This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 20335–20344 20335

Cite this: Phys. Chem. Chem. Phys., 2011, 13, 20335–20344

The fundamental Fuzzy logic operators and some complex Boolean logic

circuits implemented by the chromogenism of a spirooxazinew

Pier Luigi Gentili*

Received 1st June 2011, Accepted 9th September 2011

DOI: 10.1039/c1cp21782h

1,3-Dihydro-1,3,3-trimethyl-8 0-nitro-spiro[2H-indole-2,30-[3H]naphth[2,1-b][1,4]oxazine] (SpO) is

a photochromic, acidichromic and metallochromic compound. Its chromogenic properties are

characterized in acetonitrile, at room temperature. They are exploited to process both Boolean

and Fuzzy logic. By using HClO4, AlCl3 and Cu(ClO4)2 as chemical inputs, UV radiation as

power supply, and the absorbance at specific wavelengths in the visible as optical output, SpO

results in a five-states molecular switch whereby some complex Boolean logic circuits are

implemented. If the chemical inputs are varied in an analog manner, the solution of SpO assumes

an infinite number of colours. Therefore, by choosing the RGB colour coordinates as optical

outputs, the fundamental operators of the ‘‘infinite-valued’’ Fuzzy logic are implemented.

Particularly, two Fuzzy logic systems are built upon a new defuzzification procedure imitating

the way humans perceive colours.

Introduction

Current computers are based upon semiconductor materials

and electrical signals. In the last few decades, the performances

of the computers have been improved by the continuous

progress in the miniaturization of their components. Informa-

tion Technology is now approaching some fundamental limits

because transistors are made of a few atoms. At this level,

some technical problems arise, such as heat dissipation and

current leakage due to quantum phenomena. To overcome

these limitations, a paradigm shift is required. A proposal

consists in using molecules as computing elements, as it occurs

in all the biological systems, wherein the macromolecules are

the principal information processing devices.1–3 The choice of

molecules as computing elements allows not only electrical but

also chemical and other physical (such as optical, thermal,

magnetic and mechanical) inputs and outputs to be exploited.

It is possible to compute by using either single molecules

(through microscopic techniques reaching atomic resolution)

or large collections of molecules. By computing with atoms

and molecules, it is possible to process qubits, i.e. the elemen-

tary units of quantum information. The main technological

hindrance in devising a quantum computer comes from the

necessity of isolating the quantum systems from the environment

exerting decoherent effects on the qubits. When such detrimental

effects are unavoidable, it is still possible to use atoms and

molecules to process ‘‘classical’’ information, that is, it is

feasible to implement either Boolean or multi-valued logic

gates.4–10 A particular kind of multi-valued logic that can be

implemented also at the molecular level is Fuzzy logic,11,12

that is an ‘‘infinite-valued’’ one. Fuzzy logic is drawing much

attention of the scientific community aimed at developing

Artificial Intelligence. There is a worldwide effort to try to

simulate the living beings’ distinctive feature of soft computing,

i.e. of making decisions based upon incomplete and vague

information tainted by environmental noise. Among the consti-

tuents of soft computing, Fuzzy logic plays an important role13

because it is mainly concerned with imprecision and approxi-

mate reasoning. Its application allows any continuous, even if

very complex, mathematical function of cause and effect to be

rationalized.14 Therefore, Fuzzy logic is playing key roles in the

development of a machine intelligent quotient.

In this paper, it is shown how it is possible to implement

both Boolean and Fuzzy logic functions by exploiting the

chromogenic properties of 1,3-dihydro-1,3,3-trimethyl-80-nitro-

spiro[2H-indole-2,30-[3H]naphth[2,1-b][1,4]oxazine] (hereinafter

indicated as SpO).

UV irradiation triggers the spiro C–O bond breakage of SpO

leading to an open merocyanine (MC) that gives rise to an

absorption band in the visible. MC is metastable and thermally

reverts back to the uncoloured SpO (see Scheme 1). The

bleaching process can be hindered by the presence of complex-

ing metal ions and protons. When the merocyanine is proto-

nated or binds to some metal cations it gives rise to new

absorption bands in the visible. By using UV light as power

Dipartimento di Chimica, Universita di Perugia, 06123 Perugia, Italy.E-mail: pierluigi.gentili@unipg.itw Electronic supplementary information (ESI) available: Figures,equations, tables characterizing the chromogenism of SpO and theFuzzy logic systems FLS1 and FLS2 built on the behaviour of SpO. SeeDOI: 10.1039/c1cp21782h

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20336 Phys. Chem. Chem. Phys., 2011, 13, 20335–20344 This journal is c the Owner Societies 2011

supply, HClO4, Cu(ClO4)2 and AlCl3 as chemical inputs, and,

either the absorbance values in the visible or the RGB colour

coordinates as optical outputs, it is shown that it is possible

to process both Boolean and Fuzzy logic. When the chemical

inputs are applied in a digital manner, that is the chemicals are

added either in equimolar amounts with respect to SpO or at

all, complex binary logic circuits are implemented. When the

values of the inputs are changed in an analog manner, i.e. in a

continuous way, two Fuzzy logic systems involving the funda-

mental AND, OR, NOT operators are implemented. They are

based upon a new defuzzification procedure, inspired by the

way humans distinguish colours.

Experimental section

Materials

1,3-Dihydro-1,3,3-trimethyl-8 0-nitro-spiro[2H-indole-2,3 0-

[3H]naphth[2,1-b][1,4]oxazine] (SpO) (supplied by Great Lakes

Chemical Italia S.r.l.) was used as received after checking its

high degree of purity by an HPLC technique. Acetonitrile (from

Fluka, Z 99.8 %) and deionised water were used as solvents.

