I Guess, A part of the absorbed radiation  will be emitted back by self quencing (collision), so we will get eranius result on higher concentration.  At lower concentration the amount of radiation absorbed will be undetectable.

Go through this page which explains the deviations and limitations of Beer Lamber Law.

http://pharmaxchange.info/press/2012/05/ultraviolet-visible-uv-vis-spectroscopy-%E2%80%93-limitations-and-deviations-of-beer-lambert-law/

What kind of deviation do you observe at low concentrations? And how low are "low concentrations" for you? Do you actually mean a solution of a metal salt or a dispersion of metallic nanoparticles.

Lambert Beer law at high concentrations cannot give good correlations because when the absorbance is higher than 1, it is absorbed all light. Under these conditions the absornabance is not coorrect (see definition of absorbance).

At low concentrations, lower than 0.04 the measured has to much error, this leads to important precision of the absorbance measurement.

Lambert Beer law at high concentrations cannot give good correlations because when the absorbance is higher than 1, it is absorbed all light. Under these conditions the absornabance is not coorrect (see definition of absorbance).

At low concentrations, lower than 0.04 the measured has to much error, this leads to important precision of the absorbance measurement.

Limitations / Deviations* :

It is capable of describing absorption behavior of solutions containing relatively low amounts of solutes dissolved in it (10mM), the analyte begins to behave differently :

[i]Due to interactions with the solvent and other solute molecules.

[ii]Solute molecules can cause different charge distribution on their neighboring species.

[iii]Since UV-visible absorption is an electronic phenomenon, high concentrations would possibly result in a shift in the absorption wavelength of the analyte.

[iv] At times, even electrolyte concentrations (such as those present in buffers) play an important role in altering the charge distributions and affecting UV-visible absorbance.

[v] Some large ions or molecules show deviations even at very low concentrations. For example. methylene blue absorptivity at 436 nm fails to observe Beer Lambert law even at concentrations as low as 10μM.

[vi]High analyte concentrations MAY alter the refractive index (η) of the solution which in turn could affect the absorbance obtained. If addition of solute causes a significant change in the refractive index of the solution, then correct form of Beer Lambert is as:

A=εbc(ɳ^2+2)^2

This correction is normally not required below10mM concentrations .

* Given time/ space, one may add one/ two more deviation to this list.

Usually, when you reach the limits of Beers law, you encounter problems with your instrument sensitiity. Your measures values are I and I_0.

At very low concentrations, the difference of these values gets so small, that their ratio approaches 1, which means the observed transmittance approaches 1.

For very high concentrations, the ratio I / I_0 approaches 0, so hardly any light is transmitted.

The ratio of two very much identical large numbers (too low concentrations) or of a large and a very small number (low concentrations) is very much affected by noise and detection sensitivity.

Additionally, there are problems of self-quenching, inner filter effect, at high concentrations that introduce deviations. The reply by Manohar Sehgal gives a good overview of the limitations.

As pointed out at low concentration the problem is accuracy and taking into consideration the real reference sample, i.e. subtracting the extinction related to the cell and continuous phase.

At high extinction values, e.g. 2 and higher there is a very remarkable problem. Lambert Beer law holds for a single wavelength only. Scattering will cause an overlay with light of other wavelength leading to a drastic distortion of the spectra. There was a very detailed  work of W. A. P. LUCK in relation to these phenomena more than 50 years ago.

In continuation of my above given answer, as promised, I, humbly, mention two more deviations as follows :

[I]Depending upon concentration, the analyte molecules may undergo association, dissociation and interaction with the solvent to produce a product with different absorption characteristics. For example, phenol red undergoes a resonance transformation when moving from the acidic form (yellow) to the basic form (red). Due to this resonance, the electron distribution of the bonds of molecule changes with the pH of the solvent in which it is dissolved.

Since UV-visible is electron-related phenomenon, the absorption spectrum of the sample changes with the change in pH of the solvent.

