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Determination of concentration distribution of elements in heterogeneous polymer systems by electron probe microanalysis
Concentration distribution of elements in heterogeneous polymer systems
1589
.4. L.N. GUSEVA, Yu. A. hlIKIIEYEV and D. Ya. TOPTYGIN, Vysokomol. soyed. A20: 2006, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 9, 2253, 1978) 5. O. A. LEDNEVA, D. Ya. TOPTYGIN and Yu. MIKHEYEV, Vysokomol. soyed. A13: 931, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 4, 1050, 1971) 6. V. P. PUSTOSHNY, Yu. A. hlIKIIEYEV and D. A. TOPTYGIN, Vysokomol. soyed. A25: 1295, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 6, 1504, 1983) 7. A.L. MARC,OLIN, Dis. na soiskaniye uch. st. kand. k.him, nauk (Thesis discussion, canditate in chemical science), institute of Chemical Physics, U.S.S.R. Academy of Sciences, Moscow, 1976 8. G. B. GECIIELLE and A. MATUSSI, Europ. Polymer J. 1: 47, 1965 9. D . J . CALVERT and D. J. P L U S , Fotokhimiya (Photochemistry). Mir, /~foscow, 1968 10. L. N. GUSEYA, Ya. A. MIKHEYEV and D. Ya. TOPTYGIN, Vysokomol. soyed. B23: 360, 1981 (Not translated in Polymer Sci. U.S.S.R.) 11. G.B. PARIISKI'I, L. M. POSTNIKOV, Ye. Ya. DAYIDOV and D. Ya. TOPTYGIN, Vysokomol. soyed. AI5: 482, 1974 (Translated in Polymer Sci U.S.S.R. 16: 3, 557, 1974) 12. "V. Ya. SH.LYAPINTOKtt, Fotokhimicheskiye prevrashcheniya i stabilizatsiya potimerov (Photochemical Changes and Polymer Stabilization) Khimi.ya, Moscow, 1979 13. Kh. S. BAGDASARYAN, Teoriya radikal'noi polimerizatsii (Theory of R.adical Polymerization). 2nd ed., Nauka, Moscow, 1966 J4. A. "V. TOBOLSKY, P. M. NORLING, N. II. FRICK and H. YU, J. Amer. Chem. Soc. 86: 3925, 1964 15. N. M. BAZHIN, Kinetika i kataliz 8: 532, 1967
Polymer Science U.S.S.R. Vol. 26, No. 7, pp. 1589-1597, 1984 Printed In Poland
0032-3950184 $10.00+.00 1985 Pergamon Press Ltd.
DETERMINATION OF CONCENTRATION DISTRIBUTION OF ELEMENTS IN HETEROGENEOUS POLYMER SYSTEMS BY ELECTRON PROBE MICROANALYSIS* Y r . D. PoPovA, N. N . AVDEYEV a n d A . YE. CII^LYKH Institute of Physical Chemistry, U.S.S.R. Academy of Sciences (Received 24 December 1982)
A method is proposed for determining the concentrational distribution of elements in heterogeneous systems, applicable to the study of materials with both homogeneous and heterogeneous distribution of heterostructural components. Examples of its use are given for analysis of concentration distribution of dibromodiallyl phthalate formed in porous PVG with various treatment regimes.
* Vysokomol. soyed. A26: No. 7, 1420-1426, 1984.
