IACS Institutional Repository

Sachs, Mendel

fl/ote 
Indian J. Phys. 82(7) 907-911 (2008) CD 
On entropy and objective reality 
Mendel Sachs 
Emeritus Professor of Physics, University at Buffalo, State University of New York, USA 
E-mail : msachs@buffalo.edu 
Received 30 January 2008, accepted 14 March 2008 
Abstract : This essay discusses Schordinger's answer to his question "What is Life?" in terms of negative 
entropy, as a thermodynamic description, rather than a fundamental explanation. Discussion is given to explaining 
a life system as an objective reality. 
Keywords : Biology, entropy, quantum theory 
PACS Nos.: 03.65.-w, 05.70.-a, 87.10.+e 
Erwin Schr6dinger wrote an interesting essay entitled : "What is Life?" [1]. He calls for 
a different type of physical force to explain the maintenance of a living organism in 
terms of 'negative entropy'. 
The idea is this : According to the second law of thermodynamics, an initially 
ordered system, such as the union of a male sperm cell and a female egg, starts the 
process of continued cell division and duplication (mitosis), eventually resulting in a 
living entity that continues a lifespan until its expiration, at death. Accompanying the 
process of cell division and growth is the emergence of the ordered system proceeding 
toward increased disorder. This is described by the increase of entropy (disorder) until 
equilibrium is reached, at maximum entropy, which occurs at the death of the living 
being. In regard to human beings, the lifespan is normally much greater than the time 
of normal decay of a complex system to equilibrium. 
The question is : How does this living organism maintain its lifespan? 
Schrddinger's answer is : 'negative entropy'. That is, there is negative entropy because 
of the metabolic process of transferring energy from the outside of the living organism, 
such as intake of food, air, and so on. The disorder of the system is then decreased 
during one's lifespan. This negative entropy slows down the process that nevertheless 
© 2008 IACS 
908 Mendel Sachs 
eventually reaches the equilibrium state, (maximum entropy) at death, In accordance 
with the second law of thermodynamics. 
The concept of entropy is fundamentally explained in physics in terms of a 
statistical feature of a many-body system, such as the complex molecular system of 
a human body. But does this statistical law, expressed as the second law of 
thermodynamics, really explain the life process? Does it answer Schrodinger's question : 
What is Life? in fundamental terms? 
I don't believe so. In his book [1], Schrodinger (I believe correctly) denies the 
validity of the assertion that "all physical laws are based on statistics". As he says : 
"the order of the solar system, the motions of the planets, is maintained for almost 
indefinite time. The calculations do not imply any statistics; they are based solely on 
Newton's law of universal attraction. Nor does the motion of a good clock appear to 
have anything to do with statistics". 
As I have discussed elsewhere [2], there are two stages to scientific inquiry. 
The first is the descriptive stage. The laws of statistics applied to a physical system 
are in this category. But the descriptive stage of science is not the goal intended by 
the scientist. It must lead to an explanatory stage. This is the stage of discovering the 
fundamental principles that underlie the empirical aspects of science. 
Consider, for example, the subject of molecular biology. Fundamental principles 
{i.e. universal) are at first speculated, based on hints from the empirical facts, and 
with the further use of one's intuition, a theory is formulated, leading to the role of the 
DNA molecule, and so on. This theory then leads to particulars that relate to the 
empirical data. If these agree with the actual experimental facts, then one may say 
(at least contingently!) that the theory is an explanation that is scientifically true. 
The adjective "scientifically" implies that this is only a contingent truth — it is 
subject to refutation. This is the way that we discover truth in any scientific endeavor 
— be it physics, chemistry, or molecular biology. We proceed to the truth by 
successive approximations in the different periods of science, continually refuting ideas 
based on new empirical evidence that does not support the older ideas and continually 
accepting new ideas. I believe that the history of science is evolutionary rather than 
revolutionary. There are threads of truth that do persist from one period of normal 
science to the next (to use T S Kuhn's terminology [3]). Thus the history of science 
reveals a positive flow in our continued understanding of nature. 
On Schrddinger's question: What is Life?, I don't believe that his thermodynamic 
argument about 'negative entropy* is an explanation for the life process. Of course, the 
thermodynamic description is true, but it is only at the descriptive level. That is to say, 
this is a subjective statement about an objective reality. What the scientist wants to 
get to, eventually, is a fundamental explanation of the objective reality, independent of 
our subjective knowledge. 
I believe that Schr6dinger was stimulated to look into this biological question by 
his pioneering research on the physics of quantum mechanics. This is a statistical 
On entropy and objective reality 909 
theory of the microdomain of matter. Thus, quantum mechanics is a subjective 
description rather than an objective description. It is then understandable that the 
quantum theory is not intrinsically explanatory. 
The eminent theoretical physicist, Richard Feynman, expressed the fact that 
quantum mechanics is not an explanatory theory in physics when he said the following 
about this subject [4] : 'The next question is, will you understand what I am going to 
tell you? {i.e. does quantum mechanics explain nature?) No, you are not going to be 
able to understand it. It is my task to convince you not to turn away because you 
don't understand it. You see, my physics students don't understand it either. That is 
because I don't understand it. Nobody does". 
It is my assertion that nobody understands quantum mechanics, i.e. as an 
explanation, because it is a purely statistical theory. It is not supposed to be 
explanatory in the first place - it does not yield any fundamental understanding in 
physics. It is purely descriptive. 
As an example, consider the toss of a coin. It flip-flops into the air, turns 
around, falls toward the ground and then lands. What is the probability that it will land 
head? Because the head and tail are two equally weighted sides of the coin, the 
probability that it will land head is 1/2. Empirically, this means that if the coin is 
tossed 1000 times, it will land head close to 500 times. 
But there is an objective path of the tossed coin. If I knew the initial force on 
it to start its motion upward, the force of gravity acting on it to make it return to earth, 
the forces of the air molecules that interact with the coin, etc., then I could find a 
unique solution of the equation of motion of the coin that predicts with certainty 
whether it will land head or tail. But I do not know all of these details, so I subjectively 
use a probability theory to determine the chance that it will land head. But the latter 
is not explanatory regarding the objective path of the coin! It is only descriptive. It 
does not mean that there is not an underlying objective path of the coin! 
Similarly, the entropy of a complex molecular system, such as a living human 
body, is a subjective feature about its state of disorder, according to our observations. 
Schrodinger's description of the living process in terms of negative entropy is then 
true, but not more than a subjective description. It is not an explanation, underlying 
objective laws of nature applied to the life process. 
Another example would be the universe itself — the subject of cosmology. Is it 
meaningful to talk about the entropy of the universe? I don't believe so since it is out 
of context! The universe is a closed system, by definition. Its physical nature is not 
tied to our lack of knowledge of its total intrinsic order. This is the order that underlies 
the dynamics of the entire universe. Our knowledge (or lack of knowledge) of the 
details of the universe — the planetary systems, the galaxies and their interactions, 
the expansion of the universe ... is in a different context than the laws of the universe 
itself. To say that a law of the universe is a law of thermodynamics is to confuse 
910 Mendel Sachs 
epistemology (a theory of knowledge) with ontology (a theory of what exists, independent 
of our knowledge of it). 
Einstein was a realist. He did not believe that the laws of physics are the laws 
of statistics. Most contemporary physicists are positivists — they believe that all that 
is necessary for the scientist to do is to describe. The latter is the reason for 
Feynman's assertion about quantum mechanics that "my task is to convince you not 
to turn away because you don't understand it. Nobody does". He then believes that 
a scientist should not try to explain a physical theory, such as quantum mechanics. 
It is sufficient to describe the facts of nature. This is the philosophical view of 
positivism. Einstein, on the other hand, did believe that the final stage of a scientific 
study is explanation of natural phenomena, in terms of first principles. It is the 
philosophy of realism. 
It is my firm belief that the 21st century will see a paradigm change in the 
philosophy of physics from positivism to realism. 
I should like to re-emphasize that I do not disagree with Schrodinger on the 
description of the life process in terms of negative entropy. My only stress is that this 
is not an explanation of life. That is to say, it does not derive the physical features 
of the life process from first principles. 'First principles' are not a mere correlation of 
facts. They are the premises that lead, by logical deduction, to the empirical facts of 
nature. Indeed, it is the 'first principles' that are our 'understanding' of the facts of 
nature. 
Schr&dinger agreed (as I have quoted in this essay), that the first principles of 
the laws of nature are not the rules of statistics. Though statistics plays an important 
role in the description of many body systems, I do not believe that Schrodinger (nor 
Einstein) thought that the fundamental laws of nature are laws of chance. 
Science is presently at a very early stage in the attempt to explain the life 
process. The best hope I see for this explanation is in the field of molecular biology. 
In this field of science we presently have accurate descriptions of the elements of a 
living system — the DNA molecule, its atomic constituents and its spiral configuration. 
But there is little understanding yet of the fundamental mechanisms, based on first 
principles, that underlie the life process. 
As a non-expert in the field of biology, I would like to speculate, as a physicist, 
on the problem of life. I am quite convinced (with Schrodinger and Einstein) of the 
truth of the continuous field concept in the laws of nature, in contrast with the 
atomistic model. Applied to molecular biology, the DNA molecule, as an element of a 
biological system, has a very large number of atomic constituents. Would it be 
possible to study this problem holistically, as a closed system, from the view of many 
continuous fields (one for each atomic constituent) but not in terms of singular atoms? 
The atomic model of DNA would entail the many-body problem — seeking a solution 
for an enormous number of coupled equations and their boundary conditions - an 
intractable mathematical problem. But in the holistic, field theory of the DNA molecule, 
On entropy and objective reality 911 
there are many coupled fields (each mapped in a single space, without the 
'entanglement' that Schrodinger refers to). This mathematical representation of a 
closed system is necessarily in terms of nonlinear differential equations. This is in 
contrast with the linearity of the quantum mechanical description of a many body 
system. The mechanism that we seek to explain the life process, may be in the 
mathematical solutions of such a nonlinear, holistic field theory of DNA. This indeed 
could be a start for an explanation of the life process. It is my speculation about the 
way of representing the fundamental mechanism of the life process, holistically rather 
than atomistically. 
References 
[1] E Schrodinger What is Life? (UK: Cambridge University Press) (1967) 
[2] M Sachs Concepts of Modem Physics: The Haifa Lectures (UK: Imperial College Press) (2007) 
[3] T S Kuhn The Structure of Scientific Revolutions (Chicago, USA: University of Chicago Press) (2nd edn) 
(1970) 
[4] R P Feynmam QED (USA: Princeton University Press) p9 (1985) 