[II] Lastly, some molecule of the same substance, undergong association and the other dissociation will have two molar absorptivities ε/ and ε// at wave lengths λ/ and λ//. The absorbance (A) for such a species can be calculated as:

A=log(1/+I//)/ (I/ .10^- ε/ bc +I//.10^- ε// bc )

When the molar absorptivities are the same at both wavelengths ( ε/ = ε//) , the relationship between absorbance and concentration follows Beer-Lambert law to obtain a straight line. However, as the difference between ε/ and in ε// in creases, the deviations from linearity also increases.

it is impossible to give good answer if you do not know the chemical nature of analytical system because besides physical reasons there are many chemical ones exist.

Lambert-Beer will always be obeyed.

If  you see deviations in your experiments:

-it is related to your experimental accuracy or error (don't know the setup, but reflection losses at the air/cuvette/sample interfaces)

-your assumptions are not adequate like only the solute absorbing (absorption of the solvent may become important at low concentrations)

-or you solute undergoes some changes (e.g. aggregation,...) which will affect the extinction coefficient

Addition: an absorbance of 1 does not mean that all light is absorbed, but 90% is absorbed

Look at page 59 of Principles of Fluorescence Spectroscopy, 3rd Ed. by JR Lakowicz (Springer 2006)

In UV-Visible spectroscopy, absorption is due to presence of chromophore and auxochromes. Each color has its lowest and highest limitations of wavelength absorption range. say pink color Faint to dark out highest dark color intensity is obtained no further change is possible and it vice vars a for lower concentration.

hence with in specific concentration range only Beer Lambert's law is obayed.

The problem is a non-linearity in aborbance D which is in fact quadratic or even cubic equation. A part is described in our paper (Barankova et al. 2016, RSE) which can be donwloaded from my RG page

See Chem Educator, 2015, 20, 206-213

absorption does not obey Lambert-Beer law whenever absorption cross-sections of individual molecules are in alignment, i.e. when the solution is of high concentration

Dusan

That publication is not for solutions but remote sensing

Petr

what is the meaning of

"absorption cross-sections of individual molecules are in alignment?" and where is your reference

There is a technical problem for accurate measurement of low (

I think this link is very useful, 

http://www.instanano.com/characterization/theoretical/concentration-calculation-from-uv-vis-absorbance/

The solution is obeyed by this law at two conditions: 1.  the light is monochromatic; this condition maintaines by using monochromatic wavelength in spectrophotometer.

2. the concentration of absorbing species in solution should not change spontaneously. This condition very often not obeys. See reasons below.

Low concentration of absorbing species (metal+ligand): in this case it can be dissociation of unstable complex, hydrolysis (solvolysis) of components, or side reactions with buffer components or other additives (contaminants) as well as change the pH of solution or tautomerism. All this factors change the concentration (speciation) of absorbing species.

At high concentration the reasons for the deviations may be a formatiom of complex with another composition or dimerization (aggregation) of reagent (ligand) or complex, high ionic strength can also influence on the activity of species or their electronic state, or will have dehydration and medium polarity effects.

To avoid these confusing factors you should know the composition of your solution and foresee possible interaction inside of them.

Even if Beer's Law were perfectly obeyed which it never is   if only because of chromophore "shadowing" it would not be apparent because of imposed instrumental artifacts. Sorry . . .

For high concentrations, or long optical paths, more than 1 absorption emission event can occur resulting in a broadening in the absorption peak and a shift away from Beer's Law.  This occurs for a photon in the atmosphere, and also occurs in chloroplast in plants where this behavior is used to improve the efficiency of photosynthesis through the capture of more wavelengths of light. 

If one chromophore give you a certain absorbance value which doubles when you add a second chromophore, what happens to the absorbance level when the second chromophore passes behind the first?????

@Harry Harlow

can you give an example for the atmosphere: the optical density of most substances is low

We have published a paper by Naus et al. (Photosynthesis Research, 2018, in press) on this topic. The paper can be dowloaded on the PR site.

This thread is somewhat symptomatic for spectroscopy, where optical, physical and chemical reasons why and when Beer-Lambert fails are nearly inextricable intermixed and intertwined, as are Maxwell-confom and non-conform concepts.

