PAUL PEYSER AND ROBERT R. STROMBERG
2066
Conformation of Adsorbed Polystyrene Measured by Attenuated Total Reflection in the Ultraviolet Region’
by Paul Peyser2 and Robert R. Stromberg Institute for Materials Research, National Bureau of Standards, Washington, D. C. $0.284 (Received October 27, 1966)
A method using the technique of internal reflection spectlroscopy is described for the measurement of the extension and concentration of a film on a transparent surface. I n this method, attentuated total reflection (ATR) in the ultraviolet region was applied to polystyrene adsorbed on a quartz surface from cyclohexane solution at the 0 temperature. The ATR prism, which allowed 15-16 reflections, was constructed from synthetic crystalline quartz. It was designed to be placed in a spectrophotometer without the need of additional optical components. The measured adsorbed polymer “extension” agreed reasonably well with similar ellipsometric measurements on nearly the same system. The study reported here was restricted to the use of an adsorbed layer that could be treated as a homogeneous film. The possible use of the method to determine the concentration distribution of adsorbed segments normal to the surface is discussed. Measurements in the ultraviolet region of the refractive indexes of the polymer solutions and of the benzenemethanol and toluene-methanol solutions that were used to test the method are also described.
Introduction Measurement of the conformation of adsorbed molecules is required for an understanding of the adsorption of polymers on surfaces. Ellipsometrya and viscosity‘ measurements have previously been made to measure an average thickness of the adsorbed polymer layer in contact with the polymer solution. However, neither of these techniques permits a measurement of the distribution of segments in the layer as a function of distance normal to the surface. In this paper we describe a method for the simultaneous measurement of the thickness normal to a transparent surface and the concentration of polymer in a film. The method, employing attenuated total reflection (the technique is known as internal reflection spectroscopy), is well suited for the study of adsorbed polymer films where contact with the polymer solution is required to prevent changes in the conformation of the adsorbed molecule. We have applied the method to polystyrene adsorption on a quartz surface. I n this application of attenuated total reflection The Journal of Physical Chemistry
(ATR), polymer is adsorbed on a prism in contact with the polymer solution. Light transmitted through the prism will be totally reflected a t the boundary between the prism and the solution if the angle of incidence is greater than the critical angle. Under these circumstances it is well known that the reflected ray penetrates into the solution for distances of the order of one wavelength before reentering the prism. If the adsorbed layer absorbs light, some of the incident light will be absorbed by the layer and the process is described as attenuated total reflection. Measurement of this attenuation is related to the thickness (1) This work was supported in part by the Army Research Office, Durham. It was presented a t the 152nd National Meeting of the American Chemical Society, New York, N. Y., Sept 1966. (2) National Academy of Sciences, National Research Council Postdoctoral Resident Research Associate a t the National Bureau of Standards, 1963-1966. (3) R. R. Stromberg, D. J. Tutas, and E. Passaglia, J . Phys. Chem., 69, 3955 (1965); (4) F. W. Rowland and F. R. Eirich, J . Polymer Sci., A4, 2033 (1966); 4, 2401 (1966).
