Online - 2455-3891

Vol 14, Issue 9, 2021 Print - 0974-2441

Review Article

DIFFERENT ULTRAVIOLET SPECTROSCOPIC METHODS: A RETROSPECTIVE STUDY ON ITS

APPLICATION FROM THE VIEWPOINT OF ANALYTICAL CHEMISTRY

PROMA MUKHERJEE1*, DEBARUPA DUTTA CHAKRABORTY1, PRITHVIRAJ CHAKRABORTY2,

BHUPENDRA SHRESTHA1, NIHAR RANJAN BHUYAN1
Department of Pharmaceutical Analysis, Himalayan Pharmacy Institute, Majhitar, Rangpo, East Sikkim, India. 2Department of
1

Pharmaceutics, Himalayan Pharmacy Institute, Majhitar, Rangpo, East Sikkim, India. Email: proma96.mukherjee@gmail.com
Received: 25 May 2021, Revised and Accepted: 12 July 2021

ABSTRACT

In routine practice, some simple and rapid analytical methods are needed for the assessment of formulations containing multiple elements, complex
matrix system and for biotherapeutic products. There are several methods available for ultraviolet (UV) spectrophotometry that rely on the concept
of absorbance difference, absorbance spectra, and additivity, also included in the list are simultaneous equation method, Q-absorbance ratio method,
derivative spectrophotometry, ratio derivative spectra, successive ratio-derivative spectra, absorption and absorptivity factor method, and difference
spectrophotometry along with multivariate chemometric methods. In this review, emphasis has been given to the theories, mathematical context,
advantages, and disadvantages along with the vast applications of UV spectrophotometry. The findings further highlighted that for the analysis of
drugs, UV spectrophotometry remains as one of the most simple, cheap, and promising option for routine practice in the field of pharmaceuticals.

Keywords: Spectroscopy, Ultraviolet spectrophotometry, Absorptivity, Binary mixture.

© 2021 The Authors. Published by Innovare Academic Sciences Pvt Ltd. This is an open access article under the CC BY license (http://creativecommons.org/
licenses/by/4.0/) DOI: http://dx.doi.org/10.22159/ajpcr.2021v14i9.42172. Journal homepage: https://innovareacademics.in/journals/index.php/ajpcr

INTRODUCTION spectra, Successive ratio-derivative spectra, Absorption factor method,

Absorptivity factor method, Absorbance subtraction method, Amplitude
Spectroscopy is the science which deals with the investigation of a
modulation method, Ratio subtraction method (RSM), Extended RSM
spectra which is produced due to interaction of the molecules and is
(ERSM), Ratio difference spectrophotometric method, Constant center
concerned with the interpretation of the absorbed and emitted electro-
spectrophotometric method, and Multivariate chemometric method.
magnetic radiation when the atoms or molecules changes its electronic
state from one to another [1].

Ultraviolet (UV) spectroscopy is the study of absorption of the light Simultaneous equation method depends on the absorption of the two
which based on the Beer-Lambert law that states, the intensity of drugs in a binary or ternary mixture, each of them absorbs at the max of
absorption is directly dependent on concentration and path length other. These method follows some criteria which are:
of species which get absorbed in the solution [2]. In analytical In a binary or ternary mixture which contain two different
chemistry, this spectroscopy is widely used for the quantitative components (considered as X and Y) each of them should absorb at
estimation of different analytes and biological molecules and also for the maximum wavelength of the other
the measurement of light intensity that passes through a chemical The maximum wavelength ( max) of two different drugs should be
substance under investigation with respect to light intensity through different
a reference sample. The UV spectroscopy is also known as electronic The two different drugs should not interact in the sample mixture.
spectroscopy as it results in the promotion of electrons from low energy
to high energy state. This spectrophotometry is a simple, precise and a The information required for the equation is
quite easy method to calculate the enumeration of aromatic conjugation Absorptivity of X at 1 and 2 is considered as aX1 and aX2
and conjugated double bonds in different molecules. An analyst can Absorptivity of Y at 1 and 2 is considered as aY1 and aY2
utilize this technique for rapid analysis of multiple samples including Absorbance of diluted sample at 1 and 2 is considered as A1 and A2
liquids, solids, thin films, and glass [3]. Cx and Cy is considered as the concentration of X and Y, respectively,
in the sample
PRINCIPLE
Total of absorbance of X and Y is equivalent with the absorbance of
Any molecule or ion causes an electronic transition in its structure due mixture
to the radiation of light and therefore it will show absorption in the
UV or visible region. In general, a molecule consists of either n (non- So,
bonding), or (bonding) electrons or its combination. By the supply
of energy from light the electrons absorb radiation which promotes At , A1=aX1 b Cx+aY1 b Cy
1
(1)
the transition of electrons from low to high energy state. The structure
illustration of molecule can be done by the absorption peaks, and from At , A2=aX2 b Cx+aY2 b Cy
2
(2)
the nature of electrons [1,3].
If cell is 1 cm, then b=1
VARIOUS UV SPECTROSCOPIC ANALYTICAL TECHNIQUES Multiply the equation (1) and (2) with aX2 and aX1

In analytical chemistry, diverse UV spectroscopic techniques are available A1 aX2=aX1 Cx aX2+aY1 Cy aX2 (3)
which includes Simultaneous equation method, Q-absorbance ratio
method, Derivative spectrometry, Difference spectrometry, Derivative ratio A2 aX1=aX2 Cx aX1+aY2 Cy aX1 (4)
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Subtract the equation (4) from (3) aX1=aY1 and Cx=Cy