Let's make things very simple first and investigate the optical properties of a diluted solution (perfect homogeneously mixed) with a transparent solvent. From an optical, i.e. Maxwell-conform view of the problem, the Beer-Lambert law describes propagation inside (and not transmission through) a medium, i.e. inside the solution. Once there are interfaces and there are, since liquids need cuvettes to be measured, the Beer-Lambert law is no longer obeyed and the optical model becomes much more complicated. Nevertheless, if a reference measurement is taken with a cuvette full of solvent, it can be shown that, more ore less by accident, the Beer-Lambert law works to a good approximation (Article Employing Theories Far beyond Their Limits-The Case of the (...

Article The Electric Field Standing Wave Effect in Infrared Transmis...

The more the actual optical model deviates from a simple propagation of the light wave in a homogeneous medium, the larger are the deviations from the Beer-Lambert law in general. In particular, assuming a medium where scattering occurs, the breakdown of linearity can be expected and is not surprising. Unfortunately, this is a situation which cannot be solved and investigated analytically.

Of course, on top of this, chemical changes of the solution with increasing concentration like, e.g., association of molecules as well as instrumental limitations like sensitivity of the detector (Absorbance = 3 means that only 0.1 % of the light reaches the detector, reflection effects not included) and stray light etc can cause further deviations from the Beer-Lambert law...

P.S.: "Shadowing" is a concept that makes no sense in a homogeneous medium...

to dr Mayerhofer

Notice also that in many questions in Spectroscopy the question is completely vague like in this one

it only mentions " higher and low concentration of a particular metallic solution":

There is no way this can be answered as asked   

I admit that the nature of the question forbids an answer. Nevertheless, some answers are also revealing... probably it would make sense to start a new "discussion" about this topic. On the other hand, it is hard these days to get from researchgate questions and discussions that match one's interests... so it makes sense to stimulate those discussions in questions who have found their followers in times when the match between interest and questions was better... or do you feel you still get the right questions that match your expertise?

Ok, here is an additional reason for deviations of Beer's (empiric) law, based on the fact that the law derived from electromagnetic theory is slightly different... ;-)

Article Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration

Simple reason is state of matter. For any matter in any state the physio-chemical properties behave linearly within certain range of reference. For example foe a matter "X" the state of substance and its physio-chemical can be varied only within a certain limit which will be specific to that substance. In this case it will follow Beers-Lambert law. If we add a specific component to the matter "X" outside that limit the physio-chemical properties of the matter changes. In case the matter itself will change its form. When matter itself changes then the spectral science will also change which will be different from the primary form matter.

Basavaraj Amogi This is an oversimplification of the situation. As I wrote above, the relation between absorbance and concentration is intrinsically non-linear. This is immediately obvious for excitations with high oscillator strength. There is, however, a way to remove this problem by using integrated absorbance which is proportional to oscillator strength (and, thereby, to concentration):

Article Beer’s law – why integrated absorbance depends linearly on c...

Istrumental deviations may result in absorbances that are smaller than theoretical. Radiation exiting from a monochromator is contaminated with small amounts of scattered or stray radiation, as a result of scattering and reflections from internal surfaces. When measurements are made in the presence of stray radiation, or with polycromatic radiation (diffferent molar absorptivities), negative deviations from Beer's Law occur, specially for higher concentrations.

Dear Thomas Mayerhöfer

I am a little confused and need your help

Can we use Beer-Lambert's law for suspensions too? Consider that we have scattering phenomenon in the suspension which will affect the transmittance

Dear Masoud Sakaki ,

for suspensions I see the application of Beer-Lambert very critical. It is not only scattering, but also the size of the scatterers relative to the wavelenth and the resolution limit of light. Assume that you would investigate the particles under a microscope using the same wavelength as for your spectrometer. If you would "see" the particles under the microscope, your sample would be "micro-heterogeneous" and the additivity of intensities (transmittance / reflectance) rather than absorbances would come into play and cause band flattening (which was in former times seen as an effect of "shadowing"). There are modifications of the Beer-Lambert law around which may be able to treat scattering to some degree (empirically, certainly not analytically), but the effect of band flattening cannot be treated this way. So I would be very sceptical, in particular if the particles are larger than about 1/10 of the wavelength.

Dear Thomas Mayerhöfer

Thank you very much for your prompt reply.