CONFORMATION OF ADSORBED POLYSTYRENE
of the adsorbed film if the entire film is penetrated. As will be discussed later, it is desirable to confine this penetration to the order of the thickness of the film. The ATR process described here provides a method in addition to ellipsometry and viscosity for the measurement of the thickness (a measure of the extension of the adsorbed polymer molecule normal to the surface) and concentration of an adsorbed polymer film. In many respects it is similar to the technique of ellipsometry. Using ATR the absolute values of the two reflection coefficients are measured, whereas in ellipsometry a ratio of reflection Coefficients and a phase shift of the light are measured. Both techniques usually allow a simultaneous determination of thickness and concentration of polymer in the film. (However, if the light is totally reflected in ellipsometric measurements, both of these parameters cannot always be measured.') The sensitivity and utility of ellipsometry and ATR are dependent on the differences in refractive index among film, substrate, and surrounding medium. In the work described in this paper, we have used the difference in absorption (related to the imaginary component of the refractive index) between polymer film and solution as well as the real refractive index difference between polymer film and substrate. The most significant information that could result from ATR studies of polymer adsorption would be the segment distribution. This would require ray penetration depths of the order of the extension of the adsorbed polymer molecule normal to the surface. For sufficient sensitivity it would also be necessary to have large extinction coefficients. The ultraviolet region most closely meets these requirements, since the depth of penetration'.' decreases with decreasing wavelength and many polymers have large extinction coefficients in this region. Synthetic quartz was chosen for the prism because of its transparency and relatively high and well-established refractive index in the ultraviolet range and the availability of crystals that are homogeneous. However, the birefringent nature of crystalline quartz somewhat complicated the calculations. Here we describe the use of ATR to a measurement of the thickness and concentration of an adsorbed film of polystyrene, mol wt 76,000, and compare the results with measurements by other techniques. The method was also tested on two simpler model systems, toluenemethanol and benzene-methanol solutions, where any adsorbed film would not significantly affect the results. Toluene and benzene both absorb in the wavelength range used here for the polystyrene solutions. The methanol solutions of these two ma-
2067
-,l
10.7em
j-[/r
CELL
~ 5 ~
4 8
c------------
{-
][
1
CELL
_ _ _ >_ _ _ _ _ . .
Figure 1. Schematic representation of a single crystal quartz prism and fused quartz cell. The angle of incidence, q, varied with wavelength. The direction of the optic axis of the prism was normal to its base.
terials provided systems for which calculated reflectance values could be compared with experiment, thereby testing the experimental design and method of analysis. We also discuss the possible application of the technique to the measurement of the segment distribution for adsorbed polymer films of greater thickness.
Prism and Cell Design The prism and the cell used to contain the liquid media are shown in Figure 1. The attenuated total reflection prism was constructed from a synthetic quartz crystal and was designed to be used in a spectrophotometer without the need of additional optical components. Incident and emergent beams of light were both in the same plane and parallel to the base of the prism. The direct.ion of the optic axis of the prism was normal (measured to within 0.1') to the base of the prism. The four optical faces were optically polished flat to within one-fourth of a fringe of the green line of mercury. The cell was constructed from fused quartz. A rectangular cavity was formed in both the bottom and top portions by ultrasonic cavitation and the surfaces in contact with the ATR prism were polished optically flat. Holes for the addition of liquids and removal of air were drilled into the side of the bottom portion and the top of the upper portion of the cell. Each hole was fitted with a polytetrafluoroethylene insert pen+ trated by a stainless steel hypodermic needle. The assembly was clamped together in a holder; the liquid was retained by the close contact afforded by the opti(6) E. Paasadin and R. R. Stromberg. J . Res. N d l . Bur. Ski.. Am, 601 (1964). (6) J. Fahrenfort. Spdrochim. Ado. 17, 698 (1961): 18. 1103 (1962). (7) N. J. Hnrriek. Ann. N. Y . A d . Sci.. 101, 3, 928 (1963): J . Phya. C h . . 64, 1110 (1960).
Volume 71, Numb 7 June 1967
PAULPEYSER AND ROBERTR. STROMBERG
2068
cal finishes on the prism and cell surfaces. The holder was constructted to fit the sample compartment of the spectrophotometer in a reproducible manner.
correction factor was used. Because of this extrapolation we selected 260 nm as the lower limit for our measurements.
