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Adhesion and properties of acrylic polymers at the substrate boundary
1920
I. V. VORONIN and V. V, LAVRENT'EV
9. Yu. Ye. S H A P I R O , S. I. S H K U R E N K O , O. K. S H V E T S O V a n d A. S. K H A C H A T U R O V ,
10.
11. 12. 13. 14.
Vysokomol. soyed. A21: 803, 1979 (Translated in Polymer Sci. U.S.S.R. 21: 4, 1979) A. A. P A N A S E N K O , V. N. ODINOKOV, Yu. B. M O N A K O V , L. M. K H A L I L O V a n d A. S. BEZGINA, Vysokomol. soyed. B19: 656, 1977 (Not translated in Polymer Sei. U.S.S.R.) A. S. KHACHATUROV, E. R. DOLINSKAYA and Ye. L. ABRAMENKO, Vysokomol. soyed. B19: 518, 1977 (Not translated in Polymer Sci. U.S.S.R.) G. GATTI and A. CARBONARO, Makromolek. Chem. 175: 1627, 1974 L. P. LINDEMAN and J. O. ADAMS, Analyt. Chem. 43: 1245, 1971 G. C. LEVY and G. L. NELSON, Rukovodstvo po YaMR 13C (Handbook on lsC NMR). p. 196, "Mir", 1975 (Russian translation)
0032-3950/79/0801-1920507.50/0
Polymer Science U.S.S.R. Vol. 21. pp. 1920-1930. © Pergamon Press Ltd. 1980. Printed in Poland
ADHESION AND PROPERTIES OF ACRYLIC POLYMERS AT THE SUBSTRATE BOUNDARY* I . V. VORONIhT
and
V. V. LAVRENT'EV
(Received 2 July 1978) The effect of the chemical structure of acrylic polymers on their adhesion properties and on the characteristics of the boundary layers has been investigated. I t has been found t h a t a strong adhesion interaction between polymers and substrate leads to non-uniformity in the properties of the polymer through the thickness of t h e b o u n d a r y layer: for flexible chain polymers of low polarity, the non-uniformity is in density, and for polymers with highly polar carboxyl groups, in the mobility of the structural units. Near to the substrate surface, the mobility of the structural units of the polymers under consideration is less t h a n in the volume, a fact which is connected with the "freezing" of vibrations. The kinetics of formation and rupture of adhesive bon~ts and the characteristics of the -temperature dependence of the adhesive strength are determined b y the most mobile structural units in the polymers investigated. 'THERE is u n d o u b t e d l y a c o n n e c t i o n b e t w e e n a d h e s i o n a n d t h e specific b o u n d a r y properties of polymers. The factor which determines the characteristics of any : i n t e r a c t i o n is t h e r e d u c t i o n i n f r e e s u r f a c e e n e r g y a s a r e s u l t o f t h i s i n t e r a c t i o n [1]. However, only an appreciable adhesive interaction can lead to a substantial distinction between the boundary properties of the polymer and those in the bulk and t o a c h a n g e i n f r e e s u r f a c e e n e r g y . * Vysokomol. soyod. A21: No. 8, 1742-1750, 1979.