On Entropy and Objective Reality

Advisory Board and Editors

Kochhar, Rajesh

Cultivation of Science in the 19th Century Bengal

Indian J. Phys. 82 (10), 1243-1245 (2008) ^ B ^ 
INDIAN W 
JOURNAL ^ 
Vol. 82 # No. 10 • October 2008 
)NTENTS 
Front Title 1237 
Advisory Board and Editors 1239-1240 
From Editor's Desk 1241 
Front Contents 1243-1246 
Astrophysics, Atmospheric A Space Physics 
IMF and geomagnetic field: A new feature 
R G RASTOGI AND H CHANDRA 1247-1254 
SEPs associated CMEs affecting near earth environment 
SANTOSH KUMAR AND JANKI PAL 1255-1263 
Atomic A Molecular Physics 
Elastic cross section for electron scattering by N20 molecule 
SUNITA SINGH AND DEO RAJ 1265-1272 
Electric dipole transitions for Mg XI (Z = 12) 
GOLDEM URER AND LEYLA CZDEMIR 1273-1285 
Condensed Matter* Materials Physics 
investigation on the mechanical, dielectric and photoconductivity properties of 
N-Methyl Urea NLO single crystals 
S JANARTHANAN, T KISHORE KUMAR, S SELVAKUMAR, S PANOI, 
P SAQAYARAJ AND D PREM ANAND 1287-1292 
[ ConVd. on next page ] 
1244 Contents 
Surface and hardness studies on as-grown {100} faces of zinc (tris) thiourea 
sulphate crystals 
V GANESH AND K KISHAN RAO 1293-1300 
Exploration of space charge behaviour of polyvinyl carbazole using measurement 
of thermally stimulated discharge current 
P K KHARE, GAUTAMA BANORE, PANKAJ MISHRA AND JYOTI MISHRA 1301-1308 
Structural characterization and electrical conductivity of naphthalene doped 
polyblend films of polystyrene (PS) and polymethyl methacrylate (PMMA) 
R J DHOKNE, V S SANQAWAR, P S CHIKHALIKAR, V S THOOL, 
A U UBALE AND A R JUNQHARE 1309-1318 
Effect of firing temperature on electrical and structural characteristics of Sn02 
thick films 
R Y BORSE AND A S GARDE 1319-1328 
General Si Interdisciplinary Physics 
Universal second order Switched-Capacitor filter for different Ovalues 
G N SHINDE AND S R BHAQAT 1329-1337 
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Fluctuation and fractal characteristics of ring like and jet like events produced at 
SPS energies 
DIPAK GHOSH, ARGHA DEB, PRABIR KUMAR HALDAR AND SIMA GUPTAROY 1339-1371 
Optics A Spectroscopy 
Applications of degenerate/non-degenerate modes coupling in an optical waveguide 
SANJEEV KUMAR RAQHUWANSHI AND SRINIVAS TALABATTULA 1373-1383 
Notes 
Optical and texture property studies in a nematic liquid crystal mixture 
JITENDRA KR KUSHWAHA, V P ARORA, K K RAINA AND V K AQARWAL 1385-1394 
[Cont'd on next page] 
Contents 1245 
Double photoionization of Ar (1 s 2 2s 2 i f 3s 2 Z$) 1 S O 
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Front Contents