The reagents, perchloric acid (ACS reagent, 70%, from Sigma

Aldrich), sodium hydroxide (from J. T. Baker), aluminium

chloride (99%, from Carlo Erba), copper(II) perchlorate hexa-

hydrate (98%, from Aldrich), ethylenediaminetetraacetic acid

(Z 99%, from Fluka) and 4,40-dimethyl-2,20-bipyridyl (99%,

from Aldrich) were used as received. SpO was dissolved in

acetonitrile in concentrations of the order of 10�5 mol dm�3.

The reagents, perchloric acid, sodium hydroxide, aluminium

chloride, copper(II) perchlorate hexahydrate were dissolved

in deionised water; ethylenediaminetetraacetic acid was dis-

solved in an aqueous solution buffered at pH = 12 (purchased

from Panreac and made of boric acid, KCl and NaOH);

4,40-dimethyl-2,20-bipyridyl was dissolved in acetonitrile.

All the solutions of the reagents were prepared in the con-

centration of the order of 10�3 M. A few microlitres of

the reagents were injected into 1 mL of SpO acetonitrile

solutions.

Spectrophotometric measurements

The absorption spectra were recorded on a Perkin-Elmer

Lambda 800 spectrophotometer; the photo-colouration and

bleaching kinetics were recorded using a Hewlett-Packard

8453 diode array spectrophotometer. For the temperature

control, a cryostat (Oxford Instruments), equipped with a

temperature controller operating between 77 K (if liquid

nitrogen was adopted for cooling) and 500 K, was used. The

temperature precision was within �1 K; the accuracy in the

temperature control was on the order of �0.2 K. A 125 W Xe

lamp, filtered by a Jobin-Yvon H10 UV monochromator and

focused on the sample by a silica fiber optic, was used as an

irradiating source. The radiation of excitation was focused on

a fluorimetric 1 cm path cell, containing the solution, at a right

angle with respect to the monitoring beam of the spectrophoto-

meter. The radiation intensity was determined using potassium

ferrioxalate actinometry. The intensity of light was of the order

of 10�6–10�7 moles of quanta dm�3 s�1 at the wavelength of

irradiation. The photo-colouration quantum yield (FX) of SpO

has been determined in the absence of any reagent and in the

presence of HClO4, AlCl3 and Cu(ClO4)2, respectively.

Fluorimetric measurements

Corrected emission spectra were recorded using a Spex

Fluorolog—21680/1 spectrofluorimeter, controlled by the Spex

DM 3000F spectroscopy software. The fluorescence quantum

yield (FF) was determined by measuring and comparing

corrected areas under the spectra of the standard (9,10-diphenyl-

anthracene in cyclohexane, A= 0.015 at 354 nm, FF = 1)15 and

the sample.

Computational methods

To build the Fuzzy logic systems based on the chromogenic

behaviour of SpO, a new defuzzification procedure is proposed.

It consists in the calculation of the RGB colour coordinates

from the transmittance spectra of the coloured solutions recorded

at the different photo-stationary states. The steps of the defuzzifi-

cation are described below.

First of all, the CIE XYZ tristimulus values were calculated

through the following integrals:

X ¼ 1

k

Z800

360

DðlÞTðlÞ�xðlÞdl

Y ¼ 1

k

Z800

360

DðlÞTðlÞ�yðlÞ dl

Z ¼ 1

k

Z800

360

DðlÞTðlÞ�zðlÞdl

ð1Þ

wherein %x, %y, %z are the colour-matching functions whereby the

CIE (Commission Internationale de l’Eclairage) standardized

the sensitivity of human eye in 1964; D(l) is the energy

distribution of the CIE normalized illuminant D65 (which

closely matches that of the sky daylight); T(l) is the transmit-

tance spectrum, and k is a normalization factor defined in such

Scheme 1 UV irradiation of the spirooxazine (SpO) produces a merocyanine (MC) that thermally reverts back to SpO.

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a way that an object with a uniform transmittance T(l) = 1

gives a luminance component Y = 1:

k ¼Z800

360

DðlÞ�yðlÞdl ð2Þ

Then the XYZ tristimulus values were transformed into the

RGB coordinates by the linear transformation (3):

RGB

24

35 ¼

3:240479 �1:537150 �0:498535�0:969256 1:875992 0:0415560:055648 �0:204043 1:057311

24

35 X

YZ

24

35

ð3Þ

The RGB values should stay between 0 and 1. In some cases

they were slightly greater than 1. In these cases, the values were

rounded to 1. The final step was to scale the RGB values

obtained from (3) to values included between 0 and 255.16

Results and discussion

Photochromism

The absorption spectrum of SpO is shown in Fig. 1 (trace 1): at

wavelengths longer than 220 nm, it consists of four bands

centred at 221, 271, 303 and 358 nm, respectively, originated

by allowed electronic transitions. When SpO is dissolved in

acetonitrile at low concentrations (of the order of 10�5 M), the

solution appears uncoloured by sight. Upon UV irradiation, a

band peaked at 611 nm, comes out, whereby the solution

becomes blue. If the irradiation is discontinued, the mero-

cyanine responsible for the colour thermally reverts back to

SpO and hence the solution becomes again uncoloured. The

degree of saturation of the blue colour that is achievable upon

UV irradiation depends on the temperature of the solution.

In Fig. 1, the absorption spectra recorded at different tempera-

tures, and after reaching the photo-stationary state, are depicted.

The lower the temperature, the higher the conversion degree of

SpO to MC, the higher the absorbance of the colour band, the

higher the degree of saturation of the blue colour.