Experimental Procedure
Calculations
The liquids toluene, methanol, benzene, and cyclohexane were of reagent grade and were purified by fractional distillation and stored above molecular sieves. The toluene--methanol and the benzene-methanol mixtures were prepared in a 1:6 and a 1:4 volume ratio (before mixing) ,respectively. The polystyrene was supplied by Dr. H. W. McCormick of the Dow Chemical Co. (Dow's sample No. S 102) and was the same fractionated anionically polymerized sample that has been described previously." The molecu1;tr weight of the fractionated sample, determined by intrinsic viscosity, was 76,000 and the value of iVw/Xn was less than 1.05. The concentration of the polystyrene-cyclohexane solution used for the ATR measurements was 7.9 mg/ml. Prior to each experiment the components of the ATR prism and cell were cleaned overnight with benzene in a Soxhlet extractor. In addition, immediately before use the prism and cell were heated to 500' in a muffle furnace and held a t this temperature for 1 hr. The pieces were removed to a vacuum desiccator and allowed to cool for approximately 30 min. The two cell halves and the prism were then assembled using flamed platinum-tipped tongs, clamped, and the cells filled with liquid. Measurements were first carried out on the "solvent," Le., methanol or cyclohexane. The cells were then emptied, dried, and filled with the appropriate solution. The measurements were carried out in a recording ultraviolet spectrophotometer with a Glan-Thompson prism in the beam. Measurements were made a t two polarizations of the light. Air temperature of the sample compartment was maintained a t 35 0.1'. The wavelength range was scanned manually in one direction. Measurements were repeated for the wavelength range until the absorbance remained constant with time a t each wavelength measured. The difference in absorbance between the solution and the solvent represented the absorbance due to the solute or to the absorbing polymer film. A slight shift in the base line measured a t the nonabsorbing wavelengths of 300, 290, and 280 nm was observed between solvent and solution. This shift was identical a t each wavelength for the benzene and toluene solutions and the absorbance was adjusted accordingly. However, for the polystyrene solutions the shift was not identical for all three wavelengths, but increased with decreasing wavelength. In these cases, a linearly extrapolated
The reflection coefficients for light polarized with its electric vector parallel and perpendicular to the plane of incidence are rqspand r,SS, respectively. These can be accurately calculated from the Fresnel equations, which for our arrangement can be expressed as
*
The Journal of Physieal Chemhtly
N, cos cp1 - n , cos cp2 N, cos cp1 n, cos (a2
+
rqsP=
r g s s=
n, cos cp01 - N, cos n, cos cp1 N , cos
+
(1) (02
cp2
The subscripts q and s refer to the quartz prism and solution of solvent, respectively, nq is the refractive index of the quartz prism, and N, is the complex refractive index of the solution or solvent. The angle of incidence is paland the angle of refraction is cp2. For the case of a homogeneous film between the quartz prism and the liquid medium, the total reflection coefficients for the system are given by the exact Drude equationsg RP
++
rqfPrqtPrfSp rfSpexpD expD
= 1
where
D = - 4 ~ i N fCOS cpr(dr/X)
(3)
and an identical expression for Re, where rs is substituted for rp. The subscript f refers to the film, pi is the angle of refraction in the film, df is the film thickness, X is the wavelength of light under vacuum, and r is the reflection coefficient a t a single boundary indicated by the subscripts, as given in eq 1. The complex refractive index N of the solution or of the film measured by ATR can be expressed as
N
=
n(l
- ilc)
(4)
where n is the real part of the refractive index, and k can be directly related to the absorbance A obtained from a transmission spectrum. From the Beer-Lambert relationship, for no interaction among absorbing molecules A = ~i~~1/2.3
(5)
(8) R. R. Stromberg, E. Passaglia, and D. J. Tutas, J. Res. Nutl. Bur. Std., A67, 431 (1963). (9) P.Drude, Ann. Phyaik., 272, 532 (1889); 272, 865 (1889); 275, 481 (1890).
CONFORMATION OF ADSORBED POLYSTYRENE
2069
Table I: Refractive Indexes and Angles of Incidence for ATR Quartz Prism Av of Av of
9ENi’
9ER?
(PEN, WERI
A, A
no“
fltbdeg
nEc
nENd
nER’
nENi nER
deg
deg
deg
2500 2550 2600 2670 2680 2690
1 ,60064 1.59823 1.59487 1.59128 1.59080 1 ,59032
71.22 71.27 71.32 71.38 71.39 71.40
1.61166 1.60855 1.60567 1.60196 1.60146 1.60096
1.61048 1.60739 1.60453 1.60083 1 .60034 1.59984.
1.61047 1.60739 1.60452 1 .60083 1.60033 1.59984
1.61047 1.60739 1 .60452 1,60083 1.60033 1.59984
71.04 71.10 71.15 71.21 71.22 71.23
70.80 70.86 70.91 70.98 70.99 71.00
70.92 70.98 71.03 71.10 71.10 71.11
EN, normal-extra, refractive index. ’no, ordinary refractive index. ‘pot ordinary ray angle of incidence. n ~ extraordinary , refractive index. (DEN, angle of refraction for normal+xtraordinary ray. ordinary refractive index. e ~ E R ray-extraordinary (DER, angle of refraction for ray-extraordinary ray.