Kushwaha, Jitendra Kr

Arora, V P

Raina, K K

Aqarwal, V K

Note 
Indian J. Phys. 82(10) 1385-1394(2008) 
# 
Optical and texture property studies in a nematic liquid 
crystal mixture 
Jitendra Kr Kushwaha1*, V P Arora2, K K Raina3 and V K Agarwal4 
department of Applied Sciences, Radha Govind Engineering College, Meerut-250 004, Uttar Pradesh, India 
2Department of Physics, Vardhman PG College, Bynor-246 701, Uttar Pradesh, India 
3School of Physics and Material Sciences, Thapar University, PatiaJa-147 004, Banjab, India 
4Department of Physics, CCS University, Meerut-250 004, Uttar Pradesh, India 
E-mail : kushwahajitendra@yahoo.com 
Received 19 July 2007, accepted 11 June 2008 
Abstract : Optical (using 589 nm light source) and texture (using white light source) studies as a function of 
temperature have been made of a muiticomponent nematogen: E47 in the temperature range 288°K to 343°K. The 
temperature dependence of refractive indices (n„n0) and the birefringence (An) agree closely with those 
obtained using modified four parameter model. A linear relation is observed between birefringence (An) and the 
order parameter (S). The normalized polarizabilities (ae/a, a0/a) and order parameter have been determined at 
different temperatures. The microscopic order parameter and normalized extraordinary polarizability fall with 
rise in temperature similar to other nematic mixtures. The transition temperature measured using polarizing 
microscope and optical studies agree closely, and do not show a sharp transition. This transition temperature 
range behaviour may be due to different components in the mixture. 
Keywords : Optical texture, refractive index, order parameter, normalized polarizabilities, birefringence. 
PACSNo. : 65.30. 
1. Introduction 
Liquid crystals (LCs) have been used extensively for direct view and projection displays, 
[1,2], tunable photonics, and nonlinear optics [3,4]. Most of the LC devices use the 
electric, thermal, or optical-field induced refractive index change to modulate light. One 
of the most important characteristics of a liquid crystal, which determines the 
anisotropy in its physical property is its orientational order. The orientational order is 
expressed in terms of microscopic order parameter S [5,6]. The value of S lies 
between 1 (for complete order) and 0 (for complete disorder in an isotropic liquid). The 
microscopic order parameter S differs from the macroscopic order parameter, which can 
;Corre8poncHng Author O 2008 IACS 
1386 Jitendra KrKushwaha, VPArora, KKRaina and VKAgar^i 
be determined easily using any of the bulk tensorial properties, like electric and 
magnetic susceptibilities, elastic constants, refractive indices, etc. of the liquid crystal 
However, it is possible to obtain the microscopic order parameter (S) from the physical 
properties by applying suitable corrections for internal field [7-9]. 
In the present paper we are reporting the results of the measurements of 
extraordinary refractive index (ne), ordinary refractive index (n0) in liquid crystal phase 
and isotropic refractive index (n,) in isotropic phase of a liquid crystal sample E47 as 
a function of temperature, using Abbe refractometer with a monochromatic light source 
The multicomponent mixture E47, procured from BDH, England, is identical with E7, 
and our results at 20°C agree closely with the preliminary data sheet of this sample 
[10]. From the experimental data we have calculated different useful parameters e.g., 
birefringence (An), normalized polarizabilities (a0/a, a0 /a) and order parameter S [11] 
The experimental data have been linked to the theoretically calculated values. It is 
observed that this model satisfies the experimental data very well. In addition the 
modified Vuks equation [12] and semi empirical relationship [13] have been verified. 
2. Theory 
The classical Clausius-Mossotti equation correlates the dielectric constant (e) of an 
isotropic medium with its molecular polarizability (a) at low frequencies. Replacing 
e = n2, the Lorentz-Lorentz equation correlates the refractive index of an isotropic 
medium with molecular polarizability in the optical frequencies. 
Vuks [14] made a bold assumption that the internal field in a liquid crystal is 
the same in all directions and gave a semi-empirical equation, correlating the refractive 
indices with the molecular polarizabilities for anisotropic materials. 
In eq. (1), ne and n0 are refractive indices for the extraordinary ray and ordinary ray 
respectively, N is the number of molecules per unit volume, aei0 is the molecular 
polarizability, and <n2> is defined as 
or 
we call((n2)) the root mean square (rms) refractive index. Since the sample 
1387 
alignment is planar, the optical anisotropy (An) is given by the difference between ne 
and n0 i.e. An = na - nv 
Solving eq. (2), we get, 
«.-((*))" iH 
or 
n, = ((*)f+{!)(*») 
(3) 
(4) 
Li e\ al [15,16] have described ne and n0 as a function of (n) and An. 
In theory, both ne and n0 are functions of wavelength and temperature. Here we 
focus on the temperature effect. According to our experimental data and also as 
observed earlier [17], f (n2}) is more fundamental in nature and its temperature 
dependence may be written as, 
l(*{r))\Vd = A+Br (5) 
Eq. (5) has a negative slope. On the other hand, birefringence is dependent on the 
order parameter S. Based on Haller [18] and Wu [19], the order parameter can be 
approximated as S = 
following form : 
An(T) = (An)0 
\0 
1 - -
'Nl J 
1--L 
'M 
Thus the temperature-dependent birefringence has the 
(6) 
In eq. (6), (An)0 is the liquid crystal birefringence In the crystalline state at 7 = 0°K, 
the exponent p is a material constant, and TNt is the transition temperature of the 
liquid crystal material under investigation. Taking logarithm of eq. (6) and giving linear 
fit, the values of (An)Q and 0 are obtained [20]. 
In case of liquid crystal mixtures, it is quite difficult to find the molecular weight. 
Also Madhusudana [21] has shown that 1 % error In the measurement of density leads 
to 11% error in the measurements of (a# - a j . Therefore, the concept of normalized 
polarizability is used here, which eliminates the factor "AT containing both density and 
molecular weight. 
The normalized polarizabilities for extraordinary and ordinary rays are then given 
by : 
... ("2-1) 
m 
1388 JitendraKrKushwaha, VPArora, KKRaina and VKAganval 
«n _ K2-i) 
<«> « n 2 ) - l ) (8) 
where (a) is the average polarizability of liquid crystal molecule and is defined as 
,
 v a + 2a0 
In order to find the best fit with the experimentally values, we have also calculated the 
order parameter'S1 using modified theoretical Maier-Saupe model [22] which approximates 
'& as S = 0.1 + 0.9[1-0.99(T/TNlff4 [23]. 
Experimentally the order parameter S can be obtained in a number of ways. 
Here we calculate the orientational order parameter by using Vuks [14] hypothesis. 
' « ( ( n 2 ) - l ) (10) 
where Aot is the anisotropy of molecular polarizability. 
Aa 
For obtaining S, procedure of Haller is followed. Factor is called scaling 
'(*-*)' a „ . . 
factor and is determined by plotting log / / 2 \ A as a function of log M ~ y . The 
plot is a straight line and can be extrapolated to T = 0°K to get the required scaling 
factor. 
3. Experimental details 
In order to conduct optical studies values of n0 and ne of the mixture were measured 
using an Abbes refractometer (resolution 0.001) at A = 5893 A. The refractometer was 
precalibrated by measuring the refractive indices of distilled water and benzene. A 
stable homogeneous alignment, unaffected by temperature cycling was induced in the 
present case by coating prism surfaces with a thin film of Polyvinyl Alcohal (concentration 
0.75% in water) and nibbing unidirectionaliy repeatedly. Such a method favoured uniform 
alignment with nematic director parallel to rubbing direction. The PVA coating does not 
affect the values of refractive indices [8]. Few drops of liquid crystal sample were 
allowed to fall on both the prism surfaces and were spread with a spatula and lower 
prism was clamped to the position. A sodium light source (589 nm) is used for 
illuminating the sample. A converging lens is placed between the lamp and refractometer. 
The temperature of the sample in Abbe's refractometer is controlled using circulating 
water from a constant temperature bath. The temperature regulation was better than 
Optical and texture property studies inanematic liquid crystal mixture 1389 
±0.1 °K. T0 prevent heat loss, proper insulation is made at various points. To measure 
the temperature of liquid crystal sample a pre-calibrated copper-constant thermocouple 
is placed in the close vincinity of sample and connected with a sensitive digital micro 
voltmeter. The temperature of thermostat was increased in steps of 3°K for each 
measurement and kept constant for half-an-hour. A polaroid sheet is placed over the 
eyepiece to allow the distinct separation of dark and bright regions in the eyepiece 
corresponding to ne and n0[W], 
The texture studies of E47 were also conducted using a polarizing microscope 
(OLYMPUS Model BX51) in conjunction with a hot stage (Linkam TP94 and THMS600) 
and high resolution CCD camera connect to computer. Heating and cooling were done 
at the rate of ±1.0°C/min. The temperature of the sample was measured to an 
accuracy of ±0.1 °C in a programmable temperature controller. Sample was first heated 
to temperatures well above the isotropic transition temperature and then allowed to 
