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DIRECT MEASUREMENT OF THE SIZES OF ORGANIC MOLECULES BY AN OPTICAL METHOD
Some time ago Tolansky[^1] developed a method of interference measurements in visible light that makes it possible to investigate surface-relief details with an accuracy approaching \(1 \text{ Å}\). The author of the paper being reviewed[^2] has successfully applied this method to measuring the thickness of monomolecular layers formed by certain organic substances on the surface of a mica plate. The idea of the measurements is extremely simple, and the rather great difficulties that have to be overcome in carrying them out are of a purely technical nature.
As is well known, when a plane-parallel thin plate of thickness \(d\), made of a material with refractive index \(\mu\), is illuminated by monochromatic light of wavelength \(\lambda\), interference fringes of equal inclination are observed. In transmitted light the position of the intensity maxima is determined by the condition
\[ 2\mu d \cos \varphi = n\lambda, \tag{1} \]
where \(n\) is an integer and \(\varphi\) is the angle between the normal to the surface of the plate and the direction of the ray inside it. The width of the maxima is determined by the order of interference, i.e., by the coefficient of reflection of the surfaces of the plate. As the latter increases, the maxima become narrower; when the reflection coefficient exceeds 90%, then, for a sufficiently small plate thickness and known precautionary measures, the width of the maxima amounts to only about 2–3% of the distance between them. Such a small width of the maxima also makes it possible to measure the thickness of the plate with an accuracy of up to several thousandths, and even ten-thousandths, of a wavelength.
Let us suppose that a beam of parallel monochromatic rays falls on a plane-parallel plate, the wavelength and angle of incidence of which are so chosen that throughout the entire plate the intensity of the light passing through it is the same and equal to one half of the intensity corresponding to fulfillment of the maximum condition for the given wavelength. Then, owing to the great steepness of the slope of the intensity curve as a function of the plate thickness in the region of a maximum, the slightest changes in thickness will cause considerable changes in the intensity of the light passing through the plate. Thus, under ordinary experimental conditions, a change in the plate thickness by \(10\,\text{\AA}\) causes a change in intensity by 15–25%, which is readily measurable. Such a method is highly convenient for qualitative investigation of the degree of homogeneity of a plate in thickness over a large extent. At the same time, it reduces the measurement of variations of a plate in thickness to a purely photometric problem, which is usually rather laborious.
As an example of the application of this method, the author gives Fig. 1. A monomolecular layer of stearic acid, \((\mathrm{C}_{17}\mathrm{H}_{35}\mathrm{COOH})\), or another fatty acid, covering part of the surface of a thin mica (muscovite) plate, was deposited by the usual method. Then, by evaporation in vacuum, both sides of the mica plate were coated with semitransparent silver layers, the thickness of which was selected in such a way that the reflection coefficient exceeded 90%. The plate was placed in the path of a parallel monochromatic beam of light so that the intensity of the light passing through the portion of the plate free from adsorbate was one half of the maximum. Under these conditions the portion of the plate covered by the monomolecular layer of adsorbate stood out clearly in intensity. The photographing was carried out in transmitted light. Region \(P\) in Fig. 1 corresponds to the portion free from adsorbate; region \(MM\) to the portion covered by the monomolecular layer of stearic acid. The constancy of intensity throughout the whole extent of region \(MM\) is convincing evidence of the constancy of the layer thickness and, consequently, of the effectiveness of the technique for depositing monomolecular layers. The fine scratches covering part of region \(MM\) are the result of carelessness allowed in applying the layer.
For quantitative measurements of the layer thickness the authors used another method, based on the use of the so-called “fringes of equal chromatic order.” In contrast to the preceding one, the pla-
The plate was illuminated not with monochromatic light, but with white light; moreover, the image of the plate in transmitted light was projected by an optical system onto the slit of a spectrograph with high dispersion.
Fig. 1.