Adhesion and properties of acrylic polymers
1931
Unfortunately investigators rarely connect the structure and properties of t h e surface layers with their adhesive properties. At the same time, the establishment of a connection between these properties has considerable scientific and practical interest and would enable the processes which occur at the interface to be better understood and the properties of the adhesive joint to be predicted. The ad_kesive properties of polymers are usually characterized b y the adhesive strength. The purely adhesive strength a can be represented as 0"~---hi fay,
(1)
where n I is the concentration of bonds between active eentres of polymer molecules and active centres of the substrate and fay is the average strength of a single bond. As is shown below, the number nl is related to the average bond energy and consequently with fay as well. However, the concept of adhesive strength in the form nl fay enables analysis of the results of measurements to be simplified and enables the factors which determine such a complex phenomenon as adhesion to be more easily revealed. The two level model is quite a goo~ qualitative model of an adhesive joint. In this case, the active centres of the polymer macromolecule exist in two states [2]: 1) combined with active centres of the substrate, giving a bond concentration hi; and 2) combined with active centres of macromolecules similar to itself, giving a bond concentration n2. Thus nl-~n2=no=COnSt,
(2)
where n o is the total concentration of possible bonds, f The process of forming and breaking bonds has a kinetic character and is determined b y a frequency of formation v~ and a frequency of rupture vz of adhesive bonds. I t m a y be assumed [2] that under equilibrium conditions no n 1-
I_~Vl/V2
(3)
W e assume that v~=vo~ exp (-- U~/RT) ,
(4)
where Vol is a constant, U~ is the activation energy for the formation or rupture of adtmsive bonds, R is the universal gas constant and T the temperature, °K. Although the adhesive strength in eqn. (1) is determined b y the two quantities nl and fay, consideration of the phenomenon as being molecular kinetic indicates t h a t these quantities are closely connected through the frequency v~, since fay depends on the ratio Ut/Ul+l. On the basis of this type of concept of a~dhesive strength, it m a y be assumed t h a t changes in the density of tke polymer, p, and in its local viscosity r/occurring in the boundary layer can be related with the quantities nl and fay in eqn. (1). I f there are changes in nl, the density of the polymer's boundary layer lying
I. V. VORONIr¢ and V. V. LAVRENT'EV
1922
directly in contact with the solid surface m a y be changed, and if fay changes, the frequency r and, consequently, t/ m a y change, since t/--1/r. The effect of adhesive interaction on the boundary density of the polymer and its local viscos i t y have therefore been investigated in t h e present work. The following acrylic polymers were selected for the investigation: polymethylacrylate (PMA) with _M= 1.5 × 105, and copolymers of methylacrylate (MA) and methacrylic acid (MAA) taken at the rate of 5 (5 MAA), 10 (10 MAA) and 30~/o {30 MAA). All the polymera selected were freed from low-molecular fractions b y repeated precipitation. The following were taken as substrates: glass with a polished surface; the same glass with sputtered aluminium and a fluoroplastic film. The most mobile groups in the polymers probably determine the kinetics of formation a n d rupture of a adhesive bonds. I n the present case, if one considers the two types of groups existing in the polymers, namely, - - C = O and carboxyl groups, the former are clearly the
I
OCHa m o r e mobile since the carboxyl groups are strongly linked b y intermolecular interactions. The mobility of the - - C = O groups was therefore investigated in the work.
I OCHs
The properties of the polymers in the layers bounding the substrate surface were determined b y the molecular probe method [3]. The molecular probe (luminor 2z) was introduced into the polymer solution from which coatings of various layers were then obtained on the substrates. Fluorescence of the molecular probe was excited b y UV irradiation with ~max = 3 6 5 rim. The density of the polymers in the b o u n d a r y layers was assessed from the position of the m a x i m u m in the fluorescence spectrum [3] and the local viscosity from the t h e r m a l extinction of the molecular probe in the polymeric m a t r i x [4].
I t has been shown previously [3] that, for luminophors which form weak complexes with groups of the polymer of low activity (in particular, in the case of luminor 2z), the way in which the maximum of the fluorescence spetrum depends on the density of the polymeric matrix into which these luminophors are introduced is expressed by a single generalized curve. This curve m a y be used to assess the boundary density of MA-MAA copolymers. For this purpose, the distribution of the energy intensity in the fluorescence spectrum, I(v) o f luminor 2z in the copolymer is represented in the form: I (V) = I 1 (V)-4-I2 (V) + I 1 2 (V),
(5),,
where 11 (r) is the energy intensity of the fluorescence of the complex formed between the luminor and the - - C = O group of the copolymer; 12 (r) is the energy
I
OCH3 intensity of the fluorescence of the complex formed between the luminor and the e a r b o x y l g r o u p o f t h e c o p o l y m e r ; a n d 112 (r) is a c o m p o n e n t t h a t t a k e s a c c o u n t o f t h e m u t u a l effect o f t h e c a r b o x y l a n d - - C = O groups in the copolymer. With
I
OCH.
Adhesion and properties of acrylic polymers
1923
small concentrations of MAA in the copolymers and at low temperatures, t h e component Ii~(v ) can be neglected. Hence:
Ii(v)=I(v)-12(v).