1590
"
YE. D. POPOVAet aL
Ix is known that to measure concentration gradients o f different elements, at separations of ca. 10-100 l t m , it is convenient to use an X-ray spectral electron probe microanalytical method. This method is derived from the fact that during the motion of an electron probe perpendicular to the sample surface, the intensity o f intrinsic X-ray radiation is registered simultaneously along the direction of the concentration gradient. Thisgives information on the concentration of the element being analysed. Moreover, the more localized the concentrations which it is desired to measure, the better will be the character (relief) of the surface being analysed and the finer the phase heterogeneities in the sample structure. The permissible size o f the surface imperfections and the structural heterogeneitie s are connected directly to the practical diameter o f the electron prob e (i.e. with the size of the radiation-generating region) which is ca. 1 l t m f o r the majority of non-metallic materials. Therefore the size of the above heterogeneities must not exceed this value. The inadequacy of this variant of traditional electron probe microanalysis is such that it cannot be used in the case of heterogeneous materials having structural microheterogeneities exceeding the diameter of the probe. Meanwhile, for many material application problems, it is important to study the concentration distribution of certain substances, in just such materials of the type quoted above. These materials comprise porous laminated and fibrous structures, different dispersions, metal oxides and materials with fibrous and fabric filling. In the simplest case, the material is a two phase matrix with a third, compound distributed in it. An example of such a material is shown in Fig. la. This material is one of a series~ of samples, prepared from 2 mm thick PVC with a porous structure which was formed by sintering spherical particles of size 5 to 50 i t m for 3 min at 230 ~ To create a concentration gradient, one of the surface of a plate was treated with dibromodiallyl phthalate (DBAP) plasticizer by two methods, which provided qualitatively different types of DBAP distribution in relation to the thickness of the porous plate. Besides this, the treatment method definitely affected the final material structure. In the first case, samples were in contact with filter paper impregnated with a small amount o f plasticizer for 40 min at 70 ~ which hardly changed the initial porous structure (Fig. la). Pure plasticizer was applied to the surface of the second sample which was. subsequently thermostatted under the same conditions, which caused the formation in the pre-surface layer of an almost monolithic material due to intense particle swelling and their transformation into the viscous-flow state. We will first examine the general approach to information on concentration distribution c(x) for samples, typical of relatively uniform porosity distribution. It is clearly impossible to use local microanalysis methods to study the concentration distributions of the elements in similar materials, since on the intengity change profile, caused by concentration changes, the element of interest to us (useful signal), is superimposed a high frequency signal, arising due to sudden local changes. in the surface morphology or sample structure (noise), the amplitude of which may exceed the useful signal by several times. In the case given in Fig. 1, these heterogeneities are connected with the presence of pores in the material. The DBAP distribution in relation to plate thickness, measured. by the L~ line of bromine by a standard method, ha's the form shown in Fig. 2 (curve 1). At the same-
Concentration distribution of elements in heterogeneous polymer ststems
1591
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Ylz. D. POPOVA et aL
71592
time as the plasticizer distribution, we assessed the intensity changes of the K~CI line. Since the CI concentration in PVC is known, this information was used to calculate the absolute plasticizer concentration. In order to introduce a localized method appropriate to the true morphology and material structure, it is necessary to increase the size of the region in which X-ray radiation i s generated, to a value exceeding by 5-10 times the size of the microheterogeneities. In practice, such a radical :increase in the probe size was achieved by using an electron microscope in a system developed with television. If moreover, the sample is moved at constant velocity v relative to the television scanner probe, then the latter will play the part of a right angled cross section with uniform electron distribution within the limits of the scanner probe. In this case, the size of the electronic probe will coincide "~vith that of the probe generating X-ray radiation.
.Tsr j P,Zl.un. .L J
,
!
r
I00
Z00
J00 m~ u m