The differential kinetic equation describing the spectral

evolution for the acetonitrile solution of SpO upon UV irradia-

tion and at a wavelength where SpO does not absorb, is the

following:17

dAMC

dt¼ eMCFMCI

0SpOl� kDAMC ð4Þ

wherein AMC and eMC are the absorbance and the molar absorp-

tion coefficient of the merocyanine (MC), respectively; FMC is the

quantum yield of the photoreaction, I 0SpO is the intensity of the

radiation absorbed by SpO, l is the length of the optical path and,

finally, kD is the kinetic constant of the thermal bleaching

reaction. I 0SpO is defined by the equation below:

I 0SpO ¼A0SpOA0TOT

ð1� 10�A0TOTÞI 00 ¼ A0SpOFI

00 ð5Þ

In eqn (5), A0SpO and A0TOT are the absorbance values of SpO, and

SpO along with MC, respectively, at the irradiation wavelength

(lirr); I 00 is the intensity of the source at lirr and F represents the

photo-kinetic factor. When the irradiation is carried out at an

isosbestic point (379 nm in this case), F holds constant. Therefore,

at the photo-stationary state, it results that:

1

A1MC

¼ 1

eMClC0þ kD

eMCFMCC0I00e0SpOFl

2ð6Þ

In eqn (6), AN

MC is the absorbance of merocyanine recorded at the

photo-stationary state for a wavelength (lan) belonging to the

visible region, C0 is the analytical concentration of the photo-

chromic compound and e0SpO is the molar absorption coefficient of

SpO at lirr. When the irradiation is discontinued, AMC decays

mono-exponentially according to the following equation:

AMC = AN

MCe�kDt (7)

By performing experiments of photo-colouration and bleach-

ing at different temperatures (see the kinetics depicted in

Fig. S1 of the ESIw) and determining the respective AN

MC(lan)and kD, the values of eMC(lan) and FMC can be estimated by

applying eqn (6) (see inset of Fig. 1; the treatment at two

different wavelengths of analysis are shown in Fig. S2 of the

ESIw). The final numerical results are reported in Table 1.

Acidichromism

When SpO is irradiated by UV in the presence of HClO4,

added in an equimolar amount or in excess (for instance in a

molar ratio of nH+/nSpO = 4/1), a new absorption band,

centred at 485 nm, appears (see Fig. 2). The solution becomes

orange. This new band is due to a protonated merocyanine,

hereinafter indicated as H+–MC. The protonation of MC

shifts its spectrum towards the blue, due to the reduced electro-

nic delocalization, as it has been observed in other cases.18,19 The

protonated merocyanine exhibits a remarkable thermal stability:

the thermal bleaching process is very slow at room temperature

and it becomes irrelevant just by cooling down a few degrees,

for instance reaching 280 K. At this temperature, the differ-

ential kinetic equation describing the spectral evolution shown

Fig. 1 Absorption spectra of SpO in acetonitrile, non-irradiated

(trace 1, with C(SpO) = 3.2 � 10�5 M), and at the photo-stationary

state achieved at different temperatures by UV irradiation: (2) 298 K,

(3) 295 K, (4) 290 K, (5) 287.5 K, (6) 285 K, (7) 280 K. Inset: treatment

of the kinetic data, AN

MC at lan = 610 nm and kD, according to eqn (6).

The correlation coefficient of the straight line (red segment) fitting the

data (black points) is r = 0.99955.

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in Fig. 2 is analogous to eqn (4), but devoid of the term relative

to the thermal decolouration process (i.e. kDAH+–MC). By

irradiating the acidichromic system at its isosbestic point, that

is 320 nm, the photo-colouration process is described by the

integrated kinetic equation (8) (the detailed description for

achieving eqn (8) is presented in the ESIw):

AHþ�MCðtÞ ¼ eHþ�MClC0ð1� e�FHþ�MCFI

00e0SpO

ltÞ ð8Þ

wherein AH+–MC(t) is the absorbance of H+–MC at time t and

at the wavelength of analysis, where the molar absorption

coefficient is eH+–MC. AH+–MC(t) grows exponentially, as

shown in the inset of Fig. 2. By fitting the kinetics recorded

at 485 nm with the function of eqn (8), the photo-colouration

quantum yield, FH+–MC, and the molar absorption coefficient,

eH+–MC at 485 nm have been estimated. They are reported in

Table 1.

The coloured species H+–MC can be converted back to

SpO in a reasonable time interval (i.e. in a few minutes), both

photochemically, by irradiating at 485 nm, and chemically, by

adding NaOH in an equimolar amount with respect to HClO4.

After addition of the base, the solution becomes blue due to

the formation of MC species, that thermally reverts back

to SpO.

Metallochromism

When SpO is irradiated in the presence of AlCl3, added in an

equimolar amount or in excess (for instance in a molar ratio of

nAl3+/nSpO = 4/1), the spectral evolution represented in

Fig. 3A is observed: an absorption band centred at 485 nm

appears and the solution becomes orange. The colour band

has the same shape and spectral position of that recorded in

the presence of HClO4 and is thermally stable. However, it is

not due to H+–MC but for a reduced extent. In fact, when an

excess of NaOH is added to the orange solution, a reduced

bleaching of the colour of the solution is ascertained: the

drop in absorbance at 485 nm is just 9% of the total (see,

for instance, the spectral modification shown in the inset of

Fig. 3A). The complete bleaching is achieved either photo-

chemically by irradiating at 485 nm, or chemically by addition

of the complexing reagent 4,40-dimethyl-2,20-bipyridyl (bpy),

abstracting Al3+ cations fromMC. From this phenomenology

it can be inferred that the spectral evolution represented in

Fig. 3A is, to a large extent, due to the formation of a complex

between Al3+ and the merocyanine (hereinafter indicated as

Al3+–MC) and, to a small extent, to the formation of H+–MC.

