|
1. Well - this edition completes our first year of operation and Volume I. Perkin Elmer have agreed to continue their sponsorship, so we are set fair for 1998, Volume II and beyond! All we need is more contributions from you, the readers. My view is that IJVS must be aimed at the youngsters - students, young researchers, and industrial analysts. The young tend to be more interested in computers than do their parents so, quite obviously, the Journal's readership must be relatively youthful. A few weeks ago I had the pleasure of attending the UK Perkin Elmer Users Meeting at Daresbury, not far from Manchester in northern England. There were many interesting and valuable papers and an instrument exhibition, but by far the most intriguing session was a crystal ball gazing discussion on the future of mid-ir/Raman. The discussion got under way with a description of the method, unique within the scientific instrument business, in which near infrared equipment is supplied. The amount of fundamental research interest in this field is incredibly small, near infrared as a technique is usually not mentioned in academic courses and hence experts are in short supply. On the other hand, n.i.r. is really valuable in a rapidly expanding range of applications in industrial analysis, e.g. analysis of grain, milk, flour and more recently pharmaceutical products. To cope with the interest and lack of spectroscopic expertise in customers' laboratories, the manufacturers of n.i.r. equipment (and until recently they were not the traditional FTIR makers) have designed packages and sold them. Thus, if you are running a dairy and you want an instrumented analysis based on n.i.r., you buy a system comprising of a spectrometer, sampling system optimised for your particular dairy, computer, software/data analysis and data logging system designed to satisfy your national regulators. The system requires no skill - once installed it needs about as much intellectual input as operating a checkout at a supermarket, i.e. the spectroscopic analysis has been completely "downskilled". The packages are expensive but very cost effective to the user. They are expensive to build, but if enough closely related systems can be sold they become very profitable to the instrument builder. 2. Mid infrared equipment, NMR instruments, mass spectrometers, Raman instruments - all are sold to specialist users who, at least to some extent, know what they want, can interpret the results, and with the aid of the accessory makers can devise analytical procedures as they are needed. Infrared is particularly versatile and with skill and experience can be applied to a vast range of industrial problems. In all these spectroscopic areas, the manufacturer produces as versatile an instrument as he can and expects the user to utilise the equipment for a range of problems. [These comments do not apply, of course, to infrared based continuous or process monitoring systems]. The question is "The n.i.r. people have been so successful - should mid i.r. go the same way? Should mid i.r. packages be offered?" My view is a definite "yes" and I put this to the meeting. 3. It is clear that the accessory makers are producing ever more versatile kit and that by using appropriate methods, sampling is becoming easier and easier. Why prepare a KBr disc if diamond ATR will give the results? It is also clear that instrument makers are working with the accessory experts to produce equipment where the results are reproducible, i.e. are such that they can be properly standardised and used within Q.C. protocols. An essential part of this procedure is that the human element has to be minimised and critical operations made automatic or trivially easy. So, it seems to me, the industry is well on the way. The remaining problem is money! The number of analyses based on mid i.r. is vast, so the market for one clearly defined analytical procedure is small. On top of this, the market is split amongst six or more major manufacturers and many many more smaller ones, so the cost of developing the protocols is high and the chances of making a profit small. On the other hand, the market is likely to be driven towards packages, as manufacturers attempt to reduce labour costs by automating and downskilling. If the mid i.r. people do not respond, increasingly their market will drift away to n.i.r. This would be very retrograde because, valuable technique though it is, n.i.r. can never overcome the problem of its fundamentally low extinction coefficients and the equally soundly theoretical fact that it is based almost exclusively on hydrogenic vibrations and will always be. The low extinction coefficients can be an advantage but in a huge range of applications users should adopt a more appropriate method, like mid-i.r. or Raman. If users (and purchasers) are not expert spectroscopists, how are they to judge - they will start to believe the salesman! 4. Early in December, I had a semi-formal meeting with the people from Perkin Elmer based at Beaconsfield, near London, England. Apart from agreeing to continue their generous funding, several other topical matters were talked over. Thus, it was decided not to accept advertisements, at least for the time being, but we are prepared to test products, whether they be new instrument accessories, software libraries, or ancillary products. So, if you manufacturers would like some free publicity - give us a call! In each case we will ask an expert to give the product a thorough test and report his findings - just like the road test of an automobile. Susan Keese, the Company's representative, told me something of the readership based on those of you who have sent in addresses. It can hardly be a surprise that Americans are prominent amongst the readership, but it is also clear that folks in Eastern Europe, India and Pakistan, China and the SE Asia areas find us of value. In many cases, I presume the fact that libraries are often poorly supplied with up-to-date material and many are very distant, coupled with the further fact that no cost is involved, making IJVS very attractive. If this is so - please tell us what more we can do for you.