’
where the absorbance is obtained from a transmission spectrum for a solution of concentration CT and a path length 1 and a is a constant independent of concentration. The value of k for the solution or film measured by the ATR process is related to a by
4mk
LYCATR
= -
h
(6)
*SURFACE
where CATR is the measured concentration of the solution or polymer film obtained by ATR. Then the value of k is given by
(7) The ordinary and extraordinary refractive indexes were calculated for the birefringent quartz prism by equations given by Radhakrishnan.lo The ordinary ray, as the name implies, presents no difficulties in determining the refractive index and angle of incidence. The extraordinary ray, however, gives rise to two refractive indexes (and correspondingly, two angles of incidence) known as the ray index and the wave front normal index. The refractive indexes can be calculated geometrically by application of Huygens’ principle to doubly refracting crystals.11 Figure 2 shows the Huygens’ construction applied to our case and the results for the refractive indexes are given in Table I. The values of n, and cp used in eq 2 for the extraordinary ray were obtained by averaging the values obtained for the ray and the normal refractive indexes. Because of its height, a portion of the light beam is reflected 15 times in our prism and a portion 16 times. The average number of reflections was calculated geometrically for each wavelength and the value of A per reflection was obtained. The determination of the refractive indexes of polymer-solvent, benzene-methanol, and toluene-methanol mixtures at the wavelengths used in this study is discussed in the Appendix.
Figure 2. Huygens’ construction for light incident as shown in Figure 1 for the uniaxial negative quartz crystal. This construction was modified for our system from that given in ref 11.
For measurements on benzene or toluene solutions, the measured experimental reflectance values obtained from ATR were compared with those calculated from eq 1 and 4-7. The values of n were measured directly as described in the Appendix. For calculations involving an adsorbed polymer layer the Drude equations are used. The adsorbed polymer layer is treated as a homogeneous film. (The effect of a nonhomogeneous film is discussed later.) All of the parameters in the Drude equations are known, independently measured, or calculated, except for d,, the film thickness, and Nt, the complex refractive index of the film (which depends on the film concentration). For each wavelength and polarization of the light, (10) T. Radhakrishnan, Proc. Indian Acad. Sci., A25, 260 (1947). (11) A description of the application of Huygens’ principle to doubly refracting prisms is given by E. E. Wahlstrom, “Optical Crystallography,’’ 3rd ed, John Wiley and Sons, Inc., New York, N. Y., 1960, p 100.
Volume 71, Number 7 Juns 1067
PAUL PEYSER AND ROBERT R. STROMBERG
2070
reflectance values were calculated from eq 2 for a series of given film thicknesses at various given film concentrations. (The value of n for a given film concentration was obtained from dnldc,, which was determined as described in the Appendix, and the value of k was obtained using eq 4-7.) The measured experimental reflectance value, obtained directly from ATR, was then compared with the series of calculated reflectance values for each given concentration in order to determine the value of film thickness corresponding to the experimental reflectance value. In this manner one value of film thickness was obtained a t each concentration for each of the two polarizations at each wavelength. Curves of film thickness vs. film concentration were constructed for each of the two polarizations, as shown in Figure 3. The point of intersection of these curves was taken to represent the experimental value for film thickness and concentration, as determined a t that wavelength. The solutions of the Fresnel and Drude equations were carried out using a computer program12 that had previously been written for ellipsometry measurements.