cool. Texture photographs of the sample were taken in the nematic phase during 
cooling run. 
4. Results and discussion 
The clearing temperature of E47 as obtained by refractometer and polarizing microscope 
agree closely. The transition temperature is, however, not as sharp [24] as in the case 
of pure nematic liquid crystals which may be, due to different components in the 
mixture. Its seems that the different components in the mixtures undergo nematic 
isotropic transition through a sequence of co-existing nematic-isotropic phases. From a 
practical point of view, we therefore take the nematic-isotropic transition temperature, 
TNh as when the nematic isotropic phases are present in equal amounts. The average 
value of the broad phase region is considered as TNI = 61 ± 2°C. 
To make a fair comparison of various properties of the sample all graphs have 
been plotted with reduced temperature {T/TNI). The constant A, B, An and /? 
are calculated for the sample using eqs. (5) and (6) and their values are given in 
Table 1. 
Table 1. Calculated values of constant A, B, 4» and (3. 
Sample 
E47 
A 
1.7034 
B 
-0.0004326 
(An)o 
0.2080 
0 
0.1253 
In Figure 1, discrete points from observations and continuous curve from 
calculation as a function of reduced temperature for n0 and n0 and (</?2>)1/2 have been 
plotted. The closeness of the contimious curve with the experimental points validates 
the modified four parameter model. As temperature increases, behaviour of ne is 
different from n„ n0 depends strongly on temperature. With the increase in temperature, 
1 decreases throughout the entire nematic range whiljB nD increases initially slowly and 
1390 JitendraKrKushwaha, VPArora, KKRainaandVKAgarwai 
then increases rapidly. Near the isotropic temperature, there is a sudden decrease m 
rms refractive index because of first order in nature according to Landau rules. The rms 
refractive index decreases linearly as the temperature increases. Above the clearing 
point the optical anisotropy vanishes and the isotropic refractive index (n,) decreases 
with temperature as in normal organic liquids [25-27]. 
1.05 
Reduced Temperature 
Figure 1. Temperature dependence of refractive indices ner n0, nyand nAvg. Experimental data of n,: (D), n0: (o). 
^AVB : (*)• ni: (•) a n d s o l d ,inGS represent fitting curves of calculated data. 
In Figure 2 is shown the temperature dependence of normalized polarizabilities 
for extraordinary (a0/a) and ordinary (a0/a) components. The normalized polarizabilities 
obtained are independent of density and reduce to unity in the isotropic phase. The 
actual mean polarizability and polarizability anisotropies of the mixtures may deviate 
from the additive rule of the components in the mixture. 
In Figure 3, we have plotted the order parameter 'S' obtained experimentally, 
using modified four parameter model empirical equation correlate the refracting indices 
with the molecular polarizabilities and theoretical Maier-Saupe model for the singlet 
orientational distribution of the chain segments. The value of 'S' obtained using 
modified four parameter model agree more closely with the experimentally obtained 'S' 
Moreover, the maximum percentage deviation of 'S' with the experimentally obtained 
values is just 7% in the case of modified four parameter values in contrast to 17% for 
modified theoretical Maier-Saupe model values. The tSt value decreases with rise in 
temperature and reduce to zero as the temperature approaches at TNh This behaviour 
of 'S ' is similar to that of birefringence and it is further verified by the linear relationship 
between these two factors (S and An), as shown in Figure 4. 
The value of aja0 as a function of temperature is shown in Figure 5. aja0 
decreases gradually with increase in temperature. This variation of aja0 may be due 
O^andtextumpropWshJdiestoarMtotfclk^crystalmb^ 1391 
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1 
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< 
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e ~"^ 
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0.86 0.88 0.9 0.92 0.94 0.96 0.98 
Reduced Temperature 
1.02 
Figure 2 . Temperature dependence of normalized polarizabilities, ( a ) and (o) are represent experimental data of 
ajot and aJa respectively a n d solid lines represent fitting curves of calculated data. 
0.4 
mmtmmmmmmmm 
k- £ I 
mmmmmmmm 
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Figure 3. Temperature dependence of microscopic order parameter (S) : ( * ) represent experimental, (0) 
. represent modified MaJer-Saupe approximation data and solid tine represent fitting curves of calculated data 
usJrn3rrK>*fledfcKjrpafWTTeterrr»odel. 
to two factors, namely (a) the buckling of the end alkyl groups in the molecules and 
(b) the variation of the order parameter which is related to the orientation of the long 
molecular axis with respect to the director. Same et a/ [26] and Krishnamurti [28] have 
shown that the buckling of the end alkyl groups increases with increase in temperature, 
thereby reducing aja0 in the nematic phase of the mixture. 
In Figure 6 are shown the optical micro-textures of the sample under crossed 
1392 Jitendra Kr Kushwaha, VPArora, KKRaina and VKAgamai 
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0,16 
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fmmmmmmmmm, 
*• 
1 1 
J 
\ 
0.45 0.5 0.55 0.6 0.65 0.7 
Order Parameter 
0.75 0.8 
Figure 4. Order parameter versus birefringence ( * ) represent experimental data and solid line represent fitting 
curve of calculated data. 
1.4 
1.38 
1 1.36 
1.34 
1.32 
1.3 
1.28 
1.26 
0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 
Reduced Temperature 
Figure S. Temperature dependence a J a. Squares (d) represent experimental data points and solid line represent 
fitting curves of calculated data. 
polarizer during cooling from its isotropic phase to nematic phase. The phase transition 
occurrence is exhibited by the change in optical texture and refractive index of the 
sample. The width of transition depends upon the purity of the substance and it 
increases with lower purity. Thus the composition of the mixture may be adjusted to 
give a narrow range of melting [28,29]. 
p ' 
I—"--JEL 
; ' ! • ' 
Sample I 
i 
i •" 
q a , / a 
[-47 
\ i 
} i 
« _ ^ 
i ' 
0 
• M M M M J 
°\ I 
°\ I 
Optical and texture property studies in a nematic liquid crystal mixture 1393 
(63°C), <a> (62°C),<b> (61 °C), <c> 
(60°C), <d> (59°C), <e> (58°C), <f> 
(55°C), <g> (50°C), <h> (40°C), <i> 
(30°C),<]> 
Figure 6. Textures of E47 at different temperatures (cell thickness 10 p,m) 
Acknowledgments 
One of us, Jitendra Kumar Kushwaha is grateful to Mr. T N Soorya, Mr. Anant Kumar, 
and Mr. Sachin Jain, Department of Physics, Vardhman P G College, Bijnor, for the 
help in refractive index measurements and to Dr. Praveen Malik and Dr. Pankaj Kumar, 
Sciiool of Physics and Material Sciences, Thapar University, Patiala (Punjab) for the 
help with texture studies of the mesogen. We would like to thank Dr. B Bahadur, 
Display Center Design, Rockwell Collins, 400 Collins Road NE, Cedar Rapids, IA 
52498-0001 (USA) for useful discussions. 
References 
[1] E Lueder Liquid Crystal Displays (New York : Wiley) (2001) 
[2] E H Stupp and M S Bremesholtz Projection Displays (Yew York : Wiley) (1998) 
[3] S T Wu and D K Yang Reflective Liquid Crystal Displays (New York : Wiley) (2001) 
[4J L C Khoo and S T Wu Optics and Nonlinear Optics of Liquid Crystals (Singapore : World Scientific) 
(1993) 
[5] P G De Gennes The Physics of Liquid Crystals (London : Clarendon Press) (1974) 
[6] S Chandrasekhar Liquid Crystals (Combridge : Cambridge University Press) (1997) 
[7] Rajbir Singh, V K Agarwal, P P Anand and V P Arora National Acad. Sci. Letters 13 4 (1990) 
1394 JitendraKr Ku$hwahatVP Arora, KKRainaandVKAgami 
[8] Ved P Arora, Anuj Agarwal, Anil Kumar, Vinod Kr Agarwal and Birendra Bahadur Indian J. Pure Appi. 
Phys. 35 265 (1997) 
[9] Rajbir Singh, P P Anand, V K Agarwal Jasjit Ahuja and K K Ralna Asian J. Phya. 11 287 (2002) 
[10] Technical Information Shet from E-Merk and BDH (1992) 
[11] N V Madhusudana Mol. Cryst Liq. Cryst 59 117 (1980) 
[12] J Li and S T Wu J. Appi Phys. 96 6253 (2004) 
[13] ST\Nu J. Appi. P/rys. 69 2080 (1991) 
[14] M FVuks Opt Spectrosk. 20 644 (1966) 
[15] J Li, S Gauza and S T Wu J. Appi. Phys. 9619 (2004) 
[16] J Li and STWu J. Appi. P/?ys. 95 896 (2004) 
[17] T N Soorya, Surabhi Gupta, Anant Kumar, Sachin Jain, V P Arora and B Bahadur Indian J. Pure Appi 
Phys. 44 524 (2006) 
[18] I Halter Prog. Solid State Chem 10103 (1975) 
[19] S T Wu Phys. Rev. A33 1270 (19860 
[20] JLi, SGauzia and STWu Opf/cs Express 12 2002 (2004) 
[21] N V Madhusudana Theories of Liquid Crystals "Applications and Uses* Vol. I (ed.) B Bahadur 
[22] S J Picken Macromolecules 22 1766 (1989) 
[23] S J Picken, L Noirez and G R Luckhurst J. Chem. Phys. 109 7612 (1998) 
[24] D Demus, H G Horn and F Kuschel Mol. Cryst. Uq. Cryst. 44 61 (1978) 
[25] C P Smith Hand Book of Physics and Chem (CRC): Dielectric Behaviour and Structure (McGraw Hill) 
(57th ed.) 1955 (1976) 
[26] R K Sarna, B Bahadur and V G Bhide Mol. Cryst Uq. Cryst 51 117 (1979) 
[27] M J Bradshaw, D G Medonnell and E P Raybes Moi Cryst Uq. Cryst 79 289 (1981) 
[28] O Krishnamurti and H S Subramhanyam Mol. Cryst Uq. Cyrst 31 153 (1975) 
[29] Saswati Chakraborty, Anuradha Mukhopadhyay and S K Roy Indian J. Phys. 78 763 (2004) 