5. Even the very best things come to an end! Mrs. Wendy Hudson, our Editorial Assistant, who has been so valuable in getting the Journal off the ground, has decided to abandon her VDU and retire. All of us owe Wendy our gratitude. May we wish you, Wendy, a long and fruitful retirement. It will be bliss, I am sure, to be free of my dreadful writing and to be spared the stress of "encouraging" authors to come up with that copy they have promised. Fortunately, we have a new person to take over - Louise Martin - who has experience in the advertising industry and has worked here at the University for the past few months. Louise takes up her pen and computer immediately! If you give us a call over the next few weeks, you may well speak to Wendy - don't worry, she has not been pre-recorded and NO, you won't be talking to her ghost, Wendy has agreed to stay on for a few weeks to help Louise ease herself into place. (After all, someone has to show her how to decipher my scrawl!). P.J.HENDRA 6.What Is Raman Spectroscopy? Patrick Hendra Every year I give several lectures on FT-Raman and its applications in chemistry, pharmaceuticals and materials, and invariably find I have to start by "reminding" my audience what the Raman effect is and how it differs from infrared. It occurred to me that some readers might find this bit of my talk useful, so here goes. This account is quick and nasty and is NOT intended for the expert! 7. If you take a compound and run its infrared, then its Raman spectrum, you notice that the results are very different. This seems a little odd since both are measuring the same thing - the vibrational behaviour of the sample. Some vibrations give rise to a change in dipole as they contort and this means that they can resonate with electromagnetic radiation of the same frequency. The vibrational frequencies of most molecules are similar to those of radiation in the mid-infrared. Absorption thereof transfers energy into the molecule causing it to vibrate more violently (the amplitude increases) and so we see our familiar infrared spectrum. Other vibrations give rise to a change in polarizability as the molecule vibrates and it is these that give rise to Raman scatter. What on earth is the polarizability, you ask! Now molecules consist of a nuclear structure surrounded by a complex field or cloud of electrons. Application of a potential field causes the electrons (not the nuclei) to ebb and flow so that they are slightly concentrated towards the + and away from the - of the applied field. The ease with which they respond to a given field is described as the polarizability. If the polarizability changes as the molecule vibrates - Raman bands! 8. So - what is the Raman experiment? If you inject
monochromatic radiation at frequency vo or
wavelength 9. Let us say our molecule vibrates at 500cm-1,
i.e. vvib=500cm-1
and further the vibration causes a change in polarizability as it proceeds. We plan to use
a green laser as a source operating at 500nm wavelength
10. So, we have two methods of looking at molecular vibrations and since they originate in different phenomena, there really is no reason why the spectra should look similar. In fact, in centrosymmetric molecules modes give rise to either infrared OR Raman features but not both. Also strong infrared absorptions appear usually as weak Raman ones and vice-versa. In Fig.2 you will see a good demonstration - the infrared and Raman spectra of styrene butadiene rubber.