(6),
For the copolymers investigated, I2 (v) was found by introducing the same amounts of the luminor 2z into equal volumes of MAA, PMA and MA-MAA copolymers. The values of 11 (v) having been obtained from eqn. (6), the density .~0C7•par•$
.I 02
;00
+3
It i
1.oo
+_.+
+
0
~N 2
g'08
0"8
8 FiG. 1
80 ~,,/,rn
I -
*F 0.08
0.8
2/~"
8 FIG. 2
FIG. 1. Dependence of the density of acrylic polymers on the thickness, 5, of the polymer. layer deposited on glass (1, 2, 3, 4) a n d aluminium (1') for: 1 and I ' ' P M A ; 2 - - 5 MAA;: 3-- 10 MAA and 4-- 30 MAA. FIG. 2. Dependence of the parameters El, E= and Ttrans in eqn. (10) on the thickness of t h e layer deposited on glas s(1, 2, 3, 4) and aluminium (1') for: 1 and I ' - - P M A ; 2 - - 5 M A A ; 3--10 MAA and 4 - - 3 0 MAA. I - - E l and I I - - E v
1 of the copolymers in the layers bounding the substrate were then found from the generalized curve. Figure 1 shows how the density of the polymers depends. on the thickness of the polymer layer. For the flexible chain polymer PMA, the interaction with the substrate surface led to a non-monotonic change in the density with the polymer thickness. The densities close to the surface are thus greater than in the volume. As t h e rigidity of the polymer chain was increased with the introduction of strongly polar carboxyl groups, this relationship was converted into a monotonic one and the density of the layer close to the substrate surface gradually became less and, for the strongly polar polymer, 30 M_dA, it became less than that in the volume. For deposition of the polymers on to an inactive surface (the fluoroplastic), no change in density was obsorvedL with the thickness.
]924
I . V . VORON*~ and V. V. LAVRENT'EV
The local viscosity of the polymers was found from the relationship [5]
IT----~IT[~+fl(~II)]-~,
(7)
where IT is the fluorescence intensity at the maximum of the spectrum; T is the temperature, °K, and ~ and fl are constants. In investigations of the thermal -extinction of luminor 2z in MAA it has been found that the complexes formed between the luminor and the carboxyl groups are not subject to thermal extinction. The energy intensity of the fluorescence of the luminor 2z in the copolymers can therefore be represented b y an equation similar to eqn. (6):
I (v)=Io (v)+IT (v),
(8)
w h e r e Io(v ) is the component which does not undergo thermal extinction and is equal to the intensity of the luminescence from the complex formed b y the luminor and the carboxyl group; IT(r) is the component which does undergo t h e r m a l extinction and is equal to the intensity of the luminescence from the ~eomplex formed b y the luminor and the --C----O. Thus the thermal extinction
I
OCH8
in the copolymers is determined b y the mobility of the same groups as in PMA. Thus: IT(v)-----I (v)--Io(v ) (9) I0 (v) was found b y introducing the same quantities of the luminor 2z into equal volumes of MAA, PMA and the MA-MAA copolymers. The constants a and fl were found b y investigating the thermal extinction of luminor 2z in MA and in acetone. The temperature dependence of the local viscosities t/ of the polymers investigated was described well b y the equation: th:~/o ~ exp
(E1/RT)
,
(10)
where E1 is the activation energy for the process, R the universal gas constant, T the temperature, °K, and ~/o, is a constant. In semilogarithmic coordinates, In ~/and 1/T, this relationship was expressed b y two straight lines with different slopes with respect to the abscissa axis. The high temperature branch was found to depend on the concentration of the luminor in the polymer. This points to a cooperative mechanism in the vibrational process caused b y a joint effect of the vibrating --C----O groups.As the concentration c of the luminor 2z approaches
I
OCH3 zero, the relationship described b y eqn. (10) undergoes a change at the point T----Ttrans into a similar relationship with the constants ~]0~and E~; E~ is found to be greater than E 2. The w a y in which the parameters E 1, E 2 and Ttran, depend on the thickness of the polymer layer deposited on to the active substrate is shown in Fig. 2. •
Adhesion and properties of acrylic polymers
1925