By subtracting the contribution of H+–MC from the spectral

properties of the photo-stationary state (see the ESIw for more

details), the values of the molar absorption coefficient eAl3+–MC

(at 485 nm) and reaction quantum yield, FAl3+–MC, for Al3+–MC

could be estimated (see Table 1). They were determined at 280 K,

in order to suppress any thermal bleaching process.

When SpO is irradiated in the presence of Cu(ClO4)2, added

in an equimolar amount or in a molar ratio of nCu2+/nSpO =

4/1, the spectral evolution, characterized by an isosbestic point

at 372 nm and depicted in Fig. 3B is observed: the bands

centred at 303 and 358 nm and due to SpO deplete in favour

of a band peaked at 423 nm, conferring yellow colour to the

solution. This new band, appearing in the visible, may be attri-

buted to a complex between the copper ion and the merocyanine,

i.e. Cu2+–MC. The complex Cu2+–MC, obtained from SpO,

is thermally stable at room temperature. Moreover, if it is

irradiated in the visible, for instance at 423 nm, it does not

decompose, but it emits green light, with an intensity so high

to be detectable even by sight (see inset of Fig. 3B for the

shape of its emission and excitation spectra). Its luminescence

quantum yield is as high as 0.58. Among the four coloured

species produced by irradiation, i.e. MC, H+–MC, Al3+–MC

and Cu2+–MC, the complex between the copper ion and the

merocyanine is the only one that is luminescent.

Cu2+–MC cannot be decomposed by addition of either

NaOH or bpy, but by injecting a few microlitres of a con-

centrated solution of ethylenediaminetetraacetic acid (EDTA)

dissolved in an aqueous buffer having pH = 12. To determine

the molar absorption coefficient eCu2+–MC and the photo-

reaction quantum yield FCu2+–MC relative to Cu2+–MC, a

solution of SpO was irradiated at 372 nm in the presence of an

Table 1 Molar absorption coefficients (e) and reaction quantumyields (F) for the four coloured species: MC, H+–MC, Al3+–MC,Cu2+–MC

Compound lmax/nm ea/M�1 cm�1 FXb

MC 611 97 300 � 1400 0.15 � 0.01H+–MC 485 17 600 � 250 0.25 � 0.01Al3+–MC 485 12 500 � 300 0.17 � 0.02Cu2+–MC 423 26 300 � 140 0.30 � 0.01

a The values of e are relative to the wavelengths (lmax) corresponding

to the maxima of the colour bands, i.e. 611 nm for MC, 485 nm for

H+–MC and Al3+–MC, and 423 nm for Cu2+–MC. b The values of

photo-colouration quantum yields have been determined at the wave-

lengths corresponding to the isosbestic points: 379 nm for SpO/MC,

320 nm for SpO/H+–MC, 317 nm for SpO/Al3+–MC, and 372 nm for

SpO/Cu2+–MC. In the interval of wavelengths included between 317

and 379 nm, the photo-colouration quantum yields have been proved

to be wavelength-independent.When F was measured at wavelengths

different from the isosbestic point, the initial velocity method was used

(see the ESIw for more details).

Fig. 2 Spectral evolution for a solution of SpO irradiated at 320 nm

in the presence of HClO4, added in a molar ratio nH+/nSpO = 4/1.

Inset: experimental kinetics (black trace) of colouration recorded at

485 nm, fitted by the function of eqn (8) (red trace).

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excess of Cu(ClO4)2 and a function like that of eqn (8) was

used to fit the kinetics of colouration. The results are reported

in Table 1.

From the data of Table 1 it is evident that the free

merocyanine (i.e. MC) has the largest value of the absorption

coefficient and when it binds to either H+ or Al3+ or Cu2+,

the main electronic transition located in the visible shifts

towards the blue. This behaviour was previously revealed

for other merocyanines derived from spiropyrans.20–23 The

protonation or complexation of b-naphthoxide of MC elicits a

reduction of the electronic conjugation along the molecular

skeleton of the merocyanine and hence the hypo-chromic and

ipso-chromic spectral effects detected.

The chromogenic properties, described so far, make SpO the

right candidate to process information at the molecular level.

Hereinafter, it will be shown that it is possible to implement

both Boolean and Fuzzy logic functions.

Boolean logic functions

In crisp Boolean logic, data processing requires the encod-

ing of information in the form of binary digits. Therefore, it is

necessary to establish a threshold value and a logic convention

for each signal. The signals can be simply high or low, becoming

the digital 1 or 0, respectively, in the positive logic convention.

Based upon the reversible chromogenic properties of SpO, it

is possible to process binary logic by using UV radiation as

power supply, HClO4, AlCl3 and Cu(ClO4)2 as chemical inputs,

and the absorbance at a specific wavelength in the visible as

an optical output. An input is ‘‘off’’ (i.e. 0) when the respective

chemical is not injected at all into the solution containing

the molecular switch SpO, whereas it is ‘‘on’’ (i.e. 1) when

one equivalent or more of the chemical reagent is added.

An optical output is ‘‘on’’ (i.e. 1) whenever the absorbance at

the analysis wavelength, A(lan), is larger than 0.4, whereas it is

‘‘off’’ (i.e. 0) whenever A(lan) o 0.4.

The chromogenic behaviour of SpO, described in the pre-

ceding paragraphs, allows Scheme 2 to be depicted. SpO is a

completely reversible molecular switch that can assume five

different states. All the states are achievable by six minutes at

room temperature and for an irradiation intensity of the order

of 10�6 moles of quanta dm�3 s�1 at 379 nm. The conversion

degree of SpO to MC was 28%, those of SpO to H+–MC and

Al3+–MCwere 90% and that of SpO to Cu2+–MCwas complete.