11. Now - presentation. The infrared spectra are shown as
absorbance vs frequency in wavenumbers but the Raman presentation is very different. The
vertical axis reflects the intensity of Raman scatter and the horizontal axis - the
frequency SHIFT in wavenumbers. Why shift? When you record a Raman spectrum, you can use
any source you like from the UV to the near infrared (certainly 200nm wavelength 12. Let's go back a step and look again at the origin of Raman scatter. When a photon of source radiation hits a vibrating molecule it polarizes it instantaneously, raising its energy by vo. The effect of the interaction is endothermic BUT the excited state is not real - there are no energy levels at the excited condition. As a result we describe these states as 'virtual'. Leaving out all the jargon - the source photon interacts with the molecule, raising its energy, and the energy is immediately lost again by scattering. The idea is shown in Fig.3.
13. There are two points to note - by far the most
important mechanism produces scatter at
As a result, the
14. One of the principal methods of interpreting infrared spectra is to use the concept of group frequencies. Thus, vc=o appears around 1700cm-1, vCH aliphatic near 2930 and vOH at 3200-3500cm-1. These correlations occur because compounds containing these fragments reliably produce strong infrared features we can all identify. We have already agreed that strong infrared features are characteristically weak in the Raman effect, so it stands to reason that the infrared group frequencies cannot apply in the Raman and vice versa. To demonstrate this point - consider the C=C stretching motion: this is not a useful reliable infrared correlation - if the unsaturated group lies near the centre of a molecule, you do not see an absorption at all! On the other hand, vC=C is a really strong Raman feature near 1670cm-1. The frequency enables you to identify cis from trans from vinyl groups. 15. To pick up some of these points, below I show an infrared and a Raman spectrum together and identify some of the group frequencies.
16. So, to conclude this introduction - if you want to get the whole vibrational picture, you should run both the i.r. and the Raman and not rely on one spectrum on its own. When you listen to a tape on your Walkman, you expect to hear the sound in stereo. The music is the same in both ears of course. IR+R = Stereo vibrational spectroscopy! REF: Int.J. Vib. Spect., [www.ijvs.com] 1,
5, 6-16 (1998) 17. Reflection Spectra Dr Richard Spragg Most materials absorb infrared radiation very strongly. As a result samples have to be prepared as thin films or diluted in non-absorbing matrices in order to measure their spectra in transmission. There is no such limitation on measuring spectra by reflection, so that this might look like a more versatile way to obtain spectroscopic information. However reflection spectra often look quite different from transmission spectra of the same material. Here we shall look at the nature of reflection spectra and see when they are likely to provide useful information. 18. The nature of reflection spectra
Reflection takes place at surfaces. When radiation strikes a surface it may be reflected, transmitted or absorbed. The relative amounts of reflection and transmission are determined by the refractive indices of the two media and the angle of incidence. In the common case of radiation in air striking the surface of a medium with refractive index n at normal incidence the reflection is given by (n-1)2/(n+1)2. So for a material with a refractive index of 1.5 the reflection at the surface is 4%. At other angles of incidence the reflection depends on the polarisation of the radiation. 19. The situation becomes more complicated, but also more interesting, when the second medium is absorbing. The refractive index is closely related to the absorption. Because the amount of reflection is determined by the refractive index the reflection changes wherever there is an absorption band. For an isolated absorption band the refractive index has a minimum on the high wavenumber side of the band and a maximum on the low wavenumber side. The reflection spectrum therefore resembles a first derivative, with a minimum to high wavenumber and a maximum to low wavenumber of the band centre. This can be seen in the spectra obtained by reflection from the surface of a block of polymethyl methacrylate and by transmission through a film of the same material in Fig.2.
20. The absorption spectrum can be calculated from the measured reflection spectrum by a mathematical operation called the Kramers-Kronig transformation. This is provided in most data manipulation packages used with FTIR spectrometers. Below is a comparison between the absorption spectrum of polymethylmethacrylate obtained by Kramers-Kronig transformation of the reflection spectrum and the spectrum of a thin film.
21. The previous examples consist of reflection from the front surface of a sample, sometimes called surface or Fresnel reflection. In many situations, for example reflection from a powder, the reflection spectra do not come from the front surface alone. Radiation that penetrates into the material can reappear after scattering or reflection at a second surface. When this radiation emerges it will have experienced some absorption, depending on the path traversed. Its contribution to the spectrum will have the general character of a transmission spectrum. Spectra of this type are called diffuse reflection spectra.