The interaction of polymers with substrate surfaces did not affect the values of E1 and E2. Neither did the concentration of carboxyl groups in the copolymers affect these quantities. On the other hand, Ttrans depended essentially both on the concentration of carboxyl groups and also on the thickness of the polymer layer on the substrate surface. In sufficiently thick layers, as the chain rigidity increased with the introduction of carboxyl groups, Ttrans rose monotonically. The interaction with the surface of an active substrate led to different changes in Ttrans for the different polymers. A monotonic increase in Ttrans was observed for PMA as the layer thickness was decreased. With the introduction of carboxyl groups into the chain, the dependence of Ttrans on layer thickness became nonmonotonic. Primarily Ttrans was greater close to the substrate surface than in the volume. When the polymers were deposited on to the inactive surface of the fluoroplastic, no changes in El, E2 and Ttrans were observed with a change in the thickness of the polymer layer. The adhesive properties of the polymers selected were determined by the straight tensile method with a constant rate of loading. The temperature dependence of the adhesive strength was investigated in three conditions of testing; 1) at a constant temperature of rupture, Tr; 2) with a constant temperature of contact, To; and 3) with T r = T c . With this type of test, the adhesive strength is determined by the expression a=nafav,
(11)
where n3
n3=nl(1--Ava) ,
(12)
where A is a constant. The frequency v was expressed by an equation similar to the ~Vogel-Fulcher-Tamman eqn. [6] since it was considered that it takes t h e nature of the polymer into account better than does eqn. (4):
v~----Vo~exp [-- U~/R (T--T~)],
(13)
where T~ is a characteristic temperature related to the glass temperature of the polymer and U'~ is a temperature coefficient related to the activation energy for the process. By taking account of eqn. (3), (12) and (13) and making the approximation TI=T~=Ta, eqn. (11) m a y be written in the following way 0"=
av no
l + e x p [A U'/R (To--T,)]
{1--B exp [--U~/R(Ttrans--T3)]},
<14)
I. V. VORONINand V. V. I~VRENT'~.V
1926
where AU'-=-U~--U~ and B is a constant. Figure 3 shows the measurements of t h e way in which the adhesive strength depends on temperature in experiments u n d er the three conditions for the system PMA-glass.
~o, kS/cm~
~cal/mole f
I~
c..3
~
qO
60
30
(,, I
ro
I
~o0 ~°C
60
\
~I 3 20 " ~ ' l ~ < - " ~ i O
l~m. 3
10
% I
20
2O
30 MAA,w~.%
Fro. 4
1~io. 3. Temperaturedependence of the adhesive strength for the system PMA-glass for the following conditions: 1-- Tc ~ const = 80°C; 2-- Trupt~ const = 25°C and] 3-- Tc= Trupt. The curves correspond to the theory and the points are experimental. FIG. 4. The effect of MAA concentration in acrylic polymers on their adhesive strength (in accordemce with eqn. (14)) for the interaction between the polymers and the following: 1, 2 and 3--glass; l'--aluminium. 1 and 1' refer to ~0, 2 to T1 and 3 to U.
Figure 4 shows the effect of the MAA concentration in the polymers on t h e parameters Us, T 1 and ao-~favno/{1-~exp[AU/R(Tc--T1)]}. These parameters were found from the determination of the adhesive strength under t he three conditions testing. The increase in T1 with an increase in the MAA concentration is in agreement with the change in Ttrans (Fig. 2) and is connected with the increase in the rigidity of the polymer chains when carboxyl groups are introduced. The fact t h a t A U' (Fig. 4) and E1 and E2 (Fig. 2) are constant as t he MAA concentration is increased is clearly not a chance result. T hi s can be explained b y the fact t h a t the kinetics of forming and breaking adhesive bonds between the polymer and the substrate and the characteristics of the temperat u r e dependence of the ~adhesive strength are determined by the most mobile groups in the polymers, in this case, b y --C----O groups. These groups first
I
OCH3 form bonds with active centres on the substrate surface. Thus the number of eonformational possibilities open to t h e molecules decreases and this, according t o Eyring [1], entails an increase in the probability of the transfer of the re-
Adhesion and properties of acrylic polymers
1927
quired amount of energy in the one direction and, as a consequence, an increase in the probability of forming adhesive bonds by other groups of the polymers. The process is accompanied by lower energy losses and, during the formation of bonds by carboxyl groups thereafter, approximately the same barrier is overcome as in the formation of bonds by the - - C = O groups. The breakdown
I
OCH8 of bonds at the surface also occurs in the first instance at the location of - - C = O
I
OCH, groups. This process increases the stress applied to the remaining bonds aud this, according to Zhurkov [7], should reduce t h e activation barrier to their rupture. Let us now consider how the values of nl and fay affect a0, according to eqn. (1). The value of a0 m a y be represented as: O'O-----nllfav 1(1--c)%nlJav ~c,