A1 aX2 – A2 aX1=aY1 Cy aX2 – aY2 Cy aX1 Therefore,

A1 aX2 - A2 aX1=Cy (aY1 aX2 – aY2 aX1) A2/A1=(aX2 Fx+aY2 – aY2 Fx)/aX1

Cy=(A1 aX2- A2 aX1)/(aY1 aX2 – aY2 aX1) (5) =(aX2 Fx/aX1)+(aY2/aX1) – (aY2 Fx/aX1)

Similarly, Let Qx=aX2/aX1, Qy=aY2/aY1 and absorption ratio Qm=A2/A1

Cx=(A2 aY2- A1 aY1)/(aY1 aX2 – aY2 aX1) (6) Qm=FxQx+Qy – FxQy

From these simultaneous equation methods an analyst can determine =Fx (Qx – Qy)+Qy
drug concentration of X and Y in mixture.
Fx=(Qm – Qy)/(Qx – Qy) (9)
Advantage
The method is beneficial because it allows determination of the From the equation (7)
concentration of each component in a multicomponent system which
A1=aX1 (Cx+Cy)
is present in the empirical and simulated data. It also gives a consistent
result and a reliable calibration curve in case of a system which is not
Cx+Cy=A1/aX1
critically overlapping by choosing the relevant wavelengths [6].
Cx=(A1/aX1) – Cy (10)
Disadvantage
This method is applied only for the broad spectrum of which degree From the equation (9)
of overlap differs according to the relative concentration in case of
multicomponent system. The region where the degree of overlapping is Cx/(Cx+Cy)=(Qm – Qy)/(Qx – Qy)
more, there only the one component get absorbed therefore the molar
absorptivity tends to be less. It is also applicable for the combination of Cx/(A1/aX1)=(Qm – Qy)/(Qx – Qy)
drugs which absorbs at the maximum wavelength of other [6].
Cx=[(Qm – Qy)/(Qx – Qy)] (A1/aX1) (11)

Advantage
Q-absorbance ratio method, a modified version of the simultaneous The advantage of this method is that the ratio of absorbance does not
equation method, depends on the ratio of absorbance of a substance at two depend on the concentration and path length. It is a modified method
different wavelengths. One is the maximum wavelength of any one of two of simultaneous equation method. It is a simple, reproducible, sensitive,
component and other is the wavelength of the iso-absorptive point [4,5]. and economical method [7,8].
This method is applicable for a combination of drugs which obeys Beer’s
law and the absorbance ratio at two wavelengths is a constant value Disadvantage
which is independent of the path length and concentration. This constant It is only applicable for the combination of drugs which are having the
is termed as Q-value or Hafner’s Quotient [7,8]. isoabsorptive point and which follows Beer’s law [7,8].

To determine drug concentration, the absorbance and absorptivity DIFFERENCE SPECTROMETRY

values at these wavelengths are calculated by the following equation
Difference spectroscopy is a sensitive analytical technique which is
used to demonstrate a chromophore ionization leading to identification
At A =aX1Cx+aY1Cy (7)
1 1
and quantification of various components of a mixture [5]. This
At A2=aX2Cx+aY2Cy (8) spectrophotometric technique is used to estimate the quantity of an
2
analyte with the help of reference equimolar solution of that same
Divide the equation (8) with the equation (7) analyte in different physicochemical conditions (pH and temperature),
based on their different spectral characteristics [9,10].
A2/A1=(aX2 Cx+aY2 Cy)/(aX1 Cx+aY1 Cy)
Criteria for the assessment of a substance by difference
Divide both side with (Cx+Cy) spectrophotometry method are [5]:
The analyte which is under investigation should exist in different
A2/A1=(aX2 Cx+aY2 Cy)/(Cx+Cy)/(aX1 Cx+aY1 Cy)/(Cx+Cy) chemical forms and exhibit different absorbance values. The
absorbance difference is calculated from the amplitude difference
Put Fx=Cx/(Cx+Cy) and Fy=Cy/(Cx+Cy) in maxima and minima and plotted against concentration of test
solution
A2/A1=[aX2 Fx+aY2 Fy]/[aX1 Fx+aY1 Fy] In case of distribution of spectrum of analyte any reproducible
changes can occur by adding one or more reagent
Where, Fx is the fraction of X and Fy is the fraction of Y that is Fy=1- Fx The reagents should not alter the absorbance of interfering
substance.
Therefore,
Difference spectroscopy is used in simultaneous estimation of any
A2/A1=[aX2 Fx+aY2 (1-Fx)]/[aX1 Fx+aY1 (1-Fx)] multicomponent system as well as binary mixtures. Apart from
any pharmaceutical assay, it is applied to the development of the
=[aX2 Fx+aY2 - aY2 Fx]/[aX1 Fx+aY1 – aY1 Fx] biopharmaceutical formulation for the characterization of the protein
structure and to determine the response of the protein structure to the
At iso-absorptive point formulation composition. The fact on which this application is based is

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that the high real time physical stability is given by the stable protein If we consider that zero-order spectrum comply with Beer’s law so the
structure and it also provides difference spectra, used to quantify and circumference for all orders of derivative undergoes an identical direct
characterize the changes in protein structure [10,11]. relationship with concentration.