Fig. 3 Spectral evolution for a solution of SpO dissolved in acetonitrile in the presence of (A) AlCl3 added in a molar ratio of nAl3+/nSpO = 4/1

and upon irradiation at 317 nm; inset of (A): spectra recorded at the photo-stationary state before (1, black trace) and after (2, red trace) addition

of NaOH; (B) spectral evolution in the presence of Cu(ClO4)2 added in a molar ratio of nCu2+/nSpO = 4/1 and upon irradiation at 372 nm; inset of

(B): emission (1, black trace, lexc = 405 nm) and excitation (2, red trace, lem = 530 nm) spectra relative to Cu2+–MC.

Scheme 2 SpO as a five-states molecular switch. When one equivalent

of AlCl3 is added, the main, but not unique product is Al3+–MC: there

is also a small amount of H+–MC.

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Some cycles can be repeated without loss of performance. A

detailed study of the durability of SpO as a molecular logic

gate will be a matter of further work.

Each state has specific absorption properties, which are

shown in Fig. 4. SpO is uncoloured (see spectrum 1 of Fig. 4);

MC confers blue colour to the solution since it gives rise to an

absorption band peaked at 611 nm (see spectrum 2 of Fig. 4);

whenH+–MC and/or Al3+–MC are produced, an orange colour

arises (see spectra 3 and 5), since both of them produce a band

centred at 485 nm. On the other hand, when Cu2+–MC is

achieved by irradiation of SpO in the presence of one equivalent

of Cu(ClO4)2 (see spectrum 4), the solution becomes yellow, since

the complex between the copper cation and the merocyanine has

an absorption band in the visible that is centred at 423 nm.

When two chemical inputs are ‘‘on’’ at the same time, further

results are achieved. For instance, when one equivalent of

HClO4 and one equivalent of Cu(ClO4)2 are injected, and the

solution is UV irradiated until it reaches the photo-stationary

state, spectrum 6 is recorded; it shows the characteristic band

centred at 423 nm, due to Cu2+–MC. The initial SpO state may

be restored by addition of one equivalent of EDTA and one

equivalent of bpy, producing MC that thermally bleaches.

If one equivalent of HClO4 is added along with one

equivalent of AlCl3 and the solution is UV irradiated, spec-

trum 7 of Fig. 4 is recorded at the photo-stationary state. The

solution is orange due to the production of both H+–MC and

Al3+–MC species. If two equivalents of bpy are added, MC is

produced, conferring blue colour to the solution. MC bleaches

thermally. If the solution of SpO is UV irradiated after

addition of one equivalent of AlCl3 and one equivalent of

Cu(ClO4)2, spectrum 8 of Fig. 4 is recorded at the photo-

stationary state. It consists exclusively of the band centred at

423 nm, due to Cu2+–MC. It is possible to restore the initial

state, by injecting one equivalent of EDTA and one equivalent

of bpy that bind to the Cu2+ and Al3+ cations, respectively.

Finally, if one equivalent of all the three chemical inputs

are added upon UV irradiation, the solution becomes again

yellow at the photo-stationary state, due to the production of

the Cu2+–MC complex. It is possible to completely restore

the initial state SpO, by injecting one equivalent of EDTA

and two equivalents of bpy. This behaviour suggests that

Cu2+ binds more strongly to MC than H+ and Al3+ ions.

The difference may be due to the fact that H+ and Al3+ link

just to the oxygen atom of b-naphthoxide, whereas a Cu2+ ion

forms a chelate complex18,21 by binding to both oxygen and

imminic nitrogen of MC.

By naming HClO4, AlCl3 and Cu(ClO4)2 as inputs 1 (In1),

2 (In2) and 3 (In3), respectively, and by choosing the absor-

bance values at 611 nm (A(611 nm)), 485 nm (A(485 nm)) and

423 nm (A(423 nm)) as outputs 1 (Ou1), 2 (Ou2) and 3 (Ou3),

respectively, different Boolean logic functions can be imple-

mented. By considering the action of two inputs, such as In1(H+) and In2 (Al3+) and based on the three optical outputs,

A(611 nm), A(485 nm), A(423 nm), the NOR, OR and FALSE

logic gates are carried out (see Table 2). On the other hand, by

combining the action of the two inputs, In1 (H+) and In3(Cu2+), or that of In2 (Al3+) with that of In3 (Cu2+), the

NOR, INHIBIT and TRUE logic gates are implemented (see

Table 3). In any case, UV radiation plays the role of power

supply. Alternatively to the absorbance value at 423 nm, it is

possible to exploit the intensity of light emitted by Cu2+–MC

as optical signal. It is worthwhile noticing that the three NOR,

OR and FALSE logic gates or the three NOR, INHIBIT and

TRUE ones coexist simultaneously. It is possible to pass from

one element to another simply by changing the monitored

wavelength. In other words, SpO is a multiply configurable

Boolean logic element, similarly to other examples described

before in the literature.11,24

More complex binary logic functions can be implemented if

the actions of all the three inputs are combined together, and

Fig. 4 Absorption spectra of (1) SpO (C = 3.2 � 10�5 M) before

irradiation, and at the photo-stationary states achieved by UV irradiation

in the presence of (2) no chemical reagent, and one equivalent of each of

the following chemical inputs: (3) H+, (4) Cu2+, (5) Al3+, (6) H+ +

Cu2+, (7) H+ +Al3+, (8) Al3+ + Cu2+ and (9) Al3+ + Cu2+ +H+.

All the spectra have been recorded at room temperature.