22. The appearance of the spectra depends on the relative amounts of surface reflection and of radiation that has penetrated the sample. The main factors that influence this are the particle size and the strength of the absorptions. As the particle size increases the amount of radiation reappearing from within the sample is reduced because more is absorbed before it can be scattered or reflected back to the surface. This can be seen in the spectra of glycine below. It is clear that the derivative-like features of surface reflection are more prominent in the spectrum of the coarse powder. The spectrum of the finely ground material does show more features resembling absorption bands, but still is very different from a transmission spectrum.
23. The Kramers-Kronig transform is useful only for pure surface reflection. Spectra with a mixed character such as those above are rather intractable because the shapes and positions of the absorption bands cannot be identified. For qualitative identification it is necessary to maximise the contribution from radiation that has penetrated the sample. This can be done in the mid IR by reducing the particle size, ideally to less than 10mm, and diluting the sample in a non-absorbing matrix such as KBr. The effect of this is to reduce the amount of radiation that is absorbed internally before it can return to the surface. The resultant spectrum resembles a transmission spectrum except that there is a range of different pathlengths within the sample. In consequence the intensities of weaker bands appear enhanced relative to those of stronger bands. This distortion of the band intensities is minimised by ensuring that all the absorptions are weak. 24. Figure 6 shows diffuse reflection spectra of aspirin as a neat powder and diluted in KBr. The sample in KBr is very similar to the spectrum of a KBr disk. In the spectrum of the neat powder the stronger bands all have approximately the same intensities and their shapes are distorted by the contribution of surface reflection. However the weaker bands appear similar in both spectra.
25. Diffuse reflection spectra are often presented in what
is called the Kubelka-Munk format rather than in absorbance, or more correctly log(1/R).
The Kubelka-Munk intensity K-M is related to the measured reflectance R by an equation of
the form: K-M = (1-R)2/2R.
Reflection from a single surface is called specular reflection, as if from a mirror. Accessories for measuring specular reflection can be very simple, for example just involving two flat mirrors (Fig. 8). This type of accesssory would be suitable for measuring the reflection from a polished surface, such as the block of polymer used for the spectrum of Figure 1. For many samples the reflection spectrum is complicated by additional reflections from the back surface or by scattering within the sample. This kind of measurement is very successful for carbon-filled polymers with a suitably flat surface. The reason is that any light not reflected from the front surface is totally absorbed and so does not contribute to the spectrum.
27. This type of accessory can also be used to measure what is called a transmission-reflection (or transflectance) spectrum from thin coatings on metal surfaces. In this case the spectrum consists largely of radiation that passes through the coating and is reflected back from the metal surface. It resembles the spectrum that would be obtained from transmission through a film of the coating material. The spectrum will contain a contribution that is directly reflected from the front surface of the coating, but reflection from the metal surface is much higher. A typical spectrum from the coated inner surface of a soft drink can is seen in Fig.10. Coatings on non-metals are generally more difficult to examine. The spectra are not always dominated by the transmission-reflection component and absorption features of the substrate complicate the spectrum.
28. Transmission-reflection spectra are most useful for protective coatings and contaminants on metal surfaces. These are typically thicker than the wavelength of the infrared radiation being used. It is worth mentioning the rather different case of very thin layers on metal surfaces. Spectra of monomolecular layers can be measured fairly easily but special measurement conditions are used. These involve grazing incidence where the light path is almost parallel to the metal surface, because this greatly enhances the absorption intensity. The enhancement is caused by interaction between the electric field of the radiation and the conducting metal and extends only for a very short distance from the surface. Special grazing angle accessories are available for these measurements. 29.Diffuse Reflection The radiation contributing to a diffuse reflection spectrum is typically spread over a range of angles and so cannot be collected efficiently with accessories designed to measure specular reflection. A typical arrangement for diffuse reflection measurements is shown below.