Advantage Consider,
In case of the spectrophotometric analysis of the sample which contains
interferents, in that case accuracy and selectivity can be distinctly Wavelength=
improved using this approach of difference spectroscopy. Furthermore,
by this method absorbance difference ( A) can be measured among the Absorbance=A
two equimolar solution of analyte which exhibit both different chemical
forms and spectral characteristics [9-11]. Extinction coefficient=

Disadvantage Sample path length=b

This method cannot be applicable when the reagents alter the
absorbance of the interfering species and is only applicable for the Sample concentration=c
analyte that exist in different chemical forms and exhibit different
absorbance values [9-11]. Zero-order

DERIVATIVE SPECTROPHOTOMETRY A= bc

The concept of derivative spectroscopy deals with the transformation of First-order

a simple absorption spectrum to its derivative spectrum (first, second,
or higher) based on wavelength. This spectroscopy is a method of dA d
manipulating the spectral data for the analytical situation in which the = bc
d d
mixture exhibit interfering absorption and it is also used for spectral
analysis to describe any chemical conformation [12].
nth order
In earlier days, there was a complexity because the derivative spectra
dn A/d n=(dn /d n)
bc
were generated by wavelength modulation technique (optical method)
and electrical method by using early UV visible spectrophotometers. But
Advantage
at the present time, an advanced software such as UV probe is introduced
This method is advantageous since without any chemical pre-
for generating derivative spectra directly from spectrophotometers,
treatment the samples of complex origin can be analyzed by direct UV
thus making this method largely practicable by reducing the need of
additional mathematical process making it quicker and easier. In 1974, analysis method. It also helps to contemplate the overlapping peaks
a new mathematical technique named as Golay-savitzky method was of a multicomponent system; allows analysis at low sample content
introduced and it became commercially popular [12-14]. impurity profiling and by removing scattering and baseline shift, the
spectral quality can be enhanced [13,15,16].
Zero-order spectra are easier than derivative spectra. A first-order
derivative spectrum is a graphical representation of the rate of change of Disadvantage
absorbance against wavelength. A first-order derivative passes through When the higher order derivatives are applied then the signal-to-noise
zero point as max of the absorbance band and starts and finishes at the ratio decreases and in case of modification of UV-visible spectrum for
zero point. At the same wavelength, one side of this point shows positive the first or higher derivative it results in a more complicated profile
band and other side shows negative band with both maxima and minima compared to zero-order spectrum. These are the unwanted effect of
values, hence that point is called inflection point. In zero-order spectrum, derivative spectroscopy [12].
the maximum positive and maximum negative slope correspond with a
maximum and minimum slope of the first-order spectrum. In zero-order CONVOLUTED DERIVATIVE TECHNIQUE USING FOURIER
spectrum, the wavelength of zero slope is the max, thus, in first order
spectrum the value of dA/d becomes zero [12].
The core of harmonic analysis is that a given function, for example, D1
The second-order derivative spectrum is a graphical representation of the or D2 curves of a chromatographic peak or spectrophotometric curve,
zero-order spectrum against wavelength or a plot of d2A/d 2 versus . At ƒ( ) can be expanded in terms of the Fourier series.
the same wavelength, the minimum negative band in the second order
derivative spectrum is the maximum negative band in the zero-order If (n+1) is an even number then:
spectrum, and the maximum positive bands in the zero-order spectrum also
gives two small additional positive maxima which is called satellite band on ƒ( )=a0+a1 cos x+a2 cos 2x+…+a(n+1)/2 cos ((n+1)/2)x+b1 sin x+b2 sin
both side of the main band in the second-order derivative spectrum [12]. 2x+…+b(n-1)/2 sin ((n-1)/2) x

If a spectrum is assumed as absorbance A, as a function of wavelength The calculation of the coefficients a1,a2,a3…aj and b1,b2,b3…bj is simplified
, the derivative spectra are[12]: since the trigonometric functions are mutually orthogonal.

Zero-order Any coefficient tj, can be calculated from a set of response data measured
at equally spaced time intervals, by the following summation, in which x
A=ƒ( ) takes values from 0 to 2 -[2 /(n+1)], at intervals of 2 /(n+1):

First-order tj= ƒ( )i Txi/ (Txi)2

D1=dA/d ) Where T represents cosine or sine.

Second-order The Fourier function coefficients, (tj) are proportional to ƒ( ).i.e.:

D2=d2A/d 2
) t j= j
c

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Where is a constant and c is the concentration of the analyte. RATIO DERIVATIVE SPECTROSCOPY

In earlier days ratio derivative spectroscopy has been appeared as an

This method is advantageous because it eliminates all types of appropriate method to determine two or more compounds in the same
interferences and helps to produce high degree of purity in case of sample without any initial separation. In case of binary mixtures of
analytical peaks. compounds with strongly overlapped spectra, managing with the level
of interference was problematic with the derivative technique [23].
To fix this crisis, ratio derivative method has been established. By the
The disadvantage of this method is that it does not correct linear concurrent use of zero crossing technique [24-26] and Salinas method,
interference. When the Fourier transform is carried out, band limitation this method has been widened to determine ternary mixtures [27-29].
of the signal might result.