Results and Discussion A typical RTR spectrum in the ultraviolet region is shown in Figure 4 for a solution of benzene in methanol. Also given is a transmission spectrum of a more dilute benzene solution. The ATR spectrum qualitatively was quite similar to the transmission spectrum, offering a technique for obtaining ultraviolet spectra in a region close to a surface. For our purposes, a quantitative analysis of the attenuation a t a reflection was required. To check the technique and the apparatus, especially the alignment of the quartz prism, measurements were made on a simple system for which the reflectance values could be calculated and independently compared with experiment. The experimentally measured absorbance values for benzene and toluene solutions are compared in Table I1 with absorbances calculated from the Fresnel equations. Comparisons are made a t a number of wavelengths and for the two polarizations of light. The refractive indexes used for calculating the values of the absorbance a t the wavelengths given in Table I1 were extrapolated from the measured range shown in Table VI Severtheless, as shown in Table 11, there was reasonable agreement between the experimental and calculated values of the absorbance, demonstrating for a simple model system the validity of the experimental design and method of analysis. The thickness and concentration (relative to solution concentration) of the polystyrene layer adsorbed on the quartz prism as determined by the ATR meaThe Journal of Physical Chemistry
-
-
30
150
390
250
350
fllW THICKNESS,!
Figure 3. Concentration of the adsorbed polystyrene a function of thickness for each of the two layer polarizations of light of wavelength 2670 A: 0,light polarized with its electric vector perpendicular to the plane of incidence; a, light polarized with its electric vector parallel to the plane of incidence.
Table 11: Comparison of Calculated and Experimental ATR Absorbance for Toluene and for Benzene Solutions ---Toluene
solution-
-Benzene
solution-
DifA, A
Crlcd
Exptl
ference
Calcd
Exptl
Difference
Ordinary Ray Polarization with Electric Vector Perpendicular to Plane of Incidence ... ... 2690 0.067 0.091 0.024 2680 0.075 0.096 0.021 ... ... ... 2670 0.077 0.091 0.014 ... ... ... 2600 0.105 0.110 0.005 0.67 0.077 0.010 2550 0.094 0.090 0.004 0.087 0.102 0.015 2500 0.069 0.072 0.003 0.100 0.087 0.013 I
.
.
Extraordinary Ray Polarization with Electric Vector Parallel to Plane of Incidence 2690 0.080 0.088 0.008 ... ... ... 2680 0.089 0.093 0.004 ... ... ... 2670 0.092 0.103 0.010 .., ... ... 2600 0.125 0.132 0.007 0.070 0.088 0.018 2550 0,110 0.118 0,008 0.101 0.126 0.025 2500 0.081 0.097 0.016 0.116 0.118 0.002
surement are shown in Table 111. These values were determined at several wavelengths by the intersection of the curves obtained for the two polarizations of the light, as described in the section on calculations and (12) F. L. McCrackin and J. Colson, National Bureau of Standards Technical Note 242, 1964.
207 1
CONFORMATION OF ADSORBED POLYSTYRENE
0.8 I
'
O
I
TRANSMISSION-BASE LINE
0 220
,
1
240
I
I
260
I
280
I
300
hrnp
Figure 4. Ultraviolet spectra of benzene-methanol solution. ATR spectra were obtained us. air. No ATR cell was in the reference beam. Composition of benzene-methanol solution, 1:4 (by volume). Transmission spectra were obtained vs. methanol. Composition of benzene-methanol solution, 1 : 16 (by volume); path length 0.1 mm.
as shown in Figure 3 for one wavelength. For the larger concentration found for this film, the critical angle would not be exceeded at the quartz-film interface, but rather at the film-solution interface. Nevertheless, the Drude equations are applicable to this situation and correctly account for the absorption of light in its multiple reflections through the film. The values given in Table 111, however, represent I ( average" values of the segment distribution; the relations between these averages and various segment distributions have not yet been determined. The ATR value of the extension, 240 A, is in good agreement with the value obtained by ellipsometry and calTable 111: Thickness and Concentration of Polystyrene Layer Adsorbed on Quartz Film Wavelength, A
thickness, A
Film concn/ solution concna
2690 2680 2670 2600
230 260 240 240
39 32 34
Av 240
' Solution concentration
= 7.9 mg/ml.