Table 2 Truth tables of the logic elements NOR, OR, FALSE definedfor the five-states molecular switch based on H+ and Al3+ as chemicalinputs, A(611 nm), A(485 nm) and A(423 nm) as optical outputs, andUV radiation as power supply

In1 (H+) In2 (Al3+)

Ou1(A(611 nm))

Ou2(A(485 nm))

Ou3(A(423 nm))

0 0 1 0 01 0 0 1 00 1 0 1 01 1 0 1 0

NOR OR FALSE

Table 3 Truth tables of the logic elements NOR, INHIBIT, TRUEdefined for the five-states molecular switch based on Cu2+ and H+ orAl3+ as chemical inputs, A(611 nm), A(485 nm) and A(423 nm) asoptical outputs, and UV radiation as power supply

In1 or 2

(H+ or Al3+)In3(Cu2+)

Ou1(A(611 nm))

Ou2(A(485 nm))

Ou3(A(423 nm))

0 0 1 0 01 0 0 1 00 1 0 0 11 1 0 0 1

NOR INHIBIT TRUE

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UV irradiation plays the role of power supply. Their truth

tables are reported in Table 4. The combinational logic circuits

equivalent to these truth tables are illustrated in Fig. 5. Twenty

logic elements are necessary to reproduce the functions per-

formed by a single molecule. In the circuits, the three inputs

are elaborated through a series of AND, NOT, and OR

operations to produce the three outputs.

Fuzzy logic functions

SpO can be converted from a multiply configurable Boolean

logic element to a Fuzzy Inference Engine (this name is attributed

to any kind of system whereby Fuzzy logic can be processed.

See ref. 25) simply by switching from a digital- to an analog-

type addition of the chemical inputs. In Fig. 6A the absorption

spectra recorded at the photo-stationary state after addition of

different amounts of HClO4 (with the molar ratio nH+/nSpOranging from 0 up to 1.6) are shown. It is evident that when

HClO4 is injected in defect with respect to the moles of SpO,

both the bands at 611 nm and that at 483 nm are produced

upon UV irradiation. They are due to the production of both

free (MC) and protonated (H+–MC) merocyanines. The ratio

between the absorbance values at the two wavelengths, 611

and 483 nm, A611/A483, wanes by increasing the molar ratio

nH+/nSpO and it vanishes when one equivalent of HClO4 or

more is added to the solution of SpO. At the photo-stationary

state, the colour of the solution changes in a chameleonic way

from blue to cyan, to grey up to orange by increasing progres-

sively the amount of HClO4. The complete recovery of the

initial molecular state, SpO, can be achieved photochemically

(by irradiating with blue light) or chemically, by addition of

the right amount of NaOH that neutralizes the proton and lets

MC to thermally revert back to SpO. In Fig. 6B the absorption

spectra recorded at the photo-stationary state in the presence

of a growing concentration of AlCl3 (with the molar ratio

nAl3+/nSpO ranging from 0 up to 1) are shown. Similarly to

what occurs in the case of HClO4 addition, the injection of

AlCl3 in defect with respect to the moles of SpO, gives rise

to the formation of two bands in the visible: that centred at

611 nm, due to MC, and that centred at 483 nm, due mainly

to Al3+–MC and secondarily also to H+–MC. The value of

absorbance at 611 nm diminishes in favour of that at 483 nm

by increasing the molar ratio nAl3+/nSpO. At the photo-

stationary state, the colour of the solution changes from blue

to cyan, to grey up to orange by increasing progressively the

quantity of AlCl3. The initial molecular state, SpO, can be

restored photochemically (by irradiating with blue light) or

chemically, by addition of the right amount of bpy; bpy

abstracts Al3+ ions and neutralizes the protons, releasing the

merocyanine molecules, which finally transform thermally to

SpO. In Fig. 6C the absorption spectra recorded at the photo-

stationary state in the presence of a growing concentration of

Cu(ClO4)2 (with the molar ratio nCu2+/nSpO ranging from 0 up

to 1.5) are shown. When few moles of Cu(ClO4)2 are injected,

the band centred at 611 nm is the most intense one. By increa-

sing the content of Cu(ClO4)2, the band at 611 nm wanes in

favour of the band having a maximum at 423 nm, produced by

the complex Cu2+–MC. When nCu2+/nSpO = 1.5, the absorp-

tion in the red portion of the visible region is completely

absent, since MC is totally bound to Cu2+. At the photo-

stationary state achieved in the presence of a growing content

of Cu(ClO4)2, the colour of the solution changes from blue to

Table 4 Truth tables for the five-states molecular switch based on H+,Al3+ and Cu2+ as chemical inputs, A(611 nm), A(485 nm), A(423 nm)as optical outputs, and UV radiation as power supply

In1 (H+) In2 (Al3+) In3 (Cu

2+)Ou1(A(611 nm))

Ou2(A(485 nm))

Ou3(A(423 nm))

0 0 0 1 0 01 0 0 0 1 00 1 0 0 1 00 0 1 0 0 11 1 0 0 1 01 0 1 0 0 10 1 1 0 0 11 1 1 0 0 1

Fig. 5 The logic circuits based on the molecular switch SpO trans-

ducing the three inputs into the output Ou1 (A), Ou2 (B) and Ou3 (C)

through the AND, NOT, and OR operations.

Fig. 6 Absorption spectra recorded at the photo-stationary state in

the presence of HClO4 (A) and for different values of nH+/nSpO:

0 (1, red trace), 0.33 (2, green trace), 0.7 (3, blue trace), 1 (4, cyan trace),

1.6 (5, magenta trace); in the presence of AlCl3 (B) and for different values

of nAl3+/nSpO: 0 (1, red trace), 0.2 (2, green trace), 0.4 (3, blue trace),

0.65 (4, cyan trace), 1 (5, magenta trace); in the presence of Cu(ClO4)2(C), for different values of nCu2+/nSpO: 0 (1, red trace), 0.33 (2, green

trace), 0.66 (3, blue trace), 1 (4, cyan trace), 1.5 (5, magenta trace).