(15)
where n l l and fay, are the parameters in oqn. (1) for bonds formed by --C-----O
I
OOHs groups; n12 and fay 2 are the same quantities for bonds formed by carboxyl groups and c is the molar fraction of carboxyl groups. Since nl is proportional to the density of the boundary layer pb, eqn. (15) m a y be rearranged in the form: ao ~- apbfav l ( 1 - - c ) = apcfav zc,
(16 )
where a is a coefficient of proportionality. On t h e basis of the values obtained for ao (Fig. 4) and pb (Fig. 1), afav 1 and afav ~ were calculated. The results of t h e calculation are shown in the Table. I t follows from the Table and Fig. 1 that, when a polymer having active groups of only one type (PMA) interacts with different substrates, changes in t h e adhesive strength involve •1 and also fay. When polymers having two types of active groups (5 MAA, 10 MAA) interact with a substrate of a particular nature, the predominant formation of bonds by one type of group was not observed. Bonds with the substrate surface were distributed in proportion to the n u m b e r of groups existing in the polymer. The fact t h a t the calculated values of fay Jfav 1 were approximately the same for 5 MAA and 10 MAA points to this conclusion. Thus the specific force pertaining to one carboxyl group of the polymer is approximately 6 times as great as t h a t pertaining to one - - C = O group. When a rigid
I
OCHs chain polymer with a high concentration of carboxyl groups (30 MAA) interacted with the substrate surface, the complete possible number of contacts b e t w e e n the polymer and the substrate was not realized. The low calculated
I. V. VoRo~rn~ and V. V. LAVRENT'EV
1928
value of afar j for 30 MAA indicates this. If all possible contacts between thia polymer and the substrate were formed, by taking account of the values of pb (Fig. 1) and the calculated values afar 1 and afar 2 for complete contact (see Table), the adhesive strength a0 would be approximately 60 kg/cm 2 according to eqn. (16). C H A R A C T E R I S T I C S OF T H E A V A R A G E S T R E N G T H OF T H E A D H E S I V E B O N D F O R V A R I O U S G R O U P S OF A C R Y L I C P O L Y M E R S
Polymer
PMA
Substrate
Aluminium Glass
afay,,
I a/av2 kg" cm/g
5 MAA
20"5 28"5 28"5
170
10 MAA 30 MAA
28.5 28.5
180 7.7*
• Adhesive contact
~e&V2/faV I
6 6-4
incomplete.
In considering, in conjunction, the results from the investigation of the adhesive properties and the boundary properties of the polymers, we may note the following. When there is high adhesion of the polymer to the substrate, ~here is characteristically non-uniformity in the properties of the polymer through the thickness in the part of the polymer bounding the substrate surface. In this case, it is possible to distinguish two layers differing in their properties from the volume: a layer lying directly adjacent to the substrate surface and an intermediate layer. The first layer is thus about one-tenth the thickness of the second. For polymers with flexible chains (PMA), non-uniformity of the layer with respect to density is characteristic (Fig. 1), a fact which is evidently related to the high number of bonds between the polymer and the substrate (in accordance with eqn. (16)). In the case of a more rigid chain polymer containing highly polar carboxyl groups (5 MAA, 10 MAA, 30 MAA), a non-monotonic change ~n the mobility of the polymer chains through the thickness of the layer is observed (Fig, 2), a fact which is evidently connected with the high average bond energy (see Table). Possible structures of the boundary layers for polymers with flexible chains (PMA) and for polymers with highly polar carboxyl groups (5 MAA, 10 MAA, 30 MAA) are shown in Figures 5 and 6 respectively. The first layer of a flexible chain polymer lying directly adjacent to the substrate surface (thickness, ~1) has a dense folded structure with a fold length of approximately 3-4 segments. The second layer (thickness, ~2) has an open structure of approximately the same thickness as the length of a macromolecule. The extended macromolecules linked to t h e substrate surface impede dense packing of the macromo!ecu!es in this layer. The more rigid chains of macromolecules (copolymers 5 MAA, 10 MAA,
Adhesion and properties of acrylic polymers
1929~
30 MAA) with a high bond energy do not form a folded structure and the bounda r y layer J1, which is approximately 10-20 segments thick and has an ordered structure, gradually merges into the volume. The increase in bond energy leads.