Optical and Texture Property Studies in a Nematic Liquid Crystal Mixture

Sengupta, P

Mondal, S

Chakravorty, J N

Indian! Phys.Kl(\ 1), 1441-1446(2008) 
Microwave reflection on echelon cum lamellar grating and 
its application in astrophysics 
P Senguptau, S Mondal12 and J N Chakravorty1* 
'Indian Centre for Space Physics, 43, Chalantika, 
Garia Station Main Road, Kolkata-700 084, India 
zRamakrishna Mission Residential College, P.O.-Narendrapur, 
24 Pgs (South), Kolkata-700 103, India 
E-mail : jc<e>csp.res.in 
Received 9 May 2008, accepted 30 May 2008 
Abstract : A new approach has been presented to generate strongly intense diffraction spectra in millimeter 
and microwave region employing combined reflection echelon-lamellar grating. A theoretical investigation using 
Fourier transform technique is made to obtain the resultant intensity pattern for the diffracted waves. The results 
presented indicate their significant applications in detection of biomolecules and astrophysical studies. 
Keywords : Microwave diffraction, lamellar grating, echelon grating, astrophysics. 
PACS No«. : 84.40, 42.79.Dj, 95.30.-k 
1. Introduction 
The Grating spectroscopy has taken a spectacular advancement in recent times after its 
importance in integrated optics was felt. Lamellar and blazed type gratings are finding 
increasing applications in electronics. They could be used as wave-guides and antenna in 
the microwave region as well. Research in the millimeter and microwave bands [1,2] is 
being carried out in the forefront in radio-astronomy, communications and various other 
fields for their important operational advantages like better penetration properties over their 
high frequency counter parts. They have the ability of simultaneous recording of many 
spectral elements at a low band width. However, due to very low intensity and completely 
different penetration properties of these waves, gratings with special design would be 
necessary. The characteristics of diffracted waves from reflection echelon, echellete and 
Corresponding Author 
<D 2008 I ACS 
1442 P Sengupta, S Mondal and J N Chakravorty 
lamellar gratings have been studied in the microwave region by Chakravorty et al [3-7] in 
the present communication we have confined our attention to having an intense diffraction 
spectra which could be secured if a grating can be constructed having characteristics 
both of an echelon and that of a lamellar We anticipate, such an echelon cum lamellar 
grating would be a good candidate for a millimeter or microwave grating instrument With 
this end in view, it is considered worthwhile to investigate theoretically the properties of 
such mixed gratings specially with regard to its intensity distribution Such gratings 
operating on millimeter and microwave bands may be useful in astrophysics and astro-
chemistry [8] in detecting of bio-molecules The intensity expression has been derived 
both by using conventional scalar approach and also by using Fourier transform technique 
The results obtained are found to be identical, we present our calculations made with the 
Fourier transform technique 
2. Theory of reflection type combined echelon cum lamellar grating using fourier 
transformation 
Let us consider a special profile lamellar grating which consist of N number of echelons 
each having n number of steps as shown in Figure 1 We may call this grating as an 
Echelon Cum Lamellar Grating (ECLG) Thus each element of this new type of grating is 
an echelon of which 'a' is the breadth of each step and *cf its depth Let a plane wave be 
incident normally on the grating element (of / th kind on p th echelon) Each point such 
as S' (x\ y') acts as a source of secondary wavelets We determine the resultant intensity 
Figure 1. Geometry of combined echelon cum lamellar grating 
which makes an angle (o) with the incident wave front Therefore, formation of the ECLG 
of all kind (/ = 1, 2, n) in the p th echelon may be given as 
y'- h(x') = c for 0 < x < a, 
= c + d for a < x < 2a, 
= c + (/ - 1) d for (/ - 1) a < x < /a, 
- c + (n~1)d for (n-1)a < x < na (1) 
Microwave reflection on echelon cum lamellar grating et al 1443 
Consider the incident wave at P(x, y) on the screen due to cfx' at S* on the grating 
element, is given by, 
Co 
r' 
d£ = U 0 c>(<>t-KrQ) (2) 
Here, S'P^r' and r0 = SS' + S'P~ (6 + r ) - [ x ' smtf+ /7(x')(1 + costf)] where, r is the 
radial distance of P(x, y) from fixed origin O such that r2 = x2 + y2, s i n # - x / r , 
costf = y / r and C0 is constant, K - 2/r/>l is the propagation vector The wave at P(x, y) 
due to all elements in the p th echelon is given by, 
Tn+na 
Rn J (3) 
where, 7p is the starting value of x' for the pth echelon and Tp+na is the end value of x' for 
the said echelon Here, f has been replaced by an average distance RQ Since o is 
small in practice (#max <10°) , such replacement does not affect the result The total 
intensity at the focus for entire echelon cum lamellar consisting n kind of element in each 
of N number of echelon is finally obtained as, 
p - W/2 " 0 
--iKasint) _ A~\ 
-iKa sintf J 
[1-e *ns] 1 - e iKNna sin H 
1-e -iKna sin e (4) 
where 5 = (1 + cos 0)d + a sin 0 Hence the resultant intensity (/) at the focus will be, 
/ = N =/n 
sin' 
Ka sin 0 
sin2 <9 
, K/7r(1+cos0)d + asin0l 
sin2 - L —- - J 
,>Kf(1 + cos0)d + asin6>| 
sin2 L J 
sin 2
 KNna sin 0 
2 Kna sin 6 sin^ 
(5) 
3. Results and discussions 
Using the intensity expression, three dimensioal plot of intensity (1) vs wave length (A) 
and diffracted angle ($) are plotted for grating elements with different combinations of n 
and N Figure 2 and Figure 3 show the three dimensional plot of intensity (I) vs wave 
length (A) of the incident microwave and the diffracted angle (# ) for two types 
configurations of grating elements n = 5, N = 10 and n = 6, N = 8 respectively with a = 
cf = 1 cm Contours are also plotted against the high peak values / e for the strong 
intense spectra Therefore it is possible to detect those points Here we have considered 
1444 P Sengupta, S Mondial and J N Chakravorty 
the wave length (x) of the microwave ranging from of the 0.1 cm to 0.5 cm along X-axis 
and diffracted angle (e) within the interval - 7 to +7 degree along Y-axis. The possible 
principal maxima and secondary maxima are shown in this interval. The contours of strong 
Fig. 2 Fig 3 
Figures 2 and 3. Shows the three dimensional plot of intensity (I) vs wave length ( A ) and diffracted 
angle (# ) for the grating elements n = 5, N * 10 and n = 6, N = 8 respectively with a = d = 1 cm 
maxima's are also plotted along XY-plane which are supposed to be detectable in the 
detector. The positions of the maximal and minima's will solely depend upon the 
configuration of grating elements i.e., upon the n and N values. We have also considered 
the different values of n and N and 
found the strong secondary 
maxima's will be detectable when 
the possible configurations (n, N) 
are (5, 6), (5, 8), (5, 9), (6, 8), (6, 
9) (7, 4), (7,6), (7,7), (8, 7). Figure 
4 shows plot of intensity vs 
wavelength (x) for the three different 
values of the diffracted angle ($), 
namely solid one for $ = 3°, 
dashed one for 9 = 4°, and dotted 
for e = 5°. It is therefore possible 
to detect the different wavelengths 
(X) from the locations of the 
intensity maxima's. In Figure 5 
shows the variation of intensity (I) 
vs. diffracted angle (e) for the 
5e+05 
4e+05h 
P3e+05f 
£> 
c 
£ 2e+05!. 
1e+05U 
f 
r i 
i 
! 1 i 
r j 
r 
L • 
r * 
[ \ 
\ A A 
I \ | i 
i 
1 * i 
l • 
? <• 
1 ^ i 
1 ?* 
i 
1 '» 1 '•' 
r ' IL.liUiAJ-
e=4« 
j 
*- J -/. 
i 
\ i 
i \ \ 
i 
n=5, N=10 
8=5° 
A, 
- l l U L—J 
0.1 0.2 0.3 0.4 
Wave length (X) 
0 5 
Figure 4. Shows the variation of intensity vs wave length 
for three different values of diffracted angle. 
Microwave reflection on echelon cum lamellar grating et al 1445 
Glycine which have their wavelength ( A ) 2 46 mm and Glycolaldehyde 2 913 mm [9-10] 
and forms strong intense spectra near about 9 - 3° and e = 6° respectively Hence, 
these types of grating will be very much useful tool for detecting those molecules Therefore 
it is possible to detect those molecules Hence these types of mixed grating will be very 
much useful tool for detecting such organic and bio-molecules 
200000 
180000 
160000 
~ 140000 
| 120000f 
100000 
80000 
60000 
40000 
20000). 
n = 5 N = 10 
— Glycine 
Glycolaldehyde 
k = 2 913 mm 
A = 2 64 mm 
. - K 
I! 
(Ah iJtL..-Ji 
-10 -5 10 
Diffracted angle (*») 
Figure 6 Shows the plot of intensity vs diffracted angle ( 0) for the Glycine and Glycolaldehyde molecules 
4. Concluding remarks 
Considering the geometrical configurations for obtaining satisfactory reproducible results it 
is found that n = 5 and N = 10, is quite suitable Many organic molecules and bio 
molecules have their wave length lying in the millimeter wave range, these gratings operating 
on millimeter and microwave bands as already said will be useful in astro-physics and 
astro-chemistry in the detection of such molecules As for example, glycine and 
glycolaldehyde have their wave lengths of 0 264 cm and 0 2913 cm respectively and 
therefore can be easily detectable From Figures 4, it is evident that angle of diffraction 
close to 0-10 degree is gives satisfactory results According to the desired diffraction 
angle parameters of the gratings elements may be chosen A common component used 
in the present day microwave and millimeter wave receivers in the wide band-width limiting 
amplifier which operates in the non-linear region They have the problem of 'capture effect' 
by which the weaker signals get suppresed by stronger signals Also the tuned oscillators 
in the microwave receivers have a phase noise problem We suggest that the use of a 
microwave echelon lamellar grating would be a much more straight forward method for 
instantaneous frequency measurement would be able to detect even very weak signals 
with no capture effect Furthermore these would be no power loss or time lag usually 
associated with conventional receivers 
1446 P Sengupta, S Mondal and J N Chakravorty 
Acknowledgments 
We thank Dr. Sonali Chakrabarti and Mr Ankan Das of Indian Centre for Space Physics 
43, Chalantika, Gana, Kolkata for the discussions on the spectral identifications of different 
types of bio-molecules. We also thank Indian Centre for Space Physics for providing 
computer facility. 
References 
[1] Infrared and Millimeter waves Vol 4 Millimeter system (eds ) Kenneth J Button and James C Wiltse 
( USA Academic Press, Inc) (1981) 
[2] Handbook Microwave and optical components Vol. 1 (ed) Ka» Chang (USA John Wiley & Sons) 
(1989) 
[3] S Chakrabarti and J N Chakravorty Astrophysics and Space Science 209 99 (1993) 
[4] S Chakrabarti, K Goswami, A K Sen and J N Chakravorty Optical Engineenng 34 (4) 1105 (1995) 
[5] S Chakrabarti and J Chakravorty Optics Communication 107 184 (1994) 
[6] S Chakrabarti, S Chatterjee, U Chattopadhyay and J N Chakravorty Indian J Phys 78 (6) 431 
(2004) 
[7] S Chakrabarti, S Chatterjee, U Chattopadhyay and J N Chakravorty Indian J Phys 78 (6) 471 
(2004) 
[8] Geoffreey A Blake Proceeding of IAU Symposium of Astro Chemistry Recent Success and 
Current Challenges (31) D C Lis, G A Black and E Herbst (eds) 365 (2005) 
[9) L E Snyder, F J Lovas, J M Hollis, D N Fnedel, P R Jewell, A Remijan, V V llyushin, E A Alekseev 
and S F Dyubko The Astrophysical Journal 619 914 (2005) 
[10] J M Hollis, F J Lovas and P R Jewell The Astrophysical Journal 540 L107 (2000) 