Flo. 2. Intensity distribution for the L~ Br line, recorded by a ~tandard method (1), corresponding to the scanning probe method described (2) and the neutralized distribution, calculated by the proposed method (3). In several cases, it is more convenient to use a device with a frequency smaller than the telewision one, and also to record by points, the build-up of impulses over a set time interval with the sample location fixed relative to the line scanner, then the sample is moved to a definite separation -and so on. Figure 3a represents a survey scheme for determining the concentration distribution of any -element, along the x axis. Here L is the probe dimension in the scanning direction. The probe size in the perpendicular direction is of the same order; its precise size has no principle value and does not participate in the calculations. The rectangular function 9(x) is the determination of electrons i n the limits of the probe: h~ (x) is the experimentally registered profile; f(x) is the actual profile being sought. The curve of bromine intensity change, h~ (x) obtained using a 60 x 40 ttm probe, corresponding to the above radiation-recording system from the same sample (Fig. In) is given in Fig. 2 (curve 2), .compared with a curve obtained by the standard method. In order to estimate the actual neutralized D B A P concentration distribution f(x), based on modified experimentally recorded bromine intensity distribution, h~(x), it is necessary to introduce a correction into the experimental data by enlarging the equipment. We showed that in the experimental conditions described, there is a simple means o f introducing this correction. The essence of this lies in the construction of a new curve hN(x) (ha(x) on Fig. 3b) from the h~(x) curve, the derivative of which at each point is the value of the desired function f ( x ) and the .'same point in relative units (Fig. 3c). The physical meaning of the function ht~(x) is the bromine
Concentration distribution of elements in heterogeneous polymer systems
1593
intensity distribution which would be recorded on the probe equipment, exceeding L by N times. Moreover, for a given L the choice of N is determined b.y the extent of the profile section which interests us. The basis of the proposed working method is given below. We suggest during the survey of a certain concentration profile f(x), using a probe of length L that a profile hi(x) (Fig. 4, curve 1) :is recorded. Let x~-xo=L, then xl
ht(x)= A j ' f ( r ) dr,
Xo<.x
(1)
xo
C 1
0
L
ZL
X
b h3t'x) ,
9tx)
/
0
i
L
",[h, Cx/I ZL
JL
X
Fro. 3. Scheme for recording radiation for study of concentration distribution of elements in heterogeneous systems (a) and the main stages in treating experimental data (b, c). The X-ray radiation detection is denoted by L
The constant A plays the part of a scale factor on the ordinate axis and does not affect the curve =shape, consequently it is ultimately omitted. By differentiation of both parts of equation (1) we obtained, by definition
dlq
--=f(x), dx
Xo
(2)
If the experiment is repeated with a probe of length 2L, then the apparatus records some funcl i o n hz(x). By going through a similar argument, we find that the section xo x2 may be readily -reduced to the desired function, according to the formula
dh2 dx
--=f(x),
Xo
(3)
:By carrying out experiments with increasing L by 3,4 . . . . . N times, we would obtain functions, .h3(x), h4(x) . . . . . hn(x), permitting calculation o f f ( x ) from formulae similar to (2) and (3), for
YE. D. POPOVA.etaL
1594
segments of length 3L, 4L ..... NL. The problem reduces to the reconstruction of the hypothetical: profile, h~.(x). Let us choose as Xo x, any point such as at on Fig. 4. We will put a2 = a t + L ; a3 =a2 + L = a t + 2 L ; ...; a n = a n _ t + L = a = + ( N - l ) L . Let us write down that integral (1) in these Which is. equivalent to points, in values of the original F(x) from the function f ( x )
hi(a1 ) = F(al) - F(xo) h=(a2) = F ( a 2 ) - F(at)
(4)
hi(a3) = F ( a 3 ) - F(a2) .
.
.
.
.
.
.
.
.
.
.
.
.
.
hl(a,v) = F(a,v) -- F(a~._ t) We will add up these equalities N
ht(at) = F(as)--FCxo)
(5)i
I=l
!Bi, "Pel.un. 2
.%
\
o
Iwv I I I a" a t a'zxza a aJxaX,# m xoal t ~ 60 120 FIG. 4. Illustration of graphical constructions: l - e x p e r i m e n t a l l y recorded profile, hj (x); 2 - c o n s t r u c t e d profile, h,v(x); 3 - d e s i r e d neutralized concentration distribution, f ( x ) . By differentiating expression (5) and noting that F ' ( x o ) = 0 we obtain N
[ E h,(at)]'=F'(a.~,)=f(a2~)
(6)'
I=1
Therefore N
E h l ( a t ) = h~.(a~.)
(7),
I=1
The latter formula gives, in principle, the construction of the desired profile h,~.(x) (see Fig. 4, curve 2), by differentiation of which we obtained the neutralized true distribution intensity of intrinsic radiation, corresponding to an clement (see Fig. 4, curve 3). Transfer of the relative intensity values into absolute concentrations of the diffusant may be accomplished, for example, using standards or by starting from the overall quantity of the diffusing substance. The proposed method of surveying and treatment was tested out on a JSM-U3 microscope with a " K e r e x " microanalysis attachment. Comparison of this method with a standard for a " g o o d " sample, represented by a microsection with a triple sandwich of metallic type, A - B - A * sho~ved that the results of the two experiments agreed well. * The sandwich was prepared by vacuum atomization of Nd on to an Ni plate. Recording: was by the K= line of Ni.