DERIVATIVE TECHNIQUE UNDER ORTHOGONAL POLYNOMIAL Let us consider,

A is mixture of two compounds, A and B

In the spectrophotometric analysis of multicomponent system
orthogonal function method can be applied for correcting the The absorbance of sample mixture at 1
is AM, 1
unnecessary absorption.
Molar absorptivity of compound A and B is E A, 1 and E B, 1
In general, the core of harmonic analysis is that, a given function, for
example, D1 of absorbance curve can be expanded in terms of an Concentration of A and B is C A and C B
orthogonal function for unequal intervals.
The absorbance spectrum of the sample mixture is given by the
Thus, following equation:

D1=k0K0+k1K1+k2K2+k3K3+k4K4+k5K5+…+knKn A M, 1=E A, 1 C A+E B, 1 C B (14)

Where D1 is the first derivative which is belongs from a set of Above equation is divided by absorbance of standard solution of A at 1,
n+1 unequally spaced wavelengths. K0,K1,K2,K3,K4,K5,…Kn are the whose concentration is C0A that is E A 1 C0A then the equation becomes:
polynomials which are similar to constant, linear, quadratic, cubic,
quartic, quantic, etc., and k0,k1,k2,k3,k4,k5,…,kn are there related A M, 1/E A, 1 C0A=CA/C0A+E B, 1C B/E A, 1 C0A (15)
coefficients. From the view of orthogonality, the polynomials can be
calculated according to the method of Grandage and George [22] based This equation can be simplified to:
on the following
A M, 1/E A, 1=C A+(E B, 1/E A, 1) C B (16)
n
K ij 0 Differentiating equation (16) with respect to , gives
i 0

d/d (A M, 1/E A, )=C B d/d (E B, 1/E A, 1) (17)

n
K ijK iu 0, Where j u (12)
i 0 This equation indicates that the derivative ratio spectrum of sample
mixture is dependent only on the values of CB and it is independent of
Where j, u represent different polynomial orders. Any coefficient, kij, the value of CA.
can be calculated from a set of first derivative data by the equation

n n It allows the use of highest wavelength value of the analytical signals

k ij D1K ij / K 2ij (13) which have different maxima and minima. Thus, it gives a scope for
i 0 i 0
finding out the active compounds when the excipients and other
compounds which cause interference are present in the assay. It is an
The denominator of this equation is the sum of the squared individual appropriate method to determine two or more compounds in the same
values of Kij. sample without any initial separation. This method cancels out the
derivative step and the use of zero-crossing points and sophisticated
After the construction of the convoluted polynomial curves of each chemometric method is not required.
analyte, the orthogonal polynomial coefficient, kij, at any are
proportional to D1 and concentration, thus
The main disadvantage of this method is that it has many manipulating
kij= j
Ca steps such as division and calculation of the derivative and another
disadvantage of this technique is that it is very much dependent on the
Where j=kij (1%, 1 cm) is a constant which correspond to absorptivity instrumental parameters such as slit width and scanning speed.
of the pure compound, a, and Ca is the concentration of the absorbing
compound A. SUCCESSIVE RATIO DERIVATIVE SPECTRA METHOD

This method is established for the simultaneous estimation of

This method is advantageous because it selectively and specifically pharmaceutical drug component in ternary mixture without knowing
determines the drugs when the matrix interferences are present. In the ratio of the concentration of drugs in mixture and apart from any
case of multicomponent analysis, this method corrects the insignificant initial separation [31].
absorption.
Let’s consider the three compounds as X, Y, and Z. If Beer’s law is obeyed
in whole wavelength range used and considering the path length as
This is a time-consuming method because it has many mathematical 1 cm, absorbance of ternary mixture at each wavelength can be written
steps and requires a large amount of training sets. as:

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A m= X
CX+ Y
CY+ Z
CZ (18) which is inversed is used. Hence, the ratio is called as absorptivity factor
(F) and the crossing point is called as absorptivity factor point [32-35].
Where,
AX=aX bcX and AY=aY bcY
Am is absorbance of sample mixture.
X, Y
and Z are the absorptivity values of X, Y and Z. At crossing point of equal absorptivity having different drug
CX, CY, CZ are concentrations of X, Y and Z respectively. concentrations

Dividing the equation (18) by Z, corresponding to the spectrum of AX=AY

a standard solution of Z in ternary mixture, the first ratio spectrum
is achieved in the form of equation (19) (the zero values of Z aX bcX=aY bcY
should not be used in the divisor for the possibility of dividing
operation) aX cX=aY cY

B=Am/ Z=( CX/ +( CY/ + Z+CZ (19) aX/aY=cX/cY=F

X Z) Y Z)

When the first derivative of equation (19) is taken then CZ (derivative aX/aY=F (23)
constant) is zero, and then equation (20) would be obtained.
Am=AX+AY=aX bcX+aY bcY
dB/d =d/d ( CX/ +d/d ( CY/ (20)
X Z) Y Z)
Where,
The equation (20) is divided by (d/d ) ( Y/ Z), corresponding to
b=1
derivative of ratio of the spectra of standard solutions of Y and Z, the
second ratio spectrum is obtained as equation (21) (the zero values of
Am=aX cX+aY cY
(d/d ) ( Y/ Z) should not be used in the divisor for the possibility of
dividing operation): aX=F aY (24)