Microwave Reflection on Echelon Cum Lamellar Grating and its Application in Astrophysics

Lakshmanan, Palaniappan

Indian J. Phys. 82 (11), 1503-1512 (2008) 
Validity of theoretical models in estimating the sound 
velocity in toluene-alcohol mixtures 
Palaniappan Lakshmanan 
School of Physics, Umveisiti Sains MdUysia, Pualu ppnang 11800, Mdlaysui 
F mail Ip_ddp auwyahoo com 
Received 14 May, 200S, accepted J July 200S 
Abstract : Four different theoretical models have been applied to evaluate the sound velocity values at 303 
K for the systems studied in our previous work and they are compared with the experimental values. The validity 
of the Nomoto's relation, the ideal mixing relation, the free length theory and the Rao's specific velocity method is 
checked and a comparative study of the above models is made. The least square linear fitting equations are 
generated for additional confirmation. The non-ideal behaviour of the systems is explained in terms of molecular 
interactions of the constituents of the mixture 
Keywords . Sound velocity, theoretical models, molecular interactions 
PACSNo. : 43.35 Bf 
1. Introduction 
The assessment of the nature of molecular Interaction present in materials can be done 
by ultrasonic investigation. The departure from linearity in the values of sound velocity in 
liquid mixtures when studied as a function of concentration is found to exhibit interesting 
variations [1,2]. Of course, the acoustical and thermodynamical properties evaluated in 
the liquid mixtures signify the physico-chemical and molecular interactions that exist 
between the components of the system, an additional confirmation for the presence of 
specific interaction can be made using the estimated sound velocity values. Sound velocity 
data for three binary mixtures of toluene + aliphatic alcohols were reported in our earlier 
work [3] and the results were confirmed from the trend of thermo acoustical parameters. 
An attempt has been made in this paper to correlate the findings of experimental velocity 
obtained in the cited work with those predicted theoretically that are based on molecular 
models. Such comparisons are found to be useful in knowing the thermodynamics of the 
© 2008 IACS 
1504 Palantappan Lakshmanan 
mixtures and also provide a better means to test the validity of the various empirical and 
semi empirical theories [4,5] In recent years, various theories [6,7,8] have been in use 
for computing ultrasonic velocity in liquid mixtures and the deviation in theoretical sound 
velocity has been attributed mainly to the molecular interactions in the mixtures 
Alcohols, in particular methanol and ethanol, are found to posses the ability of azeotrope 
formation with toluene [9] As such all the azeotropes are non-ideal Further, for a 
satisfactory degree of separation, all the components of the mixture should show non-
ideality Apart from various experimental methods for estimating non-ideality of the liquid 
mixtures, many theoretical models are also available to do this The estimation of sound 
velocity and comparing them with the experimental sound velocity is one among the 
many techniques of the theoretical models Among the various models available for the 
estimation of sound velocity in the mixtures having non-ideal components, few of them 
are considered here Thus the present work aims at estimating the sound velocity values 
at 303 K for the binary mixtures of toluene with methanol, ethanol and 1-propanol and 
comparing with those of the reported experimental values 
2. Theoretical aspects 
The theoretical models include Nomoto's relation (NR) [10], ideal mixing relation (IMR) 
[11], free length theory (FLT) [12] and Rao's specific velocity method (Rao) [13] Further 
the percentage deviation, the molecular interaction parameter, the Chi-square test values 
and the linear fitting parameters were calculated for a reliable comparison The comparison 
yields the validity of the theory for these particular systems and also confirms the non-
ideahty of the systems The least square linear fitting is applicable for systems with 
weak interactions Of course, here it is taken with a view that the deviations can be 
attributed to the extent of the non-ideality existing in the systems which will offer additional 
confirmation 
Four theories as cited earlier are considered and their brief description is given hereunder 
2 1 Nomoto's relation (NR) 
Nomoto established an empirical formula for ultrasonic velocity in binary liquid mixtures 
with components 1 and 2 on the assumption of linear dependence of the molar sound 
velocity on concentration in mole fraction and the additivity for molar volume as, 
( ^ 
[x^ + x2V2 ) 
where x is the mole fraction of the component, Rv R2 the respective molar sound velocities 
and Vv V2 the molar volumes respectively The molar sound velocity is related to molecular 
Validity of theoretical models in estmatmg the sound velocity etc 1505 
weight (m) and density ( p ) as, 
P (2) 
where the molar volume obeys the additivity 
V = xft + x2V2 (3) 
2 2 Ideal Mixture Relation (IMR) 
Van Deal and Vangeal assumed the adiabatic compressibility ( f t ) of the binary mixture in 
terms of mole fraction as, 
On the basis of this equation, the sound velocity is given as, 
(4) 
U, IMR 
1 
2
 / X1 X 2 
x1m1 + x2m2 J ^ /T?^^ m2U22 (5) 
2 3 Free /engftf? f/?eory (FL7; 
Jacobson introduced the concept of intermolecular free length to determine the ultrasonic 
velocity in pure liquids and liquid mixture Further, he related the velocity of the pure 
liquids to the free length Lf by the equation, 
ULfPV2=KT (6) 
where Kr is the temperature dependent Jacobson's constant which takes a value of 199 53 
x
 10"8 in M K S units at 303 K For liquid mixtures, the above equation can be written 
as, 
U KT FLT -
Lf P2 
(7) 
where L and p represents the free length and density of the mixture The free length 
'mix 
Lf of the liquid mixtures is given by, 
u
" I (*1V1+*2V2) J (8) 
1506 Palantappan Lakshmanan 
where l/01 and V02 represent the volume [yo=vmuex&/ua~] of the pure components at 
absolute zero, Ua ~ 1800 ms-1 and 
Y = 
2V 
x If , 
\ 'fTMX / 
1-
U. expt 
u„ (9) 
is the surface area per mole 
2 4 Rao's specific velocity relation (RAO) 
According to this method, 
R^AO ~ uL,Xiri X ^Pt ) (10) 
Pi 
(11) 
where r is the Rao's specific sound velocity, PexpX is the expenmental density and />, is 
the density of the /-th component 
The results obtained using the theoretical models are compared and validated with the 
expenmental values using the respective molecular interaction parameter, percentage 
deviation, the Chi-square test and the linear least square fit 
2 5 Molecular interaction parameter 
The degree of molecular interaction a is given as, 
fu2 expt 
[u- (12) the ) 
where 1/
 t is the experimental sound velocity and Uihe is the relevant estimated sound 
velocity 
2 6 Percentage deviation 
The percentage deviation in sound velocity between the expenmental (L/expt) and computed 
(L/the) values are calculated as, 
y u 
% = ^expt ^the 
U expt 
100% (13) 
Validity of theoretical models in estmatmg the sound velocity etc 1507 
2 7 ChhSquare test for goodness of fit 
The Pearson [14] test of goodness fit is a very powerful tool to determine whether the 
deviations of the theoretical values from the experimental ones are due to chance or 
really due to the inadequacy of the theory to fit in the data If O, (/ = 1, 2, 3 n) is a set 
of observed or experimental frequencies and E, (/ = 1, 2, 3 n) is the corresponding set of 
expected or theoretical frequencies, then the Chi-square is given by 
Chi-Square (z) = X 
/=1 
(0,~Eff (14) 
3. Experiment 
The mixtures of various concentrations in mole fraction were prepared by taking purified 
AR grade samples (Aldrich make) at 303 K The ultrasonic velocities in liquid mixtures 
have been measured using the pulse-echo type ultrasound imaging system (USM-25, 
Krautkramer, Germany) with an overall accuracy of ± 0 1 ms"1 The instrument is calibrated 
with known material velocity and a probe delay of 233 ms is obtained for excellent 
overlapping of echoes The experiment is performed with the frequency range of 2 to 20 
MHz and measurement range of up to 100 mm The experimental temperature is maintained 
at 303 K by using a thermostat (Krautkramer, Germany) with an accuracy of ± 0 01 K 
4. Results and discussion 
Figures 1-3 shows the trend of the experimental velocity (EXPT) and the various theoretical 
velocity values obtained for the binary systems of toluene + methanol ethanol and 1-
~ EXPT a NR 
1350 0 
IMR . - FLT —*e- Rao FITTING 
900 0 t 
0 1 0 2 0 3 0 4 0 5 0 6 0 7 
Mole fraction of toluene 
0 8 0 9 
figure 1 Trend of sound velocity in methanol system 
1508 Palaniappan Lakshmanan 
propanol at 303 K respectively The trend of respective molecular interaction parameters 
are shown in Figures 4-6 The experimental sound velocity values were fitted to a straight 
- ^ e ~ EXPT 4 v NR - a - IMR _ « — FLT - * - Rao —+— FITTING 
1300 0 
1250 0 
1100 0 --^r- £ & 
1050 0 
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 
Mole fraction of toluene 
Figure 2. Trend of sound velocity in ethanol system 
line equation by the unweighted least squares method using Marquardts algorithm The 
generated fitting equations for the experimental sound velocity along with the standard 
deviation (a) and the correlation coefficient (R) are given in Table 1 The respective 
- ^ - E X P T -tv~NR - A - IMR ~ ^ - . FLT - * - Rao — h - FITTING 
1300 0 * — - „ 
1150 0 
0 1 02 0 3 04 05 06 0 7 0 8 0 9 
Mole fraction of toluene 
Figure 3. Trend of sound velocity in 1-propanol system 
Validity of theoretical models in estmatmg the sound velocity etc 1509 
percentage deviation of ultrasonic velocity along with Chi-square deviation values are given 
in Table 2 
Table 1. Linear fitting equations and parameters 
System Fitting equation <r R 
Methanol y = 166 94x + 112013 5 06 0 993 
Ethanol y = 143 76* + 1141 63 5 92 0 988 
1-Propanol y = 81 479x + 1190 42 2 88 0 991 
The perusal of Figures 1-3 reveals good and fair agreement between the experimental 
and calculated sound velocities owing to the several assumptions and approximation made 
in the respective theories In all the three systems the linear fitting seems to be the best 
fit that indicates that the existing interactions are weak The IMR method is based on the 
ideality of the components [11] and hence this model seems to fail more for methanol 
system Further IMR model is more suitable for mixtures in which the components 
molecules are of same size FLT treats the molecules as rigid spheres [12] and hence it 
totally fails in all the present systems This reveals that the components of the binaries 
are highly involved in interactions are also able to form or deform their structures The 
validity of Rao's method demands the additivity of specific sound velocity [13] This can 
hold good only for ideal mixtures Thus the failure of Rao's method is again an indication 
that the system is not ideal though the interactions are weak 
Of the four theories taken, NR seems to match closer with the experiment in all the 
systems Of course slight deviations in all the systems are found in the NR method also 
Such variations may be attnbuted to the fact that NR method requires the linear dependence 
— < ^ _ N R -f } IMR A F L T R a o 
0 5 0 
0 3 0 5 0 7 0 9 
Mole fraction of toluene 
Figure 4 Trend of molecular interaction parameter in methanol system 
Palantappan Lakshmanan 
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~x 
of molar sound velocity on mole 
fraction [9], where as the whole 
model is mainly based on the excess 
molar volume of the components The 
extent of excess molar volume is 
again directly related to the strength 
of interactions in the system Thus 
all the remaining theories approaches 
good match with the increasing chain 
length of alcohol or reducing 
interactions The generated linear 
fitting equations also show a larger 
standard deviation (Table 1) with lower 
correlation coefficient for ethanol 
system but they are very acceptable 
for the other two systems This 
implies that the methanol and 1-
propanol systems more or less obey 
the linear trend and hence they 
possess more ideal nature and the 
ethanol system is having more non 
ideality 
This discussion reveals that NR 
method is best suited for non-ideal 
systems whereas the other methods 
are more suitable for less non-ideal 
systems Thus it is expected that 
among the molecular interaction 
parameter calculated using the 
various models, NR should show 
minimum values The inspection of 
Figures 4-6 reveals that it is fully as 
per the expectation The larger 
magnitude of molecular interaction 
parameter noticed for other models 
shows the failure of the suitability of 
the model to the present experiment 
It is observed from Table 2 that 
the predictions based on percentage 
deviation and Chi-square tests are 
similar, however those of Chi-square 
test are evident and further they are 
Validity of theoretical models in estmating the sound velocity etc 1511 
fully in line with the above predictions. Chi-square follows Chi-square distribution with (/? -
D degrees of freedom. For a set of nine readings of the present investigations, it is noted 
that if the z2 value is less than 1.653, the theoretical values are acceptable as having 
only 1% error. To accept 5% error, x2 values may go up to 2 730. 
-e— NR IMR . F L T — Rao 
0.25 
-0 05 
0 5 0 7 0 9 0 1 0 3 
Mole fraction of toluene 
Figure 5. Trend of molecular interaction parameter in ethanol system 
Among the four theories taken up in the present study, it is unanimously found that 
the prediction by NR method fit fairly well for all the binary mixtures considered In 
particular, FLT's prediction fails completely in toluene systems This may be attributed to 
the fact that toluene posses both electron donor and acceptor tendencies. Though the 
amino group in toluene is an inherent strong electron-donor, evidences can be found for 
w_ B 
"5> E 
(6 
Q. c o 
o 2 
int
e 
_^ 
m 
s O 
s 
0 08 
0 04 
L=r' 
0 OO 
>*v 
Q— 
-0 04 
-0 .08 r^s. 
v& I 
X<* ' 
—£±—~. V^r-—-
^^^ 
-0 .12 
0.1 
NR IMR 
-\ I - + 3 ~ 
- F L T R a o 
i I 
-f ^ 
0.3 0.5 0 7 
Mole fraction of toluene 
1-J 
0.9 
Figure 6, Trend of molecular interaction parameter in 1-propanol system 
1512 Palaniappan Lakshmanan 
the H atoms in the NH2 group to play the role of electron-acceptor centres [15]. A molecule 
having two contrary natures simultaneously cannot be rigid as assumed by FLT. The 
same is true for alcohol molecules also as they have one hydrophobic and hydrophihc 
contrary groups. As all the components violate the basic assumption of FLT, the theory 
for the present binaries totally failed. 
As all the models are aiming at the sound velocity a positive value of the validation 
parameter, either molecular interaction parameter or the percentage deviation, indicates 
the existence of strong interactions. As NR is the only best suited model for the present 
systems existence of strong interactions is confirmed and the strength decreases as the 
chain length increases. This is reflected by the negative values of percentage deviation in 
1-propanol system. Thus this analysis reconfirms the following conclusions and further 
goes one step ahead that it relates the strength of interaction and the chain length of 
alcohol. 
5. Conclusions 
(i) Among the four theories taken up, NR suits well for all the binary systems. 
(ii) Components of the considered systems are not rigid and non-ideal. 
(iii) Among the various binary mixtures considered, toluene + 1-propanol system is 
approaching ideality. 
(iv) The strength of molecular interactions decreases as the chain length increases 
References 
[1] Lu Yi-Gang and Dong Yan-Wu Chinese Phys. 15 2030 (2006) 
[21 G Savaroglu and E Araj Intr. J. Therm Phys. 26 1525 (2005) 
[3] L Palaniappan and R Thiysgarajan Physics & Chemistry of Liquids (In Press DOI 10.1080/ 
00319100701312807) 
[4) P K Agnihotn and C S Adgaonkar Ultrasonics 27 248 (1989) 
[5] A Ali, A K Nain, N Kumar and M Ibrahim Chinese J. Chem 21 253 (2003) 
[6] A Ali and A K Nain Pramana 58 695 (2002) 
[7] P Resa, L Elvira, F Montero de Espinosa and Y G Omez Ullate Ultrasonics 43 247 (2005) 
[8] V Syamala, P Venkateswarlu, G Prabhakar and K Sivakumar Physics & Chemistry of Liquids 44 
127 (2006) 
[9] David R Lide CRC Handbook of Chemistry and Physics, (New York : CRC Press) pp.6 (2002-
2003) 
[10] O Nomoto J. Phys. Soc. Japan 13 1528 (1958) 
[11] W Van Deal and E Vangeal Proc. First Int. Conf. on Calorimetry and Thermodynaomics (Warsaw) 
pp.555 (1969) 
[12] B Jacobson Acta. Chem. Scand. 6 1485 (1952) 
[13] V D Gokale and K Bhagvat J Pure Appl. Ultrason. 11 21 (1989) 
[14] G Udny Yule and M G Kendall Theory of Statistics (New Delhi : S. Chand & Co.) (3rd edn.) (1987). 
[15] P Miecznik, Z Golebiewski and S Mielcarek Fluid Phase Equilibria 221 41 (2004) 