Concentration distribution of elements in heterogeneous polymer systems
1595
Figure 2 (curve 3) gives the bromine intensity distribution, calculated by the pro-posed method for PVC samples treated by the first regime. This data, presented in .f(x)[f(O)-x coordinates, agrees with the concentrational distribution of plasticizer in a heterogeneous matrix with uniform distribution of porosity in the diffusion direction. It is evident that for samples with heterogeneous porosity distribution, the above treatment must be modified, since the recorded intensity depends on 2 factors: concentration and morphology. For a quantitative comparison of different sites of a sample in relation to homogeneity, one may use the area $1 occupied by corresponding elements of the heterostructure, related to the area of the probe used, So. We will term the value S * = SdSo, the effective irradiation surface. For the sample studied, S* has the meaning of the relative total sectional area of a particle, lying within the probe limits in a given sample site. Since, with the increase in sizes of the time-base used the degree of homogeneity* of distribution of heterostnictural compositions is increased according to the curve with saturation, a minimal probe is actually used, assuring efficient neutralization. 'Then the change inintensity of an element being analyzed will be connected only with the first factor-the change of its concentration, and not with a change of effective irradiating surface in the various sample sites. When using a 60x40 mm probe for samples, treated by the second regime (Fig. lb), S* is decreased by 2 during transfer of the presurface sections to the initial structure, in the depth of the material. In order to exclude the effect of the second factor, all the measured values of intensity under the same conditions will be put in: the radiation intensity with S* = 1 which is achieved in monolitic samples with the same mean concentrations of the element being analysed which are also in the heterogeneous sample. For this it is sufficient t o separate all intensity values of the magnitude of S* in the same points, assuming proportionality of intensity and radiating surface. The determination of S* may be carried out from photomicrographs'of the surface ,,vhich are obtained along the movement trajectory of the probe. Indirect confirmation of the truth of the S* determination for given samples is given by a representation of the surface under analysis by typical bromine radiation (Fig. lc, d). It is seen that the main contribution to the intensity, in a rather large"section will be the radiation generated in sections of corresponding particles, WhOse area is not difficult to determine. For a direct estimate of the ratio between intensity and S*, a supplementary experiment was carried out, in which the intensityof the K~CI lines and CI background were recorded simultaneously with the Br radiation and Br background. The intensity 9 was measured within the probe limits of 50 k 50 Itm. S* was also determined in this segment. The areas analysed were subsequerltly joined together, forming a perpendicular sample surface trajectory, 500-700 itm long. The precision in determining S* is ca. 15yo. The intensity of the CI line in pure PVi2, extrapolated to a monolith (which . . . .
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'
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.
.
.
.
.
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:
L
* The degree of homogeneity may be characterized, for example, in magnitude, by the inverse of dispersion of So in relation to the sample.
1596
YE. D. POPOVAet aL
must coincide with the intensity measured at a point), served as a standard for estimating the D B A P concentration along the trajectory. It is clear that at a constant diffusant concentration, the graph of dependence of intensity on effective radiating surface must be represented by a straight line, the slope of which is increased with concentration. The experimental results are represented in Fig. 5. The estimated nature of the D B A P concentrations and errors found in calculating the radiation areas are explained by the fact that points over a broad concentration range lie to each straight line. Nevertheless, the orooosed equations are sufficiently clearly followed.
Dt e l un.
IBr ~ I~Lun.
3
/
\
1o / Z
1
0.5
I
s~
FIG. 5
/
I
~1
zoo
'1
I
'%,I
4oox,,~
Fro. 6
FIG. 5. Dependence of intensity I on magnitude of effective radiating surface with DBAP concentrations of 45-55 (/), 60-65 (2) and 80--90% (3). FI~. 6. Neutralized intensity distribution for the L~ Br line for the samples depicted in Fig. la (1) and b (2) (2-without and 3-with account taken of morphology). Figure 6 presents neutralized Br intensity distribution, reduced to a single area, for a surface with adhesion, either taking account of the morphology or not. For comparison there is also given a distribution for a sample with homogeneous porous structure. It is seen that a calculation of the morphology leads to a substantial change in the nature of the distribution. In particular, for the studied trajectory, the extent o f the section with constant concentration amounts to 210 a m but that of the adhered region is 140 pm, which corresponds to the beginning o f a sharp drop in concentration on the curve without calculation of morphology. We note that with the need to introduce corrections for the atomic number, absorption and fluorescence, this will be made to the differential profile. Then the ratios, similar to curves 1 and 3 (see Fig. 6), will exhibit concentration distributions with precision up to a constant factor, connected with the differentiation of the original cu l:ve.