D=(dB/d )/[(d/d ) ( Y/ Z)]=[(d/d ) ( X

CX/ Z)]/[(d/d ) ( Y/ Z)]+CY (21) Am=F aY cX+aY cY

When the first derivative of equation (21) is taken then CY (derivative =aY (F cX+cY)
constant) is zero, and then equation (22) would be obtained.
The concentration of drug Y can be determined using linear regression
dD/d =d/d [{d/d ( X
CX/ Z)}/{d/d ( Y
CY/ Z)}] (22) equation between its concentration and absorbance at the wavelength
where the maximum absorption has taken place and also there is
Equation (22) is the mathematical structure of multicomponent analysis no interference of other drugs. Concentration of drug X also can be
which allows estimation of concentration of every active compound determined from the concentration of Y using the following equation:
in the solution (X) without any interference from other compounds of
ternary mixture (Y and Z). The equation (22) builds a direct relationship Am=aY (F cX+cY)=aX (F cY+cX)
among the concentration of X in the solution and amount of d/d .
cX=[(F cX+cY) - cY]/F
A calibration curve is plotted by taking dD/d v/s concentration of X
in ternary mixture (standard). The amount of dD/d correlates with
wavelength having maximum or minimum values should be estimated It is the modified method of classical absorption method and it is a
to achieve more sensitivity. Calibration curves for Y and Z also could be novel technique. For calculating the concentration of two drugs in
plotted as stated for X. binary mixture an easy mathematical equation is used.

This method is established for the simultaneous estimation of This method is only applicable for the binary mixture of drugs which
pharmaceutical drug component in ternary mixture without knowing does not have any isoabsorptive point and it is applicable only for the
the ratio of the concentration of drugs in mixture and also there is drugs which having larger difference in absorptivity.
no need of any initial separation. Only the two successive steps of the
successive derivative of the ratio spectra are required for this method. ABSORPTION FACTOR METHOD

Absorption factor method, a spectroscopic method, also used for the

It can be applied only for the mixture of two interfering substances analysis of binary sample mixtures having overlapping spectra and,
whose ratio of the concentration is known, and it should be same for in those cases, where it is found that one compound exhibits some
the unknown sample. interference at the max of another compound, while another compound
does not exhibit any interference at the max of the other compound [36].
ABSORPTIVITY FACTOR METHOD
Let’s consider a mixture of X, Y having a wavelength maxima at X and
This is the modified UV spectroscopy method of absorption method. Y where
Y shows some interference at X but X does not show interference
For performing this method there are following criteria: [32] at Y. Then, from the binary mixture of X, Y by subtracting the value
In particular, for binary mixture this method is utilized of absorption Y at X, the absorption value of X can be calculated
There must be maximum difference in between the absorptivity quantitatively. The absorption factor which is calculated experimentally
values of both drugs is applied for the calculation [37,38]. The equation is as follows:
Iso-absorptive point should not be present.
Absorption value of X at X
=Abs x (X+Y) – Abs1/Abs2 * Abs y (X+Y)
In case of iso-absorptive point method, crossing of spectra may occur at
different concentrations of drugs. For the absorptivity method, in that Where,
crossing point absorptivity is equivalent with the ratio of concentrations Abs1 and Abs2 is the absorbance of Y at X
and Y

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Abs1/Abs2=absorption factor (it is a constant value for pure [Am]=[aXCX]+[aYCY] (25)

compound Y)
Dividing eq (25) with normalized spectrum of Y as a divisor
Abs x (X+Y) and Abs y (X+Y) are the absorption of the mixture at two
wavelengths that is X and Y. [Am]/[aYCY’]=[aXCX]/[aYCY’]+[aYCY]/[aYCY’] (26)

[Am]/[aYCY’]=[aXCX]/[aYCY’]+constant (27)
This method is applicable for the ex vivo and in vitro characterization of
the drugs for topical delivery. It is also applicable for the drugs which Pm=PX+PY
are present in the biological samples. This method is used for the
estimation of the concentration of drugs in formulation which is based Where, Pm is the amplitude of ratio spectrum of binary mixture
on nanostructured lipid carriers.
PX is the amplitude of component X

It is only used for the analysis of the drugs which has overlapping PY is the amplitude of component Y.
spectra in the binary sample mixture and also only applicable in those
cases, where it is found that one compound exhibits some interference The recorded amplitude of ratio spectrum at isosbestic point is equal to
at the max of another compound, while another compound does not the sum of amplitude which is corresponding to component X and that
exhibit any interference at the max of the other compound. corresponding to component Y.

PY is constant and can be directly determined by the spectrum where

the straight line is parallel with the axis of wavelength in the area where
The principle of this method is similar to the principle of absorption the spectrum of Y is extended.
factor method and the method is applied for the analysis of the binary
mixture of drugs (X and Y) having overlapped spectra which intersect Since, we can use the normal divisor of Y so, CY’=1 g/mL
the isoabsorptive point and also it is found that one compound exhibits
some interference at the max of another compound, while another PY=[aYCY]/[aYCY’]
compound does not exhibit any interference at the max of the other
compound. PY=[CY] (28)

The absorbance values of component X and Y at iso are calculated by the For the estimation of amplitude of component X, we have to subtract
help of absorbance factor {Aiso/A2} is a constant for the pure component the value of constant from the ratio spectrum of mixture at isosbestic
Y which represents the average of the ratio between the absorbance point
values of different concentrations of pure component Y at iso (Aiso) at
(A2) PX=Pm – PY
2

Absorbance of Y in the mixture at =(abs1/abs2)× abs (X+Y) PX={[aXCX]/[aYCY’]+constant} – constant (29)

iso 2

Absorbance of X in the mixture at =abs (X+Y) – (abs1/abs2)× abs PX=[aXCX]/[aYCY’] (30)

iso iso

2
(X+Y)
At the isosbestic point aX=aY
Where abs1 and abs2 are the absorbance of pure compound Y at iso and
; abs1/abs2 is absorbance factor and abs iso (X+Y) and abs 2 (X+Y) And the normalized divisor of Y CY’=1 g/mL
2
are the absorbance of the mixture at these wavelengths ( iso 2).
PX=[aXCX]/[aYCY’] (31)
The concentration of the drugs (X and Y) can be determined by this
PX=CX (32)
method.
The concentration X and Y can be calculated by the help of the following
regression equation.
This is a novel, simple accurate, specific spectrophotometric method
which is applied for the simultaneous determination of two drugs and
C recorded=Slope C+intercept
also there is no need of prior separation steps. Any complementary steps
of spectrophotometric method does not require for the estimation of Slope is found approximately one and intercept is almost zero.
concentration of one component from the mixture of two components.