Validity of Theoretical Models in Estimating the Sound Velocity in Toluene-Alcohol Mixtures

Oza, A T

Solanki, G K

Amin, Anand

Trivedi, Parimal

Indian J. Phys. 82 (11), 1513-1522 (2008) 
U V-visible-near IR and infrared spectroscopy of ^ carotene 
and ^ -carotene-iodine complex 
A T Oza*, G K Solanki, Anand Amin and Parimal Trivedi 
Department of Physics, Sardar Pate! University, Vallabh Vidyaridgar 388 120, Gujarat, India 
E-mail djayo^at^yahoo coin 
Received 15 October 2007, accepted 22 July 200S 
Abstract /i -carotene which a well known precursor of vitamin A forms a charge transfer complex with 
iodine fl -carotene and its iodine complex both are studied with ultraviolet- visible- near infrared and mid-
infrared spectroscopy The spectra are analyzed for the nature of transitions and free-carrier absorption // -
carotene -iodine shows a broad and intense Gaussian band around 400 nm Band assignments of the infrared 
spectra are also carried out The first derivative profiles are also plotted 
Keywords * Ultraviolet-visible spectroscopy, infrared spectroscopy, (1 -carotene, electronic transition, Gaussian 
bands 
PACS Nos. ' 78 30 JW, 87 15 Mi, 71 20 Ni 
1. Introduction 
p -carotene is extracted from carrot and is a well - known precursor of vitamin A [1] It is 
a semiconductor as well as photonconductor [2,3]. Here it is our interest to study how 
optical properties of p -carotene changes under complex formation with iodine. Optical 
absorption and electrical properties are related [4], Therefore, we study P -carotene and 
p -carotene-iodine complex with UV-visible near IR as well as IR spectroscopies between 
200 nm and 1600 nm and 400-4000 cm"1 range respectively. 
2. Experimental 
p -carotene was obtained from Sigma chemical company which was analytical reagent 
and therefore, about 99% pure, p -carotene was grinded in a mortar to make it a 
Corresponding Author 
©2008IACS 
1514 A T Oza G K Solanki Anand Amm and Panmal Trtvedi 
Ci 
CH3| 
CH3 
^ / * C H 2 
I 
< >C— CH3 
HC 
C — C H 3 
HC 
I 
CH 
HC 
I 
C - C H 3 
II 
HC 
I 
CH 
Hh -
HC 
I 
HC II 
C - C H 3 
HC 
Point of 
Cleavage 
microcrystallme powder and pasted on a visible transmitting 
strip with paraffin oil It was placed in a standard 
spectrophotometer of Perkin-Elmer Company to record the 
spectrum in the range 200-1600 nm p -carotene and iodine 
were mixed in 1 1 molecular weight proportions and gnnded 
in a mortar till the colour changed due to the formation of 
charge transfer complex The same process as in the case 
of p -carotene was followed for recording UV-visible-near 
IR spectrum Molecular structure of p -carotene is shown 
in Figure 1 
The infrared spectra (KBr mull) of p -carotene and // -
carotene-iodine (1 1) complex in the range 400-4000 cm -1 
were obtained using a GXFTIR single beam 
spectrophotometer of Perkin-Elmer Company, U S A It had 
resolution of 0 15 cm~1 scan range 15,600 - 30 crrr1 
scan time 20 scan/sec and OPD velocity of 0 20 cm/sec 
MIRTGS and FIRTGS detectors were used 
2. Results and discussion 
The UV-visible - near IR spectra of p -carotene and its 
iodine complex are shown in Figures 2 and 3 In the p -
carotene spectrum, one band is found at 300 nm A sharp 
drop in absorption is found at 500 nm Above 600 nm, the 
transmission becomes almost constant upto 1600 nm 
Three weak (compared to background) absorption bands 
are visible at 1170 nm, 1230 nm and 1350 nm There is 
also an absorption band at 750 nm and a plateau in 
transmission in the range 1400-1600 nm The spectrum of 
iodine (Figure 3) shows a rise in transmission of 300 nm 
band from 2 1 % to 77 5% There is a monotonic rise in 
transmission above 580 nm and broad and intense band 
at 1000 nm Absorption bands in the spectrum of p-
carotene at 1170 nm 1230 nm and 1350 nm show red 
shift The absorption bands in the spectrum of P -carotene 
shift to 1170 nm, 1230 nm, 1300 nm and 1420 nm in the 
iodine complex Absorption at 380 nm, 430 nm and 450 nm develop in the spectrum if 
iodine complex which are not at all observed in p -carotene spectrum 
The infrared spectra of p -carotene and p -carotene-iodine are shown in Figure 4 in 
the range 400-4000 crrr1 Several bands arising from characteristic vibrations of p -carotene 
are observed and broaden and split in the iodine complex This shows that iodine leads 
Hh 
CH I 
HC 
C - C H 3 
I 
HC 
HH 
CH I 
CH3
 V C . 
> " * ^ C - C H 3 
CH* I I 
^ CH2 v,CH2 
^Ci£ 
(J - Carotene 
Figure 1 Molecular structure of 
// -carotene 
UV-visible-near IR and infrared spectroscopy etc 1515 
to delocalization of charge carriers. The photoconductivity most probably arises from the 
absorption edge in the infrared range at 1900 crrr1 in //-carotene This somewhat reduces 
to 1800 cm"1 in the spectrum of iodine complex. 
70' 
1400 1600 
Wavelength (nm) 
Figure 2. UV-visible near IR spectrum of // -carotene. 
90-
80 
70 
60 
c 
o 
E 
m 40-1 
^ 3 0 ^ 
20 i 
1 
0 
P-CAROTENE-I, 
'V 
200 400 600 1200 1400 1600 800 1000 
Wavelength (nm) 
Figure 3. UV-visible near IR spectrum of //-carotene-iodine (1 1) complex. 
4. Analysis and interpretation 
The strong band in transmission of p -carotene at 300 nm can be ascribed to <j -> ,T * 
transition. This transition is most affected by its interaction with iodine and the transmission 
of transition rises about 2 1 % to 77.5% in iodine complex. The optical absorption edge of 
1516 A T Oza, G K Solanki, AnandAmin and Panmal Trtvedi 
p -carotene occurs around 2 4 eV (500 nm) (hindered cis-isomer) because p -carotene is 
a semiconductor A comparative graph of p -carotene and its iodine complex is shown in 
4000 3500 3000 2500 2000 
Wavenumbers (cm-1) 
1500 1000 
40 
§ 32 
to 
to 
c 
XJ 
S 2 4 
16 
(b) ft -carotene-iodine 
A/ 
! . . „ W _ _ . J i 1 
/X//| 
J 1 U 
4000 3500 3000 2500 2000 
Wavenumbers (cm-1) 
1500 1000 500 
Figure 4. Infrared spectra of (a) ft -carotene and (b) // -carotene-iodine 
Figure 5. The iodine complex reveals a broad Gaussian absorption band around 400 nm 
(3.0 eV) and optical absorption edge of p -carotene is wiped out The Gaussian distribution 
is a smooth approximation; otherwise it is absorption shape of the real part of dielectric 
constant around 340 nm 
The optical absorption edge of p -carotene reveals itself as a rise in transmission at 
500 nm. The edge is analyzed to fit the relation [4] 
Ahv = B(hv-Eg) 1/2 
UV-visible-near IR and infrared spectroscopy etc 1517 
which is the absorption (A) for a direct allowed transition in a disordered material In Ahv 
vs In {hv-Eg) is plotted (Figure 6a) and slope is found to be 1/2 After this verification, 
80 
70 
60 
50 
40" 
35 
Gaussian band around 
400 nm (3 0 eV) 
Absorption edge of 
// -Carotene 
500 nm (2 4 eV) 
200 
— I — j — 
300 400 
Wave Length (nm) 
500 
Figure 5 A comparison of absorption edge of ft -carotene with 
spectrum of the iodine complex 
(Ahv)2 vs hv is plotted (Figure 6b) which is found to be a good straight line having an 
intercept on x-axis E = 2 0 eV (600 nm) This shows that it is a direct allowed transition 
across a band gap between the top of the valence band and the bottom of the conduction 
band 
Next is the analysis of free-carrier absorption in the conduction band region, t.e hv > Eg 
[5] Log A (A in %) vs log A (A in nm) is plotted for this purpose (Figure 7) because it 
is supposed to obey a power law The slope is 1 8 showing the relation 
18 af = AA 
i e the power (exponent) is 1 8 This shows that the charge carriers are scattered by 