34
35
culated for a homogeneous adsorbed layer.13 This ellipsometric value, 225 A, was for the same sample adsorbed on a metallic surface from cyclohexane a t 34' (approximately the Flory e point). The value of 35 for the concentration of the adsorbed layer as measured by ATR appears to be high when compared with the ellipsometric results obtained at lower equilibrium concentrations at 24 and 34'. However, a similar value for this solution concentration was obtained by ellipsometry for this polystyrene sample adsorbed at 24' from a similar solution concentration.s The value for the extension can also be compared with that measured by viscometry. With this technique a value of 196 A was obtained4 for a 110,000 mol wt sample of polystyrene adsorbed from cyclohexane on glass at the e point. Although these measurements were carried out on different surfaces, i e . , silica, metal, and glass, all three surfaces were oxides and the surface energies should be of the same order of magnitude. It appears, then, that there is good agreement among the three different measurement techniques. The changes in the properties of the attenuated reflecting light beam that occur as a result of penetration beyond the boundary are accurately treated by the Fresnel and Drude equations. As described earlier, our calculations were carried out in this manner. However, in order to give a physical picture of the penetration and to emphasize its relation to dimensions of the adsorbed polymer layer, the following approximate treatment can be considered. If the absorption of the film is neglected, i e . , k is put equal to zero in eq 4, the intensity, I (square of the amplitude of the electric vector), of the light beam penetrating into the rarer medium decreases e~ponentiallyl~ as
I
=
lo exp( -@47rt/A,)
(8)
where Io is the intensity of the light before penetration, t is the penetration distance normal to the boundary, A, is the wavelength of light in the quartz and (13) In the reference cited in ref 3, the value obtained by ellipsometry was 225 A, calculated for a homogeneous film model. For an exponential distribution, this value can be related to a root-meansquare average molecular extension of 170 A, which is the value given in that reference. (14) The light is also translated (Goos-Hanchen shift) in the rarer medium parallel to the boundary by a distance d l for the perpendicular component of the light, where d l = (l/r)(sin lp cos2 rp/ cos2 q @2)(X,/p), and by a distance dll for the parallel component of the light which is given by a similar expression.16 We have found, for example, that for the toluene solution the exact value of the reflectance as calculated by the Fresnel equations was approximately the same as that calculated for a model in which the light penetrated, with decreasing intensity, into the rarer medium, returned to the vicinity of the boundary, and then translated a distance d before reentering the quartz. (15) R. H. Renard, J . Opt. SOC.Am., 54, 1190 (1964).
+
Volume 71, Number 7 June 1067
2072
PAUL PEYSER AND
0
=
[sin2 cp - (n/n,)211/*
(9)
where cp is the angle of incidence, n is the refractive index of the rarer medium (solution, solvent, or film), and n, is the refractive index of the quartz. Since the films and solutions studied here are weakly absorbing, eq 8 is a reasonably good approximation. For our discussion here, the term “penetration depth,” t1/*, is defined as the value of t where the value of I is I0/2, i.e. tl/,
=
A, In 2
04r
The “penetration depth” of the light beam is dependent on the angle of incidence and the ratio of the refractive indexes and is most sensitive to small changes in these quantities near the critical angle. If the polymer concentration in the film, and consequently its refractive index, becomes sufficiently large, the angle of incidence a t the quartz-adsorbed polymer film interface no longer exceeds the critical angle and total reflection occurs within the film or at the “film-solution” interface. The ratio of film concentrationsolution concentration for which total reflection no longer occurs at the quartz-film interface is defined here as the “critical ratio.” In principle the segment distribution normal to the surface for an adsorbed polymer layer can be determined by ATR. For the work reported here a homogeneous film was assumed and only a thickness and film concentration representing average values of the actual distribution were determined. This assumption was reasonable, as shown in Table IV for the ordinary ray for polystyrene adsorbed on quartz. These penetration depths were calculated for the polymer solution, assuming the critical angle to be exceeded at the quartz-solution interface (no adsorbed film). In our case, however, the concentration of polymer in the adsorbed film was such that the critical ratio was exceeded and reflection occurred a t the filmsolution interface. The actual penetration of light beyond the quartz boundary was, therefore, greater than the t1,* values given in Table IV as well as the thickness values given in Table 111. Thus, for the experimental conditions used here the entire film certainly was penetrated. Moreover, as shown in Table IV, little variation occurred in either the penetration depth or the critical ratio for the wavelength region of interest. Hence,’ the agreement among the measured film thicknesses and concentrations shown in Table I11 for the four wavelengths is to be expected. However, if the penetration depth is of the order of the extension of the polymer molecule and the concenThe Journal of PhyeiCal Chemistry
ROBERTR. STROMBERG
Table IV : Penetration Depth and Critical Ratio for the Ordinary Ray
X, A
nps0
A
Critical concn ratioC
2500 2550 2600 2670 2680 2690
1.48058 1.47704 1 .47378 1.46901 1.46905 1.46850
427 425 431 438 436 437
14.3 15.5 16.2 17.5 17.6 17.8
11/2,*
a npg is the refractive index of polystyrene-cyclohexane solution. * ti/, is the “penetration depth,” eq 10. The critical concentration ratio is the ratio of a concentration of polymer filmsolution for which a critical angle a t the quartz-film boundary is no longer exceeded.