Concentration distribution of elements in"heterogeneous polymer systems
1597"
Analysis of the concentration distributions shows that bromine distribution for t the 2 regimes of plasticizing heterogeneous porous samples are represented by convex lines with. practically constant concentrations close to the surface. Such a character, from a formal viewpoint, is connected with concentrational dependence of the diffusion coefficient and localized distribution of the plasticizer within the particles of sintered PVC. Measurements of a single particle (Fig. le, f ) in a section, by the point probe method, show that the treatment regime does not cause adhesion of the original porous. structure characterized by uniform DBAP distribution throughout the particles. In the second case, the distribution has an extremal character. It is clear that with neutra-. lization of the intensity with some such particles, the resulting profile in the first case, when bulk diffusion is observed, will show a sharper concentration fall than in t h e second case, where bulk diffusion occurs in parallel with plasticizer transfer in relation to the communicating porous sy,stem, leading to a rapid and deeper penetration of it. Thus the survey method described, using additional information on the morphological features of heterogeneous systems, permits a substantial widening of the aims. of the investigation. Translated by C. W. CAPP
1589
.4. L.N. GUSEVA, Yu. A. hlIKIIEYEV and D. Ya. TOPTYGIN, Vysokomol. soyed. A20: 2006, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 9, 2253, 1978) 5. O. A. LEDNEVA, D. Ya. TOPTYGIN and Yu. MIKHEYEV, Vysokomol. soyed. A13: 931, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 4, 1050, 1971) 6. V. P. PUSTOSHNY, Yu. A. hlIKIIEYEV and D. A. TOPTYGIN, Vysokomol. soyed. A25: 1295, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 6, 1504, 1983) 7. A.L. MARC,OLIN, Dis. na soiskaniye uch. st. kand. k.him, nauk (Thesis discussion, canditate in chemical science), institute of Chemical Physics, U.S.S.R. Academy of Sciences, Moscow, 1976 8. G. B. GECIIELLE and A. MATUSSI, Europ. Polymer J. 1: 47, 1965 9. D . J . CALVERT and D. J. P L U S , Fotokhimiya (Photochemistry). Mir, /~foscow, 1968 10. L. N. GUSEYA, Ya. A. MIKHEYEV and D. Ya. TOPTYGIN, Vysokomol. soyed. B23: 360, 1981 (Not translated in Polymer Sci. U.S.S.R.) 11. G.B. PARIISKI'I, L. M. POSTNIKOV, Ye. Ya. DAYIDOV and D. Ya. TOPTYGIN, Vysokomol. soyed. AI5: 482, 1974 (Translated in Polymer Sci U.S.S.R. 16: 3, 557, 1974) 12. "V. Ya. SH.LYAPINTOKtt, Fotokhimicheskiye prevrashcheniya i stabilizatsiya potimerov (Photochemical Changes and Polymer Stabilization) Khimi.ya, Moscow, 1979 13. Kh. S. BAGDASARYAN, Teoriya radikal'noi polimerizatsii (Theory of R.adical Polymerization). 2nd ed., Nauka, Moscow, 1966 J4. A. "V. TOBOLSKY, P. M. NORLING, N. II. FRICK and H. YU, J. Amer. Chem. Soc. 86: 3925, 1964 15. N. M. BAZHIN, Kinetika i kataliz 8: 532, 1967
Polymer Science U.S.S.R. Vol. 26, No. 7, pp. 1589-1597, 1984 Printed In Poland
0032-3950184 $10.00+.00 1985 Pergamon Press Ltd.
DETERMINATION OF CONCENTRATION DISTRIBUTION OF ELEMENTS IN HETEROGENEOUS POLYMER SYSTEMS BY ELECTRON PROBE MICROANALYSIS* Y r . D. PoPovA, N. N . AVDEYEV a n d A . YE. CII^LYKH Institute of Physical Chemistry, U.S.S.R. Academy of Sciences (Received 24 December 1982)
A method is proposed for determining the concentrational distribution of elements in heterogeneous systems, applicable to the study of materials with both homogeneous and heterogeneous distribution of heterostructural components. Examples of its use are given for analysis of concentration distribution of dibromodiallyl phthalate formed in porous PVG with various treatment regimes.
* Vysokomol. soyed. A26: No. 7, 1420-1426, 1984.