According to condition (1), light passes through the plate whose wavelength is determined by the condition
\[ \lambda=\frac{2\mu d}{n}\cos\varphi=\frac{Kd}{n}, \tag{2} \]
where \(K=2\mu\cos\varphi\) is constant for the given measurement conditions. As a result, a set of lines of “equal chromatic order,” corresponding to various values of \(n\), is obtained on the spectrogram. The position of these lines is entirely determined by the thickness of the plate \(d\). If, along a line of the surface of the plate projected onto the slit of the spectrograph, the thickness of the plate undergoes changes, then the lines obtained on the spectrogram will be curved, following in their form all the details of the relief of the plate. Indeed, for given \(K\) and \(n\),
\[ \Delta\lambda=\frac{K}{n}=\Delta d. \tag{3} \]
In other words, lines of equal chromatic order give an image of a section of the plate relief along the line projected onto the slit. The longitudinal magnification is then determined by the magnification of the projecting system and is close to unity. The transverse magnification, however,
Fig. 2.
determined chiefly by the dispersion of the spectrograph, proves to be of the order of 500,000 and even higher. It should be borne in mind, however, that here, as in the preceding case, what is measured is not the geometrical but the optical thickness of the plate.
The authors present a reproduction of a spectrogram (Fig. 2) obtained when a portion of the plate was projected onto the slit of the spectrograph.
along the line \(ACDB\) indicated in Fig. 1. The fringes of equal chromatic order (corresponding to \(n = 26, 27\), and 28) appear as doublets, arising as a result of the presence of double refraction in the mica. A displacement of the fringes is clearly visible in the region corresponding to the segment \(CD\), which crosses the monomolecular layer of stearic acid. This displacement is \(\Delta\lambda = 2.0 \pm 0.3\) Å, which, when converted to thickness, gives for the thickness of the adsorbed layer the value \(\Delta d = 19 \pm 3\) Å. Similar measurements for a monomolecular layer of \(C_{27}H_{55}COOH\) gave the value \(\Delta d = 30 \pm 1.5\) Å.
According to data relating to electron diffraction, molecules of fatty acids, when adsorbed as a monomolecular layer on a metal, are oriented so that the acid group faces the adsorbing surface, while the hydrocarbon chain is extended perpendicular to the surface. If this is also true for adsorption on mica, then the data obtained refer to the length of the molecule and can be compared with the data of X-ray structural analysis. According to the latter, the lengths of the molecules in the direction of the \(c\)-axis of the corresponding crystals are equal to 24.42 and 37.02 Å for \(C_{17}H_{35}COOH\) and \(C_{27}H_{55}COOH\), respectively.
As the authors note, the sharp discrepancy between the values obtained by optical and X-ray methods cannot be the result of experimental errors and is systematic in character. The authors believe that the source of the discrepancy should be sought in a possible difference of the phase shifts upon reflection of light at the boundaries adsorbed layer—silver and mica—silver, and also in the phase shifts occurring when light passes through the boundary mica—adsorbed layer. It is not difficult to see that such phase shifts would be indistinguishable from real changes in the thickness of the layer. This supposition is supported also by the equality of the differences in the lengths of the molecules \(C_{27}H_{55}COOH\) and \(C_{17}H_{35}COOH\), determined from optical and X-ray data:
optical data: \(30 - 19 = 11\) Å,
X-ray data: \(30.02 - 24.42 = 12.6\) Å.
In fact, the molecules of both substances are arranged in the adsorbed layer in the same way: the acid groups face the composite plate, and the inert groups face the silver coating. Consequently, in both cases the two phase shifts must be identical, and the errors in measuring the length introduced by neglect of this effect must be identical. Apparently, in this way there arises the possibility of a detailed study of the optical properties of monomolecular layers.
It should be noted that the experiments described, which are preliminary in character, not only illustrate the great possibilities of the method of interference of lower orders of multiply reflected rays, but also open up a new field of research, the fruitfulness of which can scarcely be doubted.
G. Rozenberg
References
- S. Tolansky, UFN 30, 103 (1946).
- J. S. Courtney-Pratt, Nature 165, 346 (1950).