tration of the adsorbed film is less than or not much greater than the critical ratio, the calculated average film thickness and concentration will be altered if the penetration or the critical ratio is varied over a significant range. It should be possible to relate such results to the segment distribution.
Aclcnowledgment. The authors wish to express their appreciation to I. H. Malitson for his advice and the use of his equipment for the refractive index measurements and M. J. Dodge for her technical assistance in those measurements. They also wish to thank Dr. F. McCrackin for many helpful conversations.
Appendix Refractive Index Measurements. Refractive indexes of the solvents and solutions used for the ATR studies were measured for wavelengths ranging from 5460 A into the ultraviolet. The determinations were carried out on a modified Gaertner spectrometer by the method of minimum deviation, using a waterjacketed hollow prism to contain the liquids. The method and instrumentation have been previously describedx6 and we will describe here only certain modifications and details relevant to our measurements. The prism was almost identical with that used by Tilton and Taylor” in their classical determination of the refractive index of water, except that the plane parallel windows were constructed of high-quality fused quartz cemented to the stainless steel body. The temperature in the prism was maintained a t 35 f 0.05’. In order to prevent a temperature gradient (16) W. S. Rodney and R. J. Spindler, J. Res. Natl. Bur. Std., 53, 185 (1954). (17) L. W. Tilton and J. K. Taylor, ibid., 20, 419 (1938).
CONFORMATION OF ADSORBEDPOLYSTYRENE
2073
near the cell windows, as evidenced by a broadening of the spectral lines, it was necessary to maintain the room at a temperature near that of the cell. The light source was a mercury lamp and a photomultiplier tube was used as a detector. The angle of minimum deviation cannot be independently obtained on the modified instrument used here because the position of the undeviated beam cannot be directly measured. However, the scale position of the undeviated beam differs from the minimum deviation angle by a constant amount.l8 This difference was determined from an average of measurements17 on distilled water at 26’ at several wavelengths in the visible region. The wavelengths in the ultraviolet region were identified from a knowledge of the emission spectrum of the mercury source, with the aid of the dispersion equation (n2
- %)-I
= (a
- b/X2) - (c/X4)
(11)
This is a slightly modified form of the equation used by Lauer20 and found by him to be applicable to cyclohexane, toluene, and methanol. His equation contains the term (n2 - 1)-l and has no fourth power term in A. Typical results at a few values of X are given in Table V for each of the solutions and solvents studied. nexptlrepresents the refractive index obtained directly from the experimental data and ncalcdrepresents the value obtained by fitting eq 11 by least squares, using 1/X2 as the independent variable and (n2 - z)-l as the dependent variable. The value of z used for each of the systems, the constants a, b, and c, which were calculated from a fit of the data to eq 11, and the standard deviation, en, are given in Table VI.