1590
"
YE. D. POPOVAet aL
Ix is known that to measure concentration gradients o f different elements, at separations of ca. 10-100 l t m , it is convenient to use an X-ray spectral electron probe microanalytical method. This method is derived from the fact that during the motion of an electron probe perpendicular to the sample surface, the intensity o f intrinsic X-ray radiation is registered simultaneously along the direction of the concentration gradient. Thisgives information on the concentration of the element being analysed. Moreover, the more localized the concentrations which it is desired to measure, the better will be the character (relief) of the surface being analysed and the finer the phase heterogeneities in the sample structure. The permissible size o f the surface imperfections and the structural heterogeneitie s are connected directly to the practical diameter o f the electron prob e (i.e. with the size of the radiation-generating region) which is ca. 1 l t m f o r the majority of non-metallic materials. Therefore the size of the above heterogeneities must not exceed this value. The inadequacy of this variant of traditional electron probe microanalysis is such that it cannot be used in the case of heterogeneous materials having structural microheterogeneities exceeding the diameter of the probe. Meanwhile, for many material application problems, it is important to study the concentration distribution of certain substances, in just such materials of the type quoted above. These materials comprise porous laminated and fibrous structures, different dispersions, metal oxides and materials with fibrous and fabric filling. In the simplest case, the material is a two phase matrix with a third, compound distributed in it. An example of such a material is shown in Fig. la. This material is one of a series~ of samples, prepared from 2 mm thick PVC with a porous structure which was formed by sintering spherical particles of size 5 to 50 i t m for 3 min at 230 ~ To create a concentration gradient, one of the surface of a plate was treated with dibromodiallyl phthalate (DBAP) plasticizer by two methods, which provided qualitatively different types of DBAP distribution in relation to the thickness of the porous plate. Besides this, the treatment method definitely affected the final material structure. In the first case, samples were in contact with filter paper impregnated with a small amount o f plasticizer for 40 min at 70 ~ which hardly changed the initial porous structure (Fig. la). Pure plasticizer was applied to the surface of the second sample which was. subsequently thermostatted under the same conditions, which caused the formation in the pre-surface layer of an almost monolithic material due to intense particle swelling and their transformation into the viscous-flow state. We will first examine the general approach to information on concentration distribution c(x) for samples, typical of relatively uniform porosity distribution. It is clearly impossible to use local microanalysis methods to study the concentration distributions of the elements in similar materials, since on the intengity change profile, caused by concentration changes, the element of interest to us (useful signal), is superimposed a high frequency signal, arising due to sudden local changes. in the surface morphology or sample structure (noise), the amplitude of which may exceed the useful signal by several times. In the case given in Fig. 1, these heterogeneities are connected with the presence of pores in the material. The DBAP distribution in relation to plate thickness, measured. by the L~ line of bromine by a standard method, ha's the form shown in Fig. 2 (curve 1). At the same-
Concentration distribution of elements in heterogeneous polymer ststems
1591
.~, -Z o 6,..'~
o o
.~_ ~ ,;~ 0
~ . o~ ~"
~'~
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u~o ~ ~.~
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Ylz. D. POPOVA et aL
71592
time as the plasticizer distribution, we assessed the intensity changes of the K~CI line. Since the CI concentration in PVC is known, this information was used to calculate the absolute plasticizer concentration. In order to introduce a localized method appropriate to the true morphology and material structure, it is necessary to increase the size of the region in which X-ray radiation i s generated, to a value exceeding by 5-10 times the size of the microheterogeneities. In practice, such a radical :increase in the probe size was achieved by using an electron microscope in a system developed with television. If moreover, the sample is moved at constant velocity v relative to the television scanner probe, then the latter will play the part of a right angled cross section with uniform electron distribution within the limits of the scanner probe. In this case, the size of the electronic probe will coincide "~vith that of the probe generating X-ray radiation.
.Tsr j P,Zl.un. .L J
,
!
r
I00
Z00
J00 m~ u m