30.Diffuse reflection spectra in the mid-IR are generally used for qualitative identification of powders. Because sample preparation need involve no more than mixing with KBr the method is simpler and more rapid than making a KBr disk. In principle diffuse reflection spectra can be used for quantitative analysis but this has proved much more successful with near IR data than in the mid-IR. Diffuse reflection can be a very convenient way of obtaining spectra from the surface of hard objects such as polymer mouldings. The method used is to rub the surface with abrasive paper so that a small amount is removed as a powder. The spectrum can be obtained simply by placing the abrasive paper in a diffuse reflection accessory. Figure 12 shows some typical spectra obtained from soft drink bottles obtained in this way.
REF: Int.J. Vib. Spect., [www.ijvs.com] 1,
5, 17-30 (1998) Editor' Note Some aspects of this whole subject were covered in IJVS Volume 1,Edition 4, paragraphs 14-25 and 26-37. 31. Background To The Use Of Specular Reflection And Reflection/Absorption Methods Dr W.Maddams Specular Reflection 32. The change in refractive index with wavelength for a given material, which is known as its dispersion, is responsible for several well known effects in the visible spectral region. The most striking of these is the rainbow. In the case of most compounds, including water, the refractive index increases in passing from the red to the blue end of the visible spectrum so that sunlight, in passing through raindrops, has its constituent wavelengths spread out, giving a bar with its inner edge violet and the outer edge red. The separation of sunlight into its constituent wavelengths by a glass prism was first reported by Sir Isaac Newton. Here also, the deviation of the violet end of the visible spectrum is greater than that of the red end because the refractive index of glass increases with decreasing wavelength. In the infrared spectral region, simple optical materials such as sodium chloride and potassium bromide, which are transparent over much of the spectral range useful for structural diagnostic work, behave in the opposite manner. Their refractive indices increase with increasing wavelength, and the rate of increase also increases with increasing wavelength. It is for this reason that the infrared spectrometers of some forty or fifty years ago, which used sodium chloride prisms, had rather poor resolving powers at 3000cm-1 but were very adequate in the vicinity of 700cm-1. What, then, is the reason for the change in refractive index with wavelength and why does it occur in opposite directions with respect to wavelength in the visible and infrared spectral regions? The answer, in its simplest form, is provided by the behaviour of the materials commonly used to make dispersing prisms for the two wavelength ranges. In the case of glass it becomes increasingly opaque, as the result of absorption, in moving from visible wavelengths to those in the near ultraviolet region. The same is true of quartz, which is transparent to somewhat shorter wavelengths. In the infrared region, sodium chloride becomes increasingly opaque as 15µ (650cm-1) is approached and the relevant value for potassium bromide is about 25µ (400cm-1). Clearly, the refractive index change is to be associated with the onset of absorption. 33. In the ultraviolet/visible region the absorption
results from changes in the electronic energy levels. These changes occur at lower
energies, and hence give absorption at longer wavelengths, for compounds where some
electrons are more loosely bound, e.g. the In the infrared spectral region, molecular vibrations are responsible for the absorption of energy. With sodium chloride and potassium bromide the absorption only occurs at relatively long wavelengths so their refractive indices and dispersions increase unidirectionally over the range commonly used for analytical purposes. However, organic compounds in general have an appreciable number of vibrational modes, and hence absorption bands, over the mid-infrared spectral range. There will therefore be refractive index changes in the vicinity of each of these bands, as noted by Dr. Spragg. Consequently, the reflection coefficient will change in a rather complex way as a function of wavelength, but one which will contain information on these absorption bands. 34. In order to formulate this process mathematically, it is necessary to modify the simple concept of refractive index and work in terms of what is known as the complex refractive index ñ, defined as ñ=n+ik. Here, i is the square root of -1 and k is an absorption coefficient which is related in a simple mathematical way to the familiar molar absorption coefficient. Hence, at normal incidence, the fractional reflection becomes (ñ-1)/(ñ+1)2 and its variation with wavelength contains information about the variation of k with wavelength. 