It is a novel spectrophotometric method which is simple to implement

In case of a component which has low concentration and the low
and also it is an economic method. For estimation of the components
absorbance value at the extended region the risk of error gets increased
in binary mixture only one divisor is required and by the help of the
when the absorbance factor is calculated by this method.
constant other mathematical manipulation steps can be reduced. By
the help of the divisor the amplitude of ratio spectrum represents the
concentration of the component directly. As there is no need for the
This method is novel spectrophotometric method of ratio spectra calculation step of absorbance factor in the lower absorbance sample,
manipulation by the help of normalized spectra. It is applied for thus there is no chance for risk of error.
the analysis of binary mixture (X and Y) where the component Y is
extended over the component X and the spectra of both drugs shows an
isoabsorptive point at the zero spectrum. In case of a drug mixture, if there is no existence of isoabsorptive point
at the ratio spectra and zero point of both components of the mixture
The absorbance of the zero-order absorption spectrum of binary this method cannot be applicable. If the spectrum of one component is
mixture at isoabsorptive point is as follows: not extended, then this method cannot be applicable.

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theory which states that there should be two requirements first one
is that the interfering substance should give some contribution at
In case of a binary mixture (x and y) having an overlapped spectra, the
each one of wavelengths and the second one is that ratio values of the
spectra of component y are more extended than component x, then
selected wavelengths should not be similar.
the component x can be determined by dividing the spectra of binary
mixture by a specific concentration of component y as a divisor (y0).
Constant center method contains two complementary steps of each
other such as constant calculation along with amplitude difference
Due to this a new curve is obtained which represents (x/y0)+constant.
method subsequent with constant multiplication.
If the constant is subtracted and the new curve which is obtained after
subtraction is multiplied by y0 then zero order D0 spectrum of x can be
First step for constant calculation along with amplitude difference
estimated. This can be represented by following equations
method based on that, in case of a binary mixture which contains two
Step 1: (x+y)/y0=(x/y0)+(y/y0)=(x/y0)+constant (33) drugs (X and Y) having overlapping spectra, then we can estimate X by
dividing binary mixture spectrum by the concentration of X which is
Step 2: (x/y )+constant – constant=x/y
0 0
(34) previously known. Then a new curve will be obtained that represents.

Step 3: (x/y0) × y0=x (35) X+Y/X’ i.e. X/X’+Y/X’

This constant can be directly estimated from curve (x+y)/y0 by the Where X/X’ is constant. This can be summarized as follows:
spectrum where the straight line is parallel with the axis of wavelength
in the area where the spectrum of y is extended. (X+Y)/X’=Y/X’+X/X’=Y/X’+constant

From the obtained ratio curve, two wavelengths ( 1 and 2) are selected
It is a novel spectrophotometric method applied for the simultaneous and at (Y/X’)1 and (Y/X’)2 points the values of ratio are subtracted then
determination of multicomponent pharmaceutical formulation without the constant (X/X’) accompanied with any instrumental error or any
having any prior separation and there is no need of derivatization. other interference from interfering substance X will cancel out. These
differences will represent only the component Y and then.

The limitation for the RSM is that it is applied only for the determination P1 - P2=(Y/X’)1+constant – {(Y/X’)2+constant}
of non-extended component; therefore, this method cannot be applied
for the determination of extended component. P1 – P2=(Y/X’)1 – (Y/X’)2

Where at 1 and 2 the ratio amplitude of ratio spectrum are P1 and P2.

For the determination of y, which is a second component, the extension Amplitude difference method starts with computation of regression
has been done for the previously developed method which is established equation representing the linear relationship between n the ratio
as a newer proposal called as ERSM. amplitudes difference of concentration of component Y at 1 and 2
using a specific concentration of X’ as a divisor against the related ratio
In this method component y can be estimated by dividing the previously
amplitude at the one wavelength of any two.
obtained D0 spectra of component x by the help of concentration of
component x which is known to calculate the value of constant (x/x0). Therefore {(Y/X’)1 – (Y/X’)2}=slope (Y/X’)1+intercept
The spectra of mixture (x+y) are divided by same divisor (x0). From
this division, a new curve is obtained that represents (x/x0)+(y/y0), Where, {(Y/X’)1 – (Y/X’)2} is the difference of ratio spectra
where x/x0 is constant which is previously obtained. If the constant is
subtracted, and the new curve which is obtained after subtraction is Amplitude at 1 and 2 and (Y/X’)1 is the corresponding ratio
multiplied by x0 then zero order D0 spectrum of y can be estimated. amplitude at 1.