/,,~/flflf/~
,,.,/l',lfJflflf/l'l/fl/fff/Tffl'l'~.
FIG. 5
FIG. 6
FxG. 5. Structure of the boundary layer of a flexible-chain polymer (PMA) for a high ad-hesion interaction with the substrat~ surface. Fie. 6. Structure of the boundary layer of a polymer having highly polar oarboxyl groups~ (5 MAA, 10 MAA and 30 MAA) in the case of a high adhesion interaction with the substrato surface. to a reduction in the possibility of the bonds migrating along the surface of the~ solid body and, as a consequence, to an increase in the number of contacting macromolecules. The mobility of --C----O groups of a flexible chain polymer (PMA) decreases.
I
OCH 3 monotonically as the thickness decreases but for polymers with carboxyl groups, the change follows a curve with a maximum. This is connected with the f a c t that, although the intermediate layer of the latter polymers is more ordered, its density is equal to the volume density; t h a t is, its density is less than t h a t characteristic of more ordered structures. Greater freedom is therefore created for the groups under consideration. I t should be noted t h a t the change in mobility is related to a change in the glass temperature of the polymer and is not related to any change in the potential barrier to vibrations. The fact t h a t Ttrans changes whereas E1 and E 2 remain unchanged as the thickness J is decreased is evidence of this (Fig. 2). In particular, vibrations appear feebly or are "frozen" in d i r e c t proximity to the substrate surface. In connection with this, the actual contact between the polymer and the substrate begins to be diminished, which is especially appreciable in the case of 30 MAA. I n order to increase the mobility of the active groups of the polymers and toincrease the real contact between the polymer and the substrate, elevated tern-
1930
I.V. VoBo~n~ and V. V. LAV~I~T'EV
peratures are generally used, lying above the transition temperatures of the pure tIolymers. I n certain eases, however, it is impossible in principle to achieve complete contact if the decomposition temperature of the polymer lies below these temperatures. This is found to be the case for the system 30 MAA-glass. Another method of increasing the area of real contact is to reduce the activation barrier to interaction between the polymer and the substrate. This is achieved by selecting an appropriate mixture of "poor" and "good" solvents or by intro~dueing highly mobile functional groups into the macromolecular chain. I n our •case, an acetone-benzene mixture was selected as a mixture of this type and - - C ~ O groups were selected as the appropriate functional groups. A negative
I
OCH3 factor in reducing the activation barrier by these methods is, in the first ease, the difficulty of removing the solvents adsorbed on to the substrate surface, a n d in the second case, the lowering of the activation barrier for rupture of the -adhesive bonds. Thus the characteristics of the adhesive interaction of acrylic polymers are also determined by their boundary properties. A change in the chemical composition of the polymers leads to a corresponding change in their adhesive and b o u n d a r y properties. Thus the most mobile groups of the polymers determine t h e characteristics of the temperature dependence both of the adhesive strength a n d also of the mobility of the polymers' maeromolecules in the boundary layer. The authors wish to t h a n k Yu. M. Malinskii for his interest in the work and f o r a number of valuable comments on the manuscript. Translated by G. F. MODLE~ REFERENCES
1. S. CLASSTONE, K. LAIDLER and G. EYRING, Teoriya absolyutnykh skorostei reaktsii (Theory of Absolute Reaction Rates). Izd-vo inostr, lit., 1948 (Russian translation) :2. L. F. PLISKO, K. K. OSTREIKO, V. V. LAVRENT'YEV, V. L. VAKULA and S. S. VOYUTSI{II~ Vysokomol. soyed. 15: 2529, 1974 (Not translated in Polymer Sci. U.S.S.R.) 3. V. V. LAVRENT'YEV and I. V. VORONIN, Kolloidn. zh. 36: 163, 1974 -4. I. V. VORONIN and V. V. LAVRENT'YEV, V kn. Termodinanicheskiye i strukturnyye svoistva granichnykh sloyev polimerov (In the book: Thermodynamic and Structural Properties of Boundary Layers in Polymers). p. 53, Izd. "Naukova dumka", 1976 -5. {~. OSTER and C. NISHIJIMA, J. Amer. Chem. Soc. 78: 1581, 1956 6. H. VOGEL, Phys. Z., 22: 645, 1921 "7. S. N. ZHURKOV and S. A. ABASOV, Vysokomol. soyed. 3: 439, 1961 (Not translated in Polymer Sci. U.S.S.R.)