acoustic phonons [6]. The phonons do not play role in the transitions across the band 
gap but do scatter free charge carriers 
1518 A T Oza, G K Solanki, AnandAmm and Panmal Tnvedi 
14000 
13000H 
12000H 
11000 
10000 
9000 H 
8000 H 
7000H 
6000 H 
5000 
P - Carotene 
0 3 
Log (hv Eg) 
(b) 
p - Carolene 
Range 500-600 nm 
Ahv-B(ho-Eg) 
Direct allowed 
transition 
0 5 
1 9 2 0 2 1 2 2 
hu (ev) 
2 3 2 4 
A broad absorption band around 
775 nm can be due to delocahzation 
of charge earners along the long /> 
carotene chain Three absorption 
bands at 1170 nm, 1230 nm and 
1350 nm can be assigned to the 
spin-orbit splitting of valence band 
[4] The gaps among triply split band 
absorb electromagnetic radiation 
This triplet is red shifted to 1180 nm 
1300 nm and 1470 nm in the iodine 
complex This can be due to band 
tailing effect in a charge transfer 
between p -carotene and iodine 
Carotene 
2 00 -
Slope = \ 8 
Scattering by 
acoustic phonon 
2 52 2 53 2 54 
Log \ (in nm) 
2 ^ 
Figure 7 Free-carrier absorption in // 
Figure 6 Nature of transition of p -carotene which is a c a r o t e r ,e T h ,s shows scattering of charge 
direct allowed transition carriers by acoustic phonons 
The enlarged diagram of the Gaussian envelope in the spectrum of /3 -carotene-iodine 
complex is shown in separately (Figure 8a) and it is fitted the relation (Figure 8b) 
/4 = 4 ) e * P | 2M? 
UV-visible-near IR and infrared spectroscopy etc 1519 
which is the Gaussian distribution where M2 is the second - moment of the distribution 
This reveals that there is density of states having Gaussian distribution within the forbidden 
energy gap. The Gaussian curve is somewhat asymmetric having long wavelength tail. 
80 
75 H 
T 
(%) 
70 H 
65-J 
(a) |J - Carotena - Iodine 
—,— 
300 
8 
1 88 
1 878 
1 876 i 
1 874 
1 872 
1 87 i 
1 868 H 
1 866 "J 
*1 864 
1 862 
1 861 
1 858 
1 86i 
1 854-j 
1 8521 
1 85 
— I — 
400 500 600 
Wave length (nm) 
(b) p - Carotene - Iodine 
Gaussian band 
around 400 nm 
(Short-Wavelength Side) 
zm0 
In A - In/% — v-i*r 
— i 1 j — 
1000 2000 3000 4000 5000 
j — 
6000 
1 1— 
7000 8000 9000 10000 
(A-A,)2 (nm)2 
Figure 8. Gaussian envelope of absorption In /i -carotene- iodine and its 
Gaussian distribution fit. 
In the spectrum of p -carotene-iodine complex, there are weak absorption bands at 
380 nm and 450 nm which are not found the spectrum only p -carotene. This can be 
related to electronic excitation induced by iodine in the long hydrocarbon chain of p -
carotene. There is a monotonic rise in transmission above 580 nm which follows an 
intense transmission band around 1000 nm. This can be ascribed to a change in dielectric 
constant of p -carotene due to its complexation with iodine. 
1520 A T Oza, G K Solanki, AnandAmm and Panmal Trivedt 
300-1 
The band at 775 nm in ft -carotene spectrum is replaced by a plateau in the spectrum 
of the iodine complex Similarly there is a plateau in transmission in ft -carotene in the 
range 1400-1600 nm while there is 
an absorption band in this range in 
/?-carotene-l2 spectrum This 
inverted behaviour shows that there 
is a borrowing of oscillator strength 
from the band at 775 nm in / ' -
carotene At 775 nm, ft -carotene 
shows an absorption band and the 
iodine complex shows a plateau 
while around 1550 nm ft -carotene 
shows a plateau and the iodine 
complex shows an absorption band 
This occurs at approximately half 
energy This band at 1550 nm for 
iodine complex is a charge transfer 
band Thus the derealization of 
charge carriers along //-carotene 
chain gets transferred to iodine 
when complex formation occurs 
For better resolution, the first 
derivative spectra are plotted (Figure 
9) The zeros of the first derivative 
mark the position of broad bands 
The red-shifting of these absorptions 
is due to the interaction of // 
carotene and iodine which leads to 
the broadening of spin orbit split 
bands of valence band, / e one type 
of band tailing reducing the energy 
gaps among three parts of the 
valence band There is a triplet 
between 1 eV and 2 2 eV with 
centre band diminished in the 
spectrum of y?-carotene-iodine 
(Figure 9b) It is absent in the 
spectrum of ft -carotene (Figure 9a) 
This proves that iodine excites and 
interacts with several methyl groups 
-200-^ 
Figure 9 First derivative of spectra of (a) p -carotene and 
(b) p -carotene- iodine 
UV'Visible-near IR and infrared spectroscopy etc 1521 
on p -carotene molecule The 
nature of transition and free 
carrier absorption in the 
spectrum of p -carotene-iodie 
complex are also ana)yzed 
(Figure 10) Acoustic phonons 
scatter charge carriers but a 
direct transition in ft -carotene 
becomes indirect in /?-
carotene-iodine complex 
Next is regarding the 
infrared spectra of ft -carotene 
and its iodine complex The 
absorption edge found at 
0 225 eV is the infrared 
spectrum of p -carotene can 
be considered as a Peierls 
absorption edge due to Kuhn 
periodicity or a Peierls 
distortion along chain of p-
carotene (Figure 11) This 
band gap reduces to 0 20 eV 
in //-carotene-iodine band 
gap by only phonon energy 
The infrared absorption edge in 
//-carotene and its iodine 
complex reveal indirect 
forbidden transitions 
9*1 
— 7-
/> - Carotene Iodine 
(a) Indirect Allowed 
Transition 
16H 
c 
9 
-J 
1 4' 
1 3" 
m r 1 1 1 1 1 r 
21 22 23 24 25 26 27 28 
hv (ev) 
/I - Carotene Iodine 
(b) Free carrier absorption 
Slope - 1 7 
Scattering by 
acoustic phonons 
24 
l 
2 45 25 2 55 
Log / in nm) 
Figure 10 (a) Nature of transition in // carotene-iodine and (b) 
free-carrier absorption in /? -carotene- iodine 
3 0 - i
 (a) 
/i -CAROTENE 
28-
-c: 
26" 
j
 r T , m-y , T r 
0 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 
ho (ev) 
5. Conclusions 
Iodine dissociates 300 nm 
exciton of /?-carotene 
molecule by Gaussian forces 
Iodine creates Gaussian 
absorption above the gap 
region of p -carotene Iodine 
reduces the gaps among the 
spin orbit split valence band 
and lowers the frequencies of 
mterband transitions There is 
3"1 
~ r 
(b) 
/I -CARO-l2 
n 1 1 1 r 
01 02 03 04 05 
hu (ev) 
Figure 11. Infrared absorption edges of (a) ji -carotene and 
(b) /?-carotene- iodine which both shows an indirect transition 
which is forbidden 
1522 A T Oza, G K Solanki, AnandAmin and Parimal Trivedi 
a borrowing of oscillator strength from 750 nm band in /?-carotene spectrum for the 
development of charge transfer band at half-energy, i.e. 1550 nm in the spectrum of iodine 
complex. Iodine changes a direct transition in [i -carotene into an indirect transition m 
p -carotene-l2 complex. The infrared gap is also reduced gap by iodine, although by a 
small amount of the order of phonon energy. 
References 
[1] A L Lehninger Principles of Biochemistry (Delhi, India CBS Publishers & Distributors) (1984) 
[2] F Gutman and L E Lyons Organic Semiconductors (New York • John Willey and Sons) (p 758 
778) (1967) 
[3] D D Eley In Organic Semiconducting Polymers (Ed) J E Katon (Marcel Dekker Co.) (1968) 
[4] J I Pankove Optical Processes in Semiconductors (Englewood Chiffs, New Jersey Prentice Hal! 
Inc) (1971) 
[5] P S Kireev Semiconductor Physics (Moscow • Mir Publishers) p. 515 (1975) 
[6] Y Fan, W G Spitzer and R J Collins Phys Rev. 101 566 (1956) 


UV-Visible-Near IR and Infrared Spectroscopy of β-Carotene and β-Carotene-Iodine Complex

Shekar, N V Chandra

Sahu, P Ch

Strong Solids

Forthcoming Publications

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