(x+y)/x0=(x/x0)+(y/x0) - (x/x0)=(y/x0) × x0=y (36) The postulated amplitude value is (Y/X’)1 (P postulated) which
is related with component Y can be determined using computed
Concentration of y can be calculated by the help of the regression
regression equation which is previously reported by using ratio
equation which represents the linear relationship among the absorbance
difference amplitude at two different wavelength.
at its maximum wavelength against the related concentration of y [40].
The constant value X/X’ can be calculated along with amplitude difference
method by subtracting the recorded amplitude of ratio spectrum of the
This method can be applied for the determination of both (extended
mixture Y/X’+X/X’ (P recorded) at ( 1), and its postulated amplitude at
and non-extended) components and there is no need of any prior
the same wavelength { P recorded – postulated}
separation step. Furthermore, there is no need of any derivative step
and it does not require any special program, special technique and
Then
any sophisticated apparatus. This method showed maximum accuracy,
precision, and reproducibility.
X/X’={Y/X’+X/X’}1 – {Y/X’}1

i.e., C.V=[P recorded] – [P postulated]

In case of estimation of the concentration of drug when it is coupled
with other methods then it requires extra processing. And also it
Where, C.V is the constant value X/X’, P recorded is recorded peal
requires more time for performing this method on each mixture.
amplitude of the mixture at ( 1) and P postulated is the postulated
peak amplitude at ( 1).

The absorption spectrum of X at zero-order can be obtained along with

It is a suitable method for the simultaneous estimation of two drugs another step which is called constant multiplication step where we
which having the overlapped spectra. This method is based on the have to multiply the constant value with the divisor X’.

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X=(X/X’) × X’ ANNs are able to achieve the convenient information from

multicomponent system when the instrumental fluctuations or
Concentration of component X can be determined by the help of background noise is present; thus, ANNs are contemplated as
corresponding regression equation which represents the linear robust models. ANNs can computerize and model the complicated
relationship among the absorbance values of zero order spectrum of X relationships among inputs and outputs and also in case of two or
at its maximum wavelength against the corresponding concentration of more than two variables and it is helpful for finding patterns from
component X. Correspondingly, concentration of component Y in binary data. ANN is applied for quantitative analysis of pharmaceutical
mixture can be estimated by the help of same two steps. preparations in multicomponent system although ANN is used for
optimization purpose in chromatographic system and currently, other
mathematical techniques and ANN were compared and explored
The method is very accurate, simple, and precise and for this method
for the purpose of their convenience in optimization of complicated
any complicated computer programs and sophisticated apparatus is
spectrophotometric reactions. The application of ANN has been
not required. As this method permits the constant value calculation;
expanded for the elaboration of fluorescence biosensors which is
thus, it is regarded as a modified approach of ratio difference method.
based on nanoparticles [45].
This method is more advantageous than the second derivative method
in case of measuring the concentration of drug in zero-order because it
is more accurate.
It is a very easy process for the estimation of nonselective signals,
and it is also done for the multiple measurement of the same sample.
It is applicable for the binary mixture of drugs and the method is not It is extensively used in bioinformatics. Chemometric methods can be
applicable when the divisor should not comprise with the maximum applied in biowaiver study for correcting the interferences. For this
sensitivity and minimum noise. reason, chemometric aided spectrophotometry can be contemplated as
an innovation in biowaiver studies.
MULTIVARIATE CHEMOMETRIC METHOD

Multivariate chemometric method can be done by the multiple The main disadvantage of this method is the correlation of the factor,
measurements of the same sample for the correlation of the physical and their effect does not get separated.
properties of the sample with analytical data. It is mainly a mathematical
technique of processing analytical data, where it is easy to estimate APPLICATION
nonselective signals, then amalgamating them in a multivariate
model [7,42]. The various applications of UV Spectrophotometric methods are
summarized in Tables 1-14.
Multivariate methods include:
1. MLR or Multiple linear regression methods Table 1: Application for estimation of binary mixture by
i. K-matrix or Classical least squares simultaneous equation method in pharmaceutical dosage forms
ii. P-matrix or Inverse least squares.
Drug Spectroscopic Beer’s Reference
2. Factor based methods max
law range
i. Principle component regression (PCR) and solvent) (µg/ml)
ii. Partial least squares (PLS). Rabeprazole sodium 283 nm, 276 nm 10–60 [4]
and Aceclofenac (methanol)
In case of MLR and PCR techniques data is organized as matrices of Levosulpiride and 232 nm, 284 nm 1–20 and [49]
the column vectors, while for PLS technique data are organized as the Rabeprazole sodium (methanol) 1–20
matrices of the row vectors [7,42]. Ofloxacin and 240.6 nm, 279.4 20–40 and [50]
Ornidazole nm (methanol) 16–32
Chemometric contrivance can be done for improving the results of Norfloxacin and 273 nm, 319 nm 2.5–20 [51]
absorbance in dissolution profiling study, which is resulting from a Tinidazole (methanol) and 5–40
lower concentration of previous points in dissolution timing by the help Paracetamol and 247 nm, 276 nm, 5–35 and [52]
of derivative method (first and second) corresponding to the Fourier Diclofenac sodium (water) 5–40
function convoluted method. Chemometric methods can be applied
in biowaiver study for correcting the interferences, for this reason
chemometric aided spectrophotometry can be contemplated as an Table 2: Application for estimation of ternary mixture by
innovation in biowaiver studies. In general, the biowaiver studies are simultaneous equation method in pharmaceutical dosage form
used for designing the change of a pharmaceutical drug after approval.
Moreover, the concept of biowaiver has increased the scope of allowance Drug Spectroscopic Beer’s Reference
of the generic drug products which is new, by the help of this irrelevant max
and law range
solvent) (µg/ml)
human experiments could be avoided and the price of generic drug
products also could be reduced. As per USFDA, if the active pharmaceutical Tenofovir, Efavirenz 259 nm, 247 nm, 272 5–30 [53]
ingredients meet the condition of solubility and permeability at the same and Lamivudine nm (methanol) 10–60
time and the dissolution profile of dosage form meets the criteria of 5–30
immediate release; therefore, there is no need of performing the human Amlodipine 236.5 nm, 254 nm, 5–25 [54]
bioequivalence study in case of biowaiver studies [43,44]. besylate, Losartan 271 nm (methanol) 10–50
potassium and 5–25
In case of advanced chemometric techniques artificial neural network Hydrochlorothiazide
(ANN) plays a very important role and also it is extensively applied in Amlodipine besylate, 359 nm, 250 nm, 317 5–25 [55]
bioinformatics. Machine-learning approaches are the main principle Valsartan, and nm (methanol) 5–25
of ANN. ANN is also can be called as a data-modeling technique. Hydrochlorothiazide 10–50
Quercetin, 371.31 nm, 5–30 [56]
Recently ANN has been extensively applied in clinical decision making
Curcumin, and 424.68 nm, 343.76 nm 1–5
and medical classification and it is also used to solve the problems of
Piperine (methanol) 1–10
medical prediction [45-48].

