral changes due to spatial electron movement and so amino acids with an aromatic bridge cannot be tested for this step directly.
Assays at pH Values >> Dye pKas
Positively Solvatochromic Dyes MV and BDF[Fig. 9] shows difference spectra (right) obtained with 50 μM MV in 20 mM borate buffer pH 9.0/10 mM β-CD ± potency at t = 100 and 220 minutes. A peak at 629 nm is evident. The λmax of a control solution of MV in the same β-CD/borate buffer is at 617 nm (left) and this is attributable to monomer, with a shoulder at c.574 nm to dimer. The new peak at 629 nm in the presence of potency can, therefore, be confidently assigned to a form of monomer. Positively solvatochromic dyes display bathochromic shifts in their spectra with increasing stabilisation of the excited (more charged) state ([Fig. 10]). It seems reasonable to conclude, therefore, that potency is stabilising something similar to the excited state of MV in which the opposite ends of the molecule are becoming more formally charged.
Fig. 9 Difference spectra of MV in 20 mM borate buffer pH 9.0 containing 10 mM β-cyclodextrin with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette. Spectra correspond to t = 100 minutes and t = 220 minutes after mixing. Maxima are at 629 nm (right-hand curves). Control solution of MV in the same β-cyclodextrin buffer (left-hand curve). Maximum is at 617 nm. See text for details. Spectra are not to scale. MV, methylene violet (Bernthsen). Fig. 10 Potencies are postulated to interact with and stabilise the ground (more polar) state of negatively solvatochromic dyes (left) and the excited (more polar) state of positively solvatochromic dyes (right).
A comparable result to that with MV is seen with BDF in 20mM borate buffer pH 9.0/10 mM β-CD ± potency. In this case, a new peak appears at 583 nm compared with the λmax of a control solution of BDF in the same buffer which is at 567 nm. Again, potency seems to be stabilising a more polar form of BDF. This can only occur if an electron density movement has occurred toward the carbonyl moiety of BDF, as previously suggested may be happening.
Negatively Solvatochromic Dyes BM, 4PP and ET33[Fig. 11] shows a difference spectrum of 50 μM ET33 in 20 mM borate buffer pH 8.5/10 mM β-CD ± potency. While the differences are small, they nevertheless show a hypsochromic shift in the presence of potency with a decrease at 470 nm and an increase at 373 nm. The λmax of a control solution of ET33 in the same buffer is at 407 nm. In contrast to results seen with the positively solvatochromic dyes BDF and MV, potency is inducing a hypsochromic shift in the spectrum of ET33. Negatively solvatochromic dyes display hypsochromic shifts in their spectra with increasing stabilisation of their ground (more charged) state ([Fig. 10]). It seems, therefore, that in the presence of potency the ground state of ET33, which is already charged, is having its polarity increased even further.
Fig. 11 Difference spectrum of ET33 in 20 mM borate buffer pH 8.5 containing 10 mM β- cyclodextrin with control added to the reference cuvette and Glycerol 50 M added to the sample cuvette showing a decrease at 470 nm and an increase at 373 nm (bottom curve). Spectrum corresponds to t = 210 minutes after mixing (see text for details). Control spectrum of ET33 in the same buffer containing 10 mM β-cyclodextrin shows an absorbance maximum at c.407 nm (top curve). Spectra are not to scale. ET33, 2, 6-dichloro-4-(2, 4, 6-triphenyl-pyridinium-1-yl)-phenolate.
Similar results have been obtained with 4PP and BM. [Table 2] shows a summary of the results obtained with all five dyes. It would appear from these results that potency is preferentially interacting with, and intensifying, the charged forms of both positively and negatively solvatochromic dyes.
The effect of potency on dye spectra in the presence of β-cyclodextrin and at pH values >> the pKa of dyes. Left-hand column gives dye maxima in control solutions of buffer/β-cyclodextrin; the right-hand column shows the effect of potency