35. However, the interpretation of a reflection spectrum is not particularly straight- forward mathematically. Kronig, in 1926, and Kramers in 1929, developed the required theory in terms of what are known as integral equations. These equations also include the effect of varying the angle of incidence, for a given value of ñ. The coefficient of reflection is a function of this angle and increases rapidly to a value of unity as the angle approaches 90°, the condition known as grazing incidence. The Kramers and Kronig equations were not put to practical use for about half a century, for two reasons. Until the development of FTIR spectrometers reflection spectra of adequate intensity and signal to noise ratio were difficult to obtain. Secondly, the calculation of the required spectrum from the experimental reflection measurements was impossibly time consuming, until the advent of modern fast and compact computer systems. Serendipitously, the computer unit required for the Fourier transform operation is equally adept at coping with the reflection calculations via what is universally known as the Kramers-Kronig transformation. Efficient algorithms for this transformation are now available and they form part of the software package of present day FTIR spectrometers. Spectra of the type shown in Fig.2 of Dr. Spragg's article may now be obtained routinely (see Paragraph 19). 36.Reflection-Absorption Spectroscopy 37. However, if the sample is in the form of a comparatively thin layer on a reflecting substrate, as is the case with coatings on metal cans, some of the radiation which has entered the sample will suffer loss by absorption, then after reflection at the substrate will return towards the surface, losing more intensity in the process and exit the sample with the radiation reflected at the surface. The outcome will be a spectrum in which the observed peaks derive part of their intensity from the specular reflection process and part from conventional absorption. The optimisation of the intensity of such spectra, for a given sample thickness, involves the angle of incidence both directly and indirectly, the latter because at near-normal incidences standing waves occur at the surface. Standing waves, or stationary waves as they are sometimes called, may occur with any type of longitudinal wave motion but are most easily demonstrated in terms of transverse waves sent down a taut horizontal cord, fixed at one end and hand held at the other, as shown in Fig.1a. Upward and downward movement of the hand generates a longitudinal wave, which is reflected back when it meets the fixed end. If the hand is moved at random there is confused movement of the cord, in which progressive waves in both directions occur for short intervals on a random basis. However, if the movement of the hand is suitably timed the cord appears to vibrate transversely as a whole, with no sign of a progressive wave. This is what is termed a standing wave. Figs. 1b, 1c and 1d show three such standing waves, whose wavelengths are in the ratio 3:1.5:1. It follows that the frequencies of these waves must be in the inverse ratio 1:2:3. When a standing wave has been established there is no sign of a progressive wave in either direction and individual points on the cord are executing simple harmonic motions at right angles to the cord. The amplitude of this simple harmonic motion is greatest at equally spaced points which are called antinodes and zero at an equally spaced set of points which are called nodes. The two ends are always nodes and the length of the cord is a whole number of half wavelengths. 38. When infrared radiation is incident normally on a surface the theory of electromagnetism predicts that there will be a node at the surface and this was verified experimentally by Wiener as long ago as 1890. Hence, the electromagnetic wave will have zero amplitude at the surface, so that the absorption will be very small. It may also be shown that for non-normal incidence there is no longer a node on the surface and absorption will occur. It is therefore necessary to use non-normal incidence for this type of measurement. If the film is very thin, near-grazing incidence will give maximum penetration of the sample, and surface reflection is then also at a maximum. The thin films examined at grazing incidence fall into two categories: they may be of the type where the metal substrate simply acts as a support. Alternatively, there may be adsorption on to the surface, so that interaction forces between the sample and the substrate come into play. In this latter case, an additional factor influences the spectrum. The molecular vibrations of the adsorbed molecules which occur in directions such that the resulting dipole moment changes lie parallel to the surface give no absorption, whereas dipole moment changes perpendicular to the surface give absorption peaks of maximum intensity. For this reason measurements with polarised radiation may prove advantageous. However, this is a specialist area of activity and it does not warrant detailed discussion in this general and introductory account. REF: Int.J. Vib. Spect., [www.ijvs.com] 1,