Flo. 2. Intensity distribution for the L~ Br line, recorded by a ~tandard method (1), corresponding to the scanning probe method described (2) and the neutralized distribution, calculated by the proposed method (3). In several cases, it is more convenient to use a device with a frequency smaller than the telewision one, and also to record by points, the build-up of impulses over a set time interval with the sample location fixed relative to the line scanner, then the sample is moved to a definite separation -and so on. Figure 3a represents a survey scheme for determining the concentration distribution of any -element, along the x axis. Here L is the probe dimension in the scanning direction. The probe size in the perpendicular direction is of the same order; its precise size has no principle value and does not participate in the calculations. The rectangular function 9(x) is the determination of electrons i n the limits of the probe: h~ (x) is the experimentally registered profile; f(x) is the actual profile being sought. The curve of bromine intensity change, h~ (x) obtained using a 60 x 40 ttm probe, corresponding to the above radiation-recording system from the same sample (Fig. In) is given in Fig. 2 (curve 2), .compared with a curve obtained by the standard method. In order to estimate the actual neutralized D B A P concentration distribution f(x), based on modified experimentally recorded bromine intensity distribution, h~(x), it is necessary to introduce a correction into the experimental data by enlarging the equipment. We showed that in the experimental conditions described, there is a simple means o f introducing this correction. The essence of this lies in the construction of a new curve hN(x) (ha(x) on Fig. 3b) from the h~(x) curve, the derivative of which at each point is the value of the desired function f ( x ) and the .'same point in relative units (Fig. 3c). The physical meaning of the function ht~(x) is the bromine
Concentration distribution of elements in heterogeneous polymer systems
1593
intensity distribution which would be recorded on the probe equipment, exceeding L by N times. Moreover, for a given L the choice of N is determined b.y the extent of the profile section which interests us. The basis of the proposed working method is given below. We suggest during the survey of a certain concentration profile f(x), using a probe of length L that a profile hi(x) (Fig. 4, curve 1) :is recorded. Let x~-xo=L, then xl
ht(x)= A j ' f ( r ) dr,
Xo<.x
(1)
xo
C 1
0
L
ZL
X
b h3t'x) ,
9tx)
/
0
i
L
",[h, Cx/I ZL
JL
X
Fro. 3. Scheme for recording radiation for study of concentration distribution of elements in heterogeneous systems (a) and the main stages in treating experimental data (b, c). The X-ray radiation detection is denoted by L
The constant A plays the part of a scale factor on the ordinate axis and does not affect the curve =shape, consequently it is ultimately omitted. By differentiation of both parts of equation (1) we obtained, by definition
dlq
--=f(x), dx
Xo
(2)
If the experiment is repeated with a probe of length 2L, then the apparatus records some funcl i o n hz(x). By going through a similar argument, we find that the section xo x2 may be readily -reduced to the desired function, according to the formula
dh2 dx
--=f(x),
Xo
(3)
:By carrying out experiments with increasing L by 3,4 . . . . . N times, we would obtain functions, .h3(x), h4(x) . . . . . hn(x), permitting calculation o f f ( x ) from formulae similar to (2) and (3), for
YE. D. POPOVA.etaL
1594
segments of length 3L, 4L ..... NL. The problem reduces to the reconstruction of the hypothetical: profile, h~.(x). Let us choose as Xo x, any point such as at on Fig. 4. We will put a2 = a t + L ; a3 =a2 + L = a t + 2 L ; ...; a n = a n _ t + L = a = + ( N - l ) L . Let us write down that integral (1) in these Which is. equivalent to points, in values of the original F(x) from the function f ( x )
hi(a1 ) = F(al) - F(xo) h=(a2) = F ( a 2 ) - F(at)
(4)
hi(a3) = F ( a 3 ) - F(a2) .
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hl(a,v) = F(a,v) -- F(a~._ t) We will add up these equalities N
ht(at) = F(as)--FCxo)
(5)i
I=l
!Bi, "Pel.un. 2
.%
\
o
Iwv I I I a" a t a'zxza a aJxaX,# m xoal t ~ 60 120 FIG. 4. Illustration of graphical constructions: l - e x p e r i m e n t a l l y recorded profile, hj (x); 2 - c o n s t r u c t e d profile, h,v(x); 3 - d e s i r e d neutralized concentration distribution, f ( x ) . By differentiating expression (5) and noting that F ' ( x o ) = 0 we obtain N
[ E h,(at)]'=F'(a.~,)=f(a2~)
(6)'
I=1
Therefore N
E h l ( a t ) = h~.(a~.)
(7),
I=1
The latter formula gives, in principle, the construction of the desired profile h,~.(x) (see Fig. 4, curve 2), by differentiation of which we obtained the neutralized true distribution intensity of intrinsic radiation, corresponding to an clement (see Fig. 4, curve 3). Transfer of the relative intensity values into absolute concentrations of the diffusant may be accomplished, for example, using standards or by starting from the overall quantity of the diffusing substance. The proposed method of surveying and treatment was tested out on a JSM-U3 microscope with a " K e r e x " microanalysis attachment. Comparison of this method with a standard for a " g o o d " sample, represented by a microsection with a triple sandwich of metallic type, A - B - A * sho~ved that the results of the two experiments agreed well. * The sandwich was prepared by vacuum atomization of Nd on to an Ni plate. Recording: was by the K= line of Ni.