Table V : Refractive Indexes Material
X, A
%XRtl
%led
Cyclohexane
5461 3650 3126 2576 2378
1.41968 1.43645 1.44856 1.47277 1 ,48768
1.41973 1.43640 1.44855 1.47272 1.48762
PS 1
5461 3650 3126 2753 2378
1.41985 1.43663 1 ,44880 1.46321 1.48803
1.41990 1.43660 1.44879 1.46324 1 * 48801
5461 3650 2760 2378
1.42004 1.43688 1.46322 1 .48853
1.42010 1.43683 1.46325 1.48851
(5.61 mg/ml)
5461 3650 2753
1 ,42065 1.43759 1.46450
1.42067 1.43758 1.46449
Benzene-methanol (1:4 v/v)
5461 2756
1.35718 1.40485
1.35742 1 ,40458
Toluene-methanol (1:6 v/v)
5461 2803
1,35248 1.39485
1.35261 1.39461
(0.95 mg/ml)
PS 2 (2.12 mg/ml)
PS 3
A value of dn/dc, was calculated using the three polystyrene solutions. These calculations were carried out in 50-A increments for the wavelength range 55002300 A for values of n obtained from eq 11 for cyclohexane and the polymer solutions. The average value of dnldc, at each wavelength was fitted to an equation of the formz1 dnldc, = a
+ @/A2) + (c/X4)
(12)
The values of a, b, and c and the standard deviation are given in Table VI. In Figure 5, dnldc, is given as a function of 1/X2 (eq 12). Also shown are two literature values22~2a of dnldc,
Figure 5. Dependence of dn/dcR on 1/Xs for polyatyrene in cyclohexane at 35O: , from eq 12; -, h e a r extrapolation of two lowest points; 0,values obtained from ref 22; 0,values obtained from ref 23; A, value obtained from ref 24 ( T = 30”).
-
---
(18) It has been found19 that the scale position of the undeviated beam is constant for prisms having nearly identical refracting angles, provided the scale of the instrument has not been moved between change of prisms. Under such experimental conditions, refractive indexes have been determined with fifth decimal place accuracy. We have considered the exchange of liquids in the hollow prism to be the equivalent of this exchange. (19) I. H. Malitson, private communication. (20) J. L. Lauer, J . Chem. Phys., 16, 612 (1948). (21) The form of eq 12 with c = 0 was used by Spencer for a number of polystyrene-eolvent systems as reported by R. F. Boyer and R. Simha in “Styrene, Its Polymers, Copolymers, and Derivatives,” R. H. Boundy and R. F. Boyer, Ed., Reinhold Publishing Corp., New York, N. Y., 1952, p 374. (22) J. H. O’Mara and D. McIntyre, J . Phy8. Chem., 63, 1436 (1959). (23) H. J. Cantow, 2. Physik. Chem. (Frankfurt), 7 , 58 (1956).
Voluma 71, Number 7 June 1967
PAULPEYSER AND ROBERT R. STROMBERG
2074
Table VI : Constants and Standard Deviations for Dispersion Equation
Material
Cyclohexane PS l(0.95 mg/ml) PS 2 (2.12mg/ml) PS 3 (5.61mg/ml)
Benaene-methanol(l:4v/v) Toluene-methanol (1:6v/v) dn/dcp
Wavelength range, A
No. of wavelengths measured
5461-2378 5461-2378 5461-2378 5461-2753 5461-2756 5461-2803
17 16 13 13 11 10
b
a
1.0188 1.0183 1.0178 1.0166 0.6394 0.8555
1.001 X 1.002 X 1.001 X 1.014 X 0.31 X 0.55 X
1.545 x 10-'3.0
x
C
10' 10' 10' 10' 10' 10' loa
5.6 X 5.7 X 5.8 X 5.3 X 11 X 15 X
2
10" 10" 10" 10" 10" 1011
1 1 1 1 0.25 0.63265
an"
4.6 x 5.2 x 4.0x 1.8 x 31.4 X 16.0X ('dn/do
4.98 x loo
lo-'
lo-' 10-6 lo-' lo-' b
7.7 x 10-7
-
U, was obtained by first computing the standard deviation of the residuals of the fit in terms of (n2 z)-l,converting it to cn The standard deviation of dnldc, does not reflect experimental errors in the usual a t the extremes of the range, and averaging. manner, but rather the closeness of the fit of eq 12 to smoothed values of dnldc,.
for 35' at 546 nm and one valuez4for 30' in the ultraviolet region - at 313 nm. The values in the visible good agreement with the cullre' region are in However, the value at 313 nm is low both with respect
to the curve and with respect to a linear extrapolation of the other literature values at 546 and 436 nm. (24) W. R. Krigbaum, P. Smith, and F.G . Mark, J . A p p l . Phys., 34, 3218 (1963).