I. V. VORONIN and V. V, LAVRENT'EV
9. Yu. Ye. S H A P I R O , S. I. S H K U R E N K O , O. K. S H V E T S O V a n d A. S. K H A C H A T U R O V ,
10.
11. 12. 13. 14.
Vysokomol. soyed. A21: 803, 1979 (Translated in Polymer Sci. U.S.S.R. 21: 4, 1979) A. A. P A N A S E N K O , V. N. ODINOKOV, Yu. B. M O N A K O V , L. M. K H A L I L O V a n d A. S. BEZGINA, Vysokomol. soyed. B19: 656, 1977 (Not translated in Polymer Sei. U.S.S.R.) A. S. KHACHATUROV, E. R. DOLINSKAYA and Ye. L. ABRAMENKO, Vysokomol. soyed. B19: 518, 1977 (Not translated in Polymer Sci. U.S.S.R.) G. GATTI and A. CARBONARO, Makromolek. Chem. 175: 1627, 1974 L. P. LINDEMAN and J. O. ADAMS, Analyt. Chem. 43: 1245, 1971 G. C. LEVY and G. L. NELSON, Rukovodstvo po YaMR 13C (Handbook on lsC NMR). p. 196, "Mir", 1975 (Russian translation)
0032-3950/79/0801-1920507.50/0
Polymer Science U.S.S.R. Vol. 21. pp. 1920-1930. © Pergamon Press Ltd. 1980. Printed in Poland
ADHESION AND PROPERTIES OF ACRYLIC POLYMERS AT THE SUBSTRATE BOUNDARY* I . V. VORONIhT
and
V. V. LAVRENT'EV
(Received 2 July 1978) The effect of the chemical structure of acrylic polymers on their adhesion properties and on the characteristics of the boundary layers has been investigated. I t has been found t h a t a strong adhesion interaction between polymers and substrate leads to non-uniformity in the properties of the polymer through the thickness of t h e b o u n d a r y layer: for flexible chain polymers of low polarity, the non-uniformity is in density, and for polymers with highly polar carboxyl groups, in the mobility of the structural units. Near to the substrate surface, the mobility of the structural units of the polymers under consideration is less t h a n in the volume, a fact which is connected with the "freezing" of vibrations. The kinetics of formation and rupture of adhesive bon~ts and the characteristics of the -temperature dependence of the adhesive strength are determined b y the most mobile structural units in the polymers investigated. 'THERE is u n d o u b t e d l y a c o n n e c t i o n b e t w e e n a d h e s i o n a n d t h e specific b o u n d a r y properties of polymers. The factor which determines the characteristics of any : i n t e r a c t i o n is t h e r e d u c t i o n i n f r e e s u r f a c e e n e r g y a s a r e s u l t o f t h i s i n t e r a c t i o n [1]. However, only an appreciable adhesive interaction can lead to a substantial distinction between the boundary properties of the polymer and those in the bulk and t o a c h a n g e i n f r e e s u r f a c e e n e r g y . * Vysokomol. soyod. A21: No. 8, 1742-1750, 1979.