5, 31-38 (1998) 39. Thermodynamics Exam
Author Unknown A thermodynamics professor had written a take-home exam for his graduate students. It
had one question: Is hell exothermic or endothermic? Support your answer with
proof. First, we postulate that if souls exist, then they must have some mass. If they do, then a mole of souls can also have a mass. So, at what rate are souls moving into hell and at what rate are souls leaving? I think that we can safely assume that once a soul gets to hell, it will not leave. Therefore, no souls are leaving. As for souls entering hell, let's look at the different religions that exist in the world today. Some of these religions state that if you are not a member of their religion, you will go to hell. Since there are more than one of these religions and people do not belong to more than one religion, we can project that all people and all souls go to hell. With birth and death rates as they are, we can expect the number of souls in hell to increase exponentially. Now, we look at the rate of change in volume in hell. Boyle's Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of souls and volume needs to stay constant. So which is it? If we accept the postulate given me by Therese Banyan during Freshman year, and take into account the fact that I still have not succeeded in having sexual relations with her, then No.2 cannot be true, and hell is exothermic. THE STUDENT GOT THE ONLY A.
Dr. Howard Schaffer In fact, the issue of the evidence of Ms. Banyan may indicate that there is not even a well-defined temperature in hell. In this case, it could be true both that all hell has broken loose ("hotter than hell") and that hell has frozen over. Hence the phrase "come hell or high water", indicating that hell may involve either ice or water vapour, but not liquid water. Which all goes to verify the opening of David Goodstein's text, which we paraphrase here for the illiterate among us: "Ludwig Boltzmann, a founder of the science of statistical mechanics, died by his own hand in 1906. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it would be wise to approach the subject cautiously." It should be clear, at least to those among us who subscribe to religions which canonically condemn self-inflicted mortality, just where it is that Ludwig and Paul are calculating their partition functions these days. In fact, as has been previously reported (and how could this be known other than by a momentary fluctuation of a soul out of hell to provide a report?), there is a particular department of hell reserved for students of probability and statistics. Each morning, all residents of said department file into an auditorium, where they spend the entire day watching a hundred blindfolded monkeys peck away, totally at random, at a hundred computer keyboards. At the end of the day, one hundred members of the audience chosen, of course, at random, relieve one monkey each from their random pecking and print out the resulting file. The printing inmate finds, to his severe disappointment, that each monkey has, in that day of totally random pecking, produced an absolutely error-free reproduction of one of Shakespeare's plays or sonnets (first folio edition). This should give pause to those who use the expression "A snowball's chance in hell" to describe an event that cannot reasonably be expected to occur. Or, to summarize, in the words of the ballad of 5.60 - "Glory, glory,
dear old thermo, we'll pass you by and by".
|
![[lambda]](../../resources/lambda.gif){kind=small}
o into a sample and look at the
light scattered off it - surprise, surprise, it seems to be at the same wavelength as the
source. Careful inspection however reveals that in addition to this so-called elastic
scatter, a tiny proportion is shifted and it is this shifted radiation that is named after
Sir C.V.Raman, the Indian scientist who discovered it in 1928. ![[equivalent to]](../../resources/triple_bond.gif){kind=small}
20,000cm-1. Then the scattered light will
be composed of a component at 20,000cm-1 plus two
incredibly weak side-bands at 19,500 and another at 20,500cm-1,
i.e. at vo ± vvib.
We see the experiment below in 
1.3µ). As a
result 
o
can vary over a huge range. We are interested in the vibrational frequency, so we use as a
scale the Raman frequency vs the laser frequency i.e. vo
± vvib - vo
= ± vvib. Presented this way, the infrared and
Raman data can be presented on one diagram. 
v.
-electrons in aromatic compounds. Hence, in the visible
spectral region, particularly at the blue end, the refractive index of benzene increases
more rapidly with decreasing wavelength than that of n-hexane, and its dispersion is
correspondingly greater. 