Concentration distribution of elements in heterogeneous polymer systems
1595
Figure 2 (curve 3) gives the bromine intensity distribution, calculated by the pro-posed method for PVC samples treated by the first regime. This data, presented in .f(x)[f(O)-x coordinates, agrees with the concentrational distribution of plasticizer in a heterogeneous matrix with uniform distribution of porosity in the diffusion direction. It is evident that for samples with heterogeneous porosity distribution, the above treatment must be modified, since the recorded intensity depends on 2 factors: concentration and morphology. For a quantitative comparison of different sites of a sample in relation to homogeneity, one may use the area $1 occupied by corresponding elements of the heterostructure, related to the area of the probe used, So. We will term the value S * = SdSo, the effective irradiation surface. For the sample studied, S* has the meaning of the relative total sectional area of a particle, lying within the probe limits in a given sample site. Since, with the increase in sizes of the time-base used the degree of homogeneity* of distribution of heterostnictural compositions is increased according to the curve with saturation, a minimal probe is actually used, assuring efficient neutralization. 'Then the change inintensity of an element being analyzed will be connected only with the first factor-the change of its concentration, and not with a change of effective irradiating surface in the various sample sites. When using a 60x40 mm probe for samples, treated by the second regime (Fig. lb), S* is decreased by 2 during transfer of the presurface sections to the initial structure, in the depth of the material. In order to exclude the effect of the second factor, all the measured values of intensity under the same conditions will be put in: the radiation intensity with S* = 1 which is achieved in monolitic samples with the same mean concentrations of the element being analysed which are also in the heterogeneous sample. For this it is sufficient t o separate all intensity values of the magnitude of S* in the same points, assuming proportionality of intensity and radiating surface. The determination of S* may be carried out from photomicrographs'of the surface ,,vhich are obtained along the movement trajectory of the probe. Indirect confirmation of the truth of the S* determination for given samples is given by a representation of the surface under analysis by typical bromine radiation (Fig. lc, d). It is seen that the main contribution to the intensity, in a rather large"section will be the radiation generated in sections of corresponding particles, WhOse area is not difficult to determine. For a direct estimate of the ratio between intensity and S*, a supplementary experiment was carried out, in which the intensityof the K~CI lines and CI background were recorded simultaneously with the Br radiation and Br background. The intensity 9 was measured within the probe limits of 50 k 50 Itm. S* was also determined in this segment. The areas analysed were subsequerltly joined together, forming a perpendicular sample surface trajectory, 500-700 itm long. The precision in determining S* is ca. 15yo. The intensity of the CI line in pure PVi2, extrapolated to a monolith (which . . . .
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* The degree of homogeneity may be characterized, for example, in magnitude, by the inverse of dispersion of So in relation to the sample.
1596
YE. D. POPOVAet aL
must coincide with the intensity measured at a point), served as a standard for estimating the D B A P concentration along the trajectory. It is clear that at a constant diffusant concentration, the graph of dependence of intensity on effective radiating surface must be represented by a straight line, the slope of which is increased with concentration. The experimental results are represented in Fig. 5. The estimated nature of the D B A P concentrations and errors found in calculating the radiation areas are explained by the fact that points over a broad concentration range lie to each straight line. Nevertheless, the orooosed equations are sufficiently clearly followed.
Dt e l un.
IBr ~ I~Lun.
3
/
\
1o / Z
1
0.5
I
s~
FIG. 5
/
I
~1
zoo
'1
I
'%,I
4oox,,~
Fro. 6
FIG. 5. Dependence of intensity I on magnitude of effective radiating surface with DBAP concentrations of 45-55 (/), 60-65 (2) and 80--90% (3). FI~. 6. Neutralized intensity distribution for the L~ Br line for the samples depicted in Fig. la (1) and b (2) (2-without and 3-with account taken of morphology). Figure 6 presents neutralized Br intensity distribution, reduced to a single area, for a surface with adhesion, either taking account of the morphology or not. For comparison there is also given a distribution for a sample with homogeneous porous structure. It is seen that a calculation of the morphology leads to a substantial change in the nature of the distribution. In particular, for the studied trajectory, the extent o f the section with constant concentration amounts to 210 a m but that of the adhered region is 140 pm, which corresponds to the beginning o f a sharp drop in concentration on the curve without calculation of morphology. We note that with the need to introduce corrections for the atomic number, absorption and fluorescence, this will be made to the differential profile. Then the ratios, similar to curves 1 and 3 (see Fig. 6), will exhibit concentration distributions with precision up to a constant factor, connected with the differentiation of the original cu l:ve.
Concentration distribution of elements in"heterogeneous polymer systems
1597"
Analysis of the concentration distributions shows that bromine distribution for t the 2 regimes of plasticizing heterogeneous porous samples are represented by convex lines with. practically constant concentrations close to the surface. Such a character, from a formal viewpoint, is connected with concentrational dependence of the diffusion coefficient and localized distribution of the plasticizer within the particles of sintered PVC. Measurements of a single particle (Fig. le, f ) in a section, by the point probe method, show that the treatment regime does not cause adhesion of the original porous. structure characterized by uniform DBAP distribution throughout the particles. In the second case, the distribution has an extremal character. It is clear that with neutra-. lization of the intensity with some such particles, the resulting profile in the first case, when bulk diffusion is observed, will show a sharper concentration fall than in t h e second case, where bulk diffusion occurs in parallel with plasticizer transfer in relation to the communicating porous sy,stem, leading to a rapid and deeper penetration of it. Thus the survey method described, using additional information on the morphological features of heterogeneous systems, permits a substantial widening of the aims. of the investigation. Translated by C. W. CAPP