Could you please also provide some information about the measuring of the absorption coefficient of the sintered samples (e.g. sintered Alumina which is not transparent. Please see the attached image)

Which part of the spectrum? Sintered aluminum oxide is very hard, but if you can polish it, for the infrared spectral range I would go for specular reflectance. If the crystallites are smaller than the resolution limit, you can obtain the averaged absorption coefficient, but if the crystallites are larger, you can only get a pseudo averaged absorption coefficient, since aluminum oxide is anisotropic, and for large crystallites the light is split into two waves in each crystallite... in the visible spectral range you will generally have this problem, since, as we can see from the picture, the crystallite are not small, otherwise they would not scatter...

would have been better, to put this as a separate discussion.

Lambert Beer law applies to suspensions also. It relates to extinction, which includes also loss due to scattering. It does, however, not include light scattered onto the detector. And of course as for dissolved matter, composition of suspension has to be the same when varying concentration. Lambert Beer law is basic for application of photocentrifuges and is found valid for a defined concentration range.

I will not deny, that the extended Beer-Lambert law including scattering might be a practically usefull approximation at times. My approach is to judge from an electromagnetic point of view (wave optics and dispersion theory), and this may be (too) harsh at times, since I am working on how to solve inverse problems, which rely on analytical solutions. Once scattering comes into play, there are no analytical solution any more. It is the same with diffuse reflection, again a technique others may consider as useful and which might be applied for the alumina tablet... determining the absorption/scattering coefficients is a problem of determining the optical constants in the end. What if the particles in the suspensions are anisotropic? How to determine the dielectric tensor function of the particles from their transmittance spectra in solution?

2 pairs of shoes, the question was, can we use Lambert-Beer law for suspensions - yes we can. Is a straight forward theoretical calculation possible, is another question.

Well... it is always possible to force a straight line through a cloud of data points... but an analytical answer (like a concentration) can also be obtained by not assuming that there must be a linear dependence... a monotonously increasing function might be all you need... ;-)

We have recently reviewed the theoretical limitations of the Beer-Lambert law and why it should better be called Ideal Absorption law: Article The Bouguer-Beer-Lambert Law: Shining Light on the Obscure

Hi,

Thank you all for the valuable information. I have another question based on the Beer-Lambert law.

I have a solution consisting of three species: the concentration of them is going up over time, and I can calculate their concentration.

I want to know how I can determine the exact optical path length to be ensured that I determine the optimum OPL? Because I have this challenge that when I plot Absorbance .vs Concentration for each species, there is non-linearity behavior in a specific range of Absorbance value. Note that I know the Beer-Lambert law is not valid in high concentration. Or maybe the species cover each other when light passes through the sample.

Thank you in advance for your responses.

Neda Jalali Farahani "Or maybe the species cover each other when light passes through the sample" This is not possible as long as we are talking about ions or molecules small compared to wavelength - light behaves as a wave in this regime and you cannot avoid "getting wet" from a wave even if someone is directly in front of you (this is also covered inArticle The Bouguer-Beer-Lambert Law: Shining Light on the Obscure

Thomas Mayerhöfer Thank you for your prompt answer.

Indeed I want to design a flow cell for my experience, and I need to ensure that for the low and high concentration of species, the OPL should be in a range which saturation does not occur, and the Beer-Lambert law also is valid. As I mentioned already, the concentration of species is going up over time. For instance, at the beginning of the production time, the concentration measurement is not accurate due to the very low concentration. (Note that the used flow cell in my case has a length of 1 cm). I do not know when I can say absorbance is saturated.

Neda Jalali Farahani Then perform measurements with a usual cuvette and higher concentrations. You are in the range of saturation when absorbance does no longer increase with increasing concentration (within experimental errors). As long the increase is noticeable you can fit a (non-linear) curve. See e.g. Article A Gausssian Accommodation of Beer's Law Deviations

Thomas Mayerhöfer Thank you for the information it will definitely help

maybe its not linear part of equation then.

We have dealt wth high-concentrated sultons of "living" system. Perhaps, it might be intersng for somebody.

Article On the source of non-linear light absorbance in photosynthetic samples

Maybe you find the following manuscript useful in this respect (belongs to a lecture series called "optics for spectroscopists"): Preprint Wave optics in Infrared Spectroscopy