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green, to different tones of yellow. In any case, the initial mole-

cular state, SpO, can be restored chemically by addition of the

right amount of EDTA that abstracts copper ions and allows

MC to thermally disappear through the ring-closure reaction.

The simultaneous injection of two chemical inputs into the

solution of SpO favours the achievement of photo-stationary

states with further spectral properties with respect to those

evidenced in Fig. 6 (see figures from Fig. S3 up to Fig. S14

in the ESIw). In particular, if Al3+ and H+ are added together,

both of them contribute to the formation of the same spectral

band centred at 483 nm, whereas if H+ is added along with

Cu2+, or Al3+ along with Cu2+, the former cation favours the

appearance of the band with a maximum at 483 nm, whereas

the latter gives rise to the most blue-shifted coloured band,

having a maximum at 423 nm.

These results reveal that, although SpO can be switched

reversibly just among five different molecular states by using

UV light as power supply and HClO4, AlCl3 and Cu(ClO4)2 as

chemical inputs, when the additions of the chemicals are

carried out in an analog manner, the solution can acquire an

‘‘infinite’’ number of colours (reminding that two colours are

different when just one of the three RGB colour coordinates

assumes a different value) because there exists an infinite

number of photo-stationary states which are achievable. Each

photo-stationary state is characterized by a specific ratio of the

coloured species. Therefore, the chromogenic compound SpO

can be exploited to implement also Fuzzy logic functions with

UV radiation as power supply, HClO4, AlCl3 and Cu(ClO4)2as chemical inputs, and the RGB colour coordinates as the

optical outputs. To process Fuzzy logic, it is necessary to build

a Fuzzy logic system (FLS). A FLS consists of three main

elements:11,25 a Fuzzifier, a Fuzzy Inference Engine and a

Defuzzifier. If the Mamdani’s method26 is chosen, in order to

build the Fuzzifier and Defuzzifier, the granulation of all the

variables involved must be performed by the operator.13 Each

input, consisting in the molar ratios nchem/nSpO (where nchemare the moles of either HClO4 or AlCl3 or Cu(ClO4)2 injec-

ted into the solution containing nSpO moles of spirooxazine),

is partitioned into four Fuzzy sets, labelled as Low (L),

Medium (M), High (H) and Very High (VH) (whose shapes

and positions are shown in Fig. 7: graph A for H+ and Cu2+,

and graph B for Al3+). The Fuzzifier maps crisp inputs into

specific Fuzzy sets of the input variables. For the granulation

of the output, consisting in the optical signal of visible light

transmitted by the different solutions at the photostationary

state, the fuzzy nature of the human colour perception is

imitated.10,13 Human beings have three types of cones whereby

they distinguish colours. The absorption spectra of the three

sorts of cones can be conceived as Fuzzy sets. When visible

radiation hits the retina of our eyes, it will have specific values

of membership functions in the three types of fuzzy sets and it

will activate the three types of cones in a specific proportion.

The combination of these values will be transduced into the

perception of a specific colour inside our brain. Similarly, for

the FLS based on SpO, the visible spectral region, representing

the output variable, is partitioned in three fuzzy sets that

are the colour-matching functions, %x, %y, %z, whereby the CIE

(Commission Internationale de l’Eclairage) standardized the

sensitivity of human eye in 1964 (see Fig. 7). The Defuzzifier

maps output fuzzy sets into crisp physical numbers, by trans-

forming the transmittance spectra (T(l)) recorded at the photo-

stationary states, into values of the RGB colour coordinates,

according to the procedure explained in the Computational

methods of the Experimental section.

The third fundamental element of a FLS is the Inference

Engine. It requires the formulation of Fuzzy rules, i.e. linguistic

Fig. 7 Schematic structure of the Fuzzy logic systems based on the chromogenism of SpO and the Mamdani’s method. The fuzzy sets for H+ and

Cu2+ inputs are shown in A, whereas those for Al3+ are shown in B. The output fuzzy sets are the colour-matching functions, %x, %y, %z defined by

CIE in 1964. UV radiation is the power supply.

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statements of the type ‘‘IF. . ., THEN. . .’’ wherein the IF-portion

is called the antecedent, whereas the THEN-part is named as

consequence. In case of multiple-antecedent, the different inputs

can be connected through the AND, OR and NOT operators.

The chromogenic behaviour of SpO allows two FLSs to be

implemented. These two FLSs differ in the combination of the

inputs: one is based on the couple HClO4 plus AlCl3 and it will

be named as FLS1, whereas the other on HClO4 (or AlCl3)

plus Cu(ClO4)2 and it will be named as FLS2. The collection of

crisp values for the input and output variables (the crisp values

for the RGB colour coordinates have been achieved through

the defuzzification method described in Experimental section)

are plotted in Fig. 8 and are listed in the Tables S1–S3 of the

ESI.wBased on the profiles of the RGB coordinates graphed in

Fig. 8, Fuzzy rules are formulated for the two FLSs. In the

case of the FLS1, the rules are ‘‘IF. . ., THEN. . .’’ statements

with multiple antecedents involving the AND, NOT, OR

operators. The complete list of the eleven rules is reported

on page 14 of the ESIw and the rules’ matrix is shown in

Table 5. When B is the colour coordinate having the largest

value, it means that the transmittance spectrum belongs

mainly to the %z fuzzy set (i.e. it has the highest degree of

membership in %z), and it occurs when both inputs are null. If R

is the principal colour coordinate, it means that the transmit-

tance spectrum belongs mainly to the %x fuzzy set. For instance,

it occurs when both inputs are applied and they assume values

which do not belong to the Low Fuzzy sets. When the values

of two colour coordinates differ for less than thirty units,

they are both considered in the formulation of the rule (in the

rules’ matrix they are reported in decreasing order). The

combination of red with green (R, G) gives rise to yellow;

blue with green (B, G) gives rise to cyan, and finally red with

green and blue (R, G, B) originates the grey colour. The use of

the operator OR is made possible by the symmetric distribu-

tion of colours when the two inputs are applied separately.