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Table 3: Application of Q absorbance ratio method Table 8: Application of absorptivity factor method

Drug Wavelength Reference Drug Wavelength used Reference

Rabeprazole sodium 256 nm (iso-absorptive point), [4] for analysis
and Aceclofenac max
of Aceclofenac) Salmeterol xinafoate and 227.8 nm [32]
Carvedilol and 229.2 nm (iso-absorptive point), [8] Fluticasone propionate
Hydrochlorothiazide max
of Carvedilol) Sodium cromoglicate 241 nm [70]
Atenolol and 286.40 nm (iso-absorptive [57] and Fluorometholone
Ivabradine max
of Atenolol)
Propanolol and 272.8 nm (iso-absorptive point), [58]
Flunarizine max
of Flunarizine) Table 9: Application of absorption factor method
Prednisolon and 283 nm (iso-absorptive point), [59]
5-amino salicylic acid max
of 5-ASA) Drug Wavelength Wavelength Reference
(5-ASA) 1 (both 2 (one
Naproxen and 234 nm (iso-absorptive point), [60] drug shows drug shows
Paracetamol max
of Paracetamol) absorbance) absorbance)
Cefixime and 276 nm (iso-absorptive point), [61]
Betamethasone valerate 234 nm 347 nm [36]
Moxifloxacin of Moxifloxacin)
Difluprednate and
max
236 nm (iso-absorptive point), [62] and Tazarotene
Sodium cromoglicate 241 nm 325 nm [70]
Gatifloxacin of Difluprednate)
max
and Fluorometholone

binary mixture
binary mixture
Drug Solvent Wavelength of Reference
zero crossing Drug Wavelength Reference
Pioglitazone Phosphate buffer 228.1 nm and [63] Ezetimibe and Simvastatin 248.5 nm, 256 nm [39]
and (pH 9) and Chloride 228.2 nm
Metformin buffer (pH 2)
Table 11: Application of amplitude modulation method in
binary mixture

estimation of binary mixture Drug Wavelength Reference

Drug Order of Wavelength of zero Reference Ezetimibe and Simvastatin 248.5 nm, 256 nm [39]
spectra crossing point
Ofloxacin and 1 278 nm and 293.6 [50] Table 12: Application of ratio subtraction method and extended
Ornidazole nm
ratio subtraction method
Gatifloxacin and 1 348 nm and 263 nm [64]
Prednisolon
Drug Wavelength used Reference
Imipenim and 1 243 nm and 300 nm [65]
Cilastatin Paracetamol and 248 nm and 220 nm [71]
Ezetimibe and 1 265.20 nm and [66] Orphenadrine Citrate
Lovastatin 245.4 nm
Minoxidil and 1 290 nm and 351 nm [67]
Tretinoin Table 13: Application of ratio difference and constant center
method
Table 6: Application of derivative spectrophotometry for
Drug Wavelength used Reference
estimation of ternary mixture
Ezetimibe and (233.5 nm and 243.5 nm), [42]
Drug Order of Wavelength of zero Reference Simvastatin (238.5 nm and 246.5 nm)
spectra crossing point
Amiloride 1, 3, 1 365 nm, 265 nm, and [68]
hydrochloride, 385 nm
estimation of binary mixture of drugs in combined dosage form
Hydrochlorothiazide,
Timolol maleate
Drug Method used Reference
Salbutamol sulfate, 1, 1, 1 273 nm, 323 nm, and [69]
Bromhexine and 279 nm Minoxidil and Tretinoin PLS [72]
Etofylline Levodopa and Benserazide PLS [73]
Moexipril and Hydrochlorothiazide PLS, PCR [74]
Cypermethrin and tetramethrin PLS [75]

Drug Wavelength Reference CONCLUSION

Naphazoline and Antazoline 227.2 nm and 235 nm [23] Diverse analytical methods, including chromatography,
Salbutamol sulfate, Bromhexine 247.8 nm, 248.6 nm, [69]
electrophoresis, and spectrophotometry are available for the study of
hydrochloride and Etofylline 276.8 nm
multicomponent samples, biological products, and matrix complexes

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Asian J Pharm Clin Res, Vol 14, Issue 9, 2021, 1-11

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