The FLS2 (based on HClO4 and Cu(ClO4)2 as inputs) involve

other colours, differently distributed among the combinations of

the input Fuzzy sets. For instance, G is the principal colour

coordinate, when the transmittance spectrum recorded at the

photo-stationary belongs mainly to the %y Fuzzy set, and it occurs

when nCu2+/nSpO is low. FLS2 can be based on the formulation

of sixteen rules (such as those reported on page 15 of the ESIw),whose matrix is shown in Table 6. The rules are ‘‘IF. . .,

THEN. . .’’ statements with multiple antecedents involving just

the AND, NOT operators, since the colours are not symmetri-

cally distributed among the input Fuzzy sets as it occurs in FLS1.

Finally, it is evident that the different colours that the solution

of the spirooxazine acquires for the different combinations of

Fig. 8 Profiles of the Blue (B), Green (G) and Red (R) coordinates as a function of the molar ratios nH+/nSpO and nAl3+/nSpO in a1, a2, a3, and as a

function of the molar ratios nH+/nSpO and nCu2+/nSpO in b1, b2, b3.

Table 5 Rules’ matrix for the FLS1 based on the chromogenicbehaviour of SpO with H+ and Al3+ as inputs

nAl3+/nSpO, nH+/nSpO B L M H VH

B B (B, G) (R, G, B) R RL (B, G) (R, G) R R RM (R, G, B) R R R RH R R R R RVH R R R R R

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chemical inputs, i.e. the chameleonic chromogenism of SpO

allows two molecular Fuzzy logic systems to be built: FLS1involves all the fundamental Fuzzy logic operators, AND, OR,

NOT, whereas FLS2 requires just the AND, NOT operators.

Conclusions

SpO exhibits the noticeable property of being photochromic,

acidichromic and metallochromic at room temperature and

dissolved in an organic solvent, such as acetonitrile. Although

the photo-colouration quantum yields are not very large, the

absorption coefficients of the coloured species are high, espe-

cially for MC, having a broader intramolecular electronic

delocalization than H+–MC, Al3+–MC and Cu2+–MC. By

using HClO4, AlCl3 and Cu(ClO4)2 as chemical inputs and UV

irradiation as power supply, the chromogenic properties of

SpO can be exploited to process both Boolean and Fuzzy

logic. If the chemicals are added in a digital manner, some

complex Boolean logic circuits can be implemented. SpO has

resulted to be a multiply configurable Boolean logic element,

because simply by changing the wavelength of analysis in the

visible, it is possible to carry out different logic functions. On

the other hand, if the inputs are varied in an analog manner, it

has been shown that it is possible to build Fuzzy logic systems

based on Fuzzy rules with multiple antecedents, involving all the

fundamental logic operators, AND, OR, NOT. These FLSs

have been implemented by a new defuzzification method. The

new defuzzification procedure is based on the transformation of

the transmittance spectra, recorded at the photo-stationary

states, in crisp values of the RGB colour coordinates, with the

colour-matching functions representing the sensitivity of human

eye. This work constitutes a proof of principle and further

technological efforts are needed to carry out a promising device

spurring the development of chemical computers.

Acknowledgements

This work was supported by the Ministero per l’Universita e

la Ricerca Scientifica e Tecnologica (Rome, Italy) and the

University of Perugia [PRIN2008, 20088NTBKR].

Notes and references

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8 F. M. Raymo, Adv. Funct. Mater., 2002, 14, 401–414.9 D. Gust, T. A. Moore and A. L. Moore, Chem. Commun., 2006,1169–1178.

10 P. L. Gentili, ChemPhysChem, 2011, 12, 739–745.11 P. L. Gentili, Chem. Phys., 2007, 336, 64–73.12 P. L. Gentili, J. Phys. Chem. A, 2008, 112, 11992–11997.13 L. A. Zadeh, IEEE Software, 1994, 11, 48–56.14 L. A. Zadeh, IEEE Trans. Syst., Man, Cybern., 1973, SMC–3,

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17 For more details see: (a) P. L. Gentili, F. Ortica and G. Favaro,Chem. Phys. Lett., 2007, 444, 135–139; (b) M. R. di Nunzio,P. L. Gentili, A. Romani and G. Favaro, ChemPhysChem, 2008,9, 768–775 and references therein.

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20 J. T. C. Wojtyk, P. M. Kazmaier and E. Buncel, Chem. Mater.,2001, 13, 2547–2551.

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25 J. M. Mendel, Proc. IEEE, 1995, 83, 345–377.26 E. H. Mamdani, IEEE Trans. Comput., 1977, 26, 1182–1191.

Table 6 Rules’ matrix for the FLS2 based on the chromogenicbehaviour of SpO with H+ and Cu2+ as inputs

nCu2+/nSpO, nH+/nSpO B L M H VH

B B G (G, R) (R, G) (G, R)L (B, G) (R, G) R R (G, R)M (R, G, B) R R R (G, R)H R R R R (G, R)VH R R R R (G, R)

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