Adhesion and properties of acrylic polymers
1931
Unfortunately investigators rarely connect the structure and properties of t h e surface layers with their adhesive properties. At the same time, the establishment of a connection between these properties has considerable scientific and practical interest and would enable the processes which occur at the interface to be better understood and the properties of the adhesive joint to be predicted. The ad_kesive properties of polymers are usually characterized b y the adhesive strength. The purely adhesive strength a can be represented as 0"~---hi fay,
(1)
where n I is the concentration of bonds between active eentres of polymer molecules and active centres of the substrate and fay is the average strength of a single bond. As is shown below, the number nl is related to the average bond energy and consequently with fay as well. However, the concept of adhesive strength in the form nl fay enables analysis of the results of measurements to be simplified and enables the factors which determine such a complex phenomenon as adhesion to be more easily revealed. The two level model is quite a goo~ qualitative model of an adhesive joint. In this case, the active centres of the polymer macromolecule exist in two states [2]: 1) combined with active centres of the substrate, giving a bond concentration hi; and 2) combined with active centres of macromolecules similar to itself, giving a bond concentration n2. Thus nl-~n2=no=COnSt,
(2)
where n o is the total concentration of possible bonds, f The process of forming and breaking bonds has a kinetic character and is determined b y a frequency of formation v~ and a frequency of rupture vz of adhesive bonds. I t m a y be assumed [2] that under equilibrium conditions no n 1-
I_~Vl/V2
(3)
W e assume that v~=vo~ exp (-- U~/RT) ,
(4)
where Vol is a constant, U~ is the activation energy for the formation or rupture of adtmsive bonds, R is the universal gas constant and T the temperature, °K. Although the adhesive strength in eqn. (1) is determined b y the two quantities nl and fay, consideration of the phenomenon as being molecular kinetic indicates t h a t these quantities are closely connected through the frequency v~, since fay depends on the ratio Ut/Ul+l. On the basis of this type of concept of a~dhesive strength, it m a y be assumed t h a t changes in the density of tke polymer, p, and in its local viscosity r/occurring in the boundary layer can be related with the quantities nl and fay in eqn. (1). I f there are changes in nl, the density of the polymer's boundary layer lying
I. V. VORONIr¢ and V. V. LAVRENT'EV
1922
directly in contact with the solid surface m a y be changed, and if fay changes, the frequency r and, consequently, t/ m a y change, since t/--1/r. The effect of adhesive interaction on the boundary density of the polymer and its local viscos i t y have therefore been investigated in t h e present work. The following acrylic polymers were selected for the investigation: polymethylacrylate (PMA) with _M= 1.5 × 105, and copolymers of methylacrylate (MA) and methacrylic acid (MAA) taken at the rate of 5 (5 MAA), 10 (10 MAA) and 30~/o {30 MAA). All the polymera selected were freed from low-molecular fractions b y repeated precipitation. The following were taken as substrates: glass with a polished surface; the same glass with sputtered aluminium and a fluoroplastic film. The most mobile groups in the polymers probably determine the kinetics of formation a n d rupture of a adhesive bonds. I n the present case, if one considers the two types of groups existing in the polymers, namely, - - C = O and carboxyl groups, the former are clearly the
I
OCHa m o r e mobile since the carboxyl groups are strongly linked b y intermolecular interactions. The mobility of the - - C = O groups was therefore investigated in the work.
I OCHs
The properties of the polymers in the layers bounding the substrate surface were determined b y the molecular probe method [3]. The molecular probe (luminor 2z) was introduced into the polymer solution from which coatings of various layers were then obtained on the substrates. Fluorescence of the molecular probe was excited b y UV irradiation with ~max = 3 6 5 rim. The density of the polymers in the b o u n d a r y layers was assessed from the position of the m a x i m u m in the fluorescence spectrum [3] and the local viscosity from the t h e r m a l extinction of the molecular probe in the polymeric m a t r i x [4].
I t has been shown previously [3] that, for luminophors which form weak complexes with groups of the polymer of low activity (in particular, in the case of luminor 2z), the way in which the maximum of the fluorescence spetrum depends on the density of the polymeric matrix into which these luminophors are introduced is expressed by a single generalized curve. This curve m a y be used to assess the boundary density of MA-MAA copolymers. For this purpose, the distribution of the energy intensity in the fluorescence spectrum, I(v) o f luminor 2z in the copolymer is represented in the form: I (V) = I 1 (V)-4-I2 (V) + I 1 2 (V),
(5),,
where 11 (r) is the energy intensity of the fluorescence of the complex formed between the luminor and the - - C = O group of the copolymer; 12 (r) is the energy
I
OCH3 intensity of the fluorescence of the complex formed between the luminor and the e a r b o x y l g r o u p o f t h e c o p o l y m e r ; a n d 112 (r) is a c o m p o n e n t t h a t t a k e s a c c o u n t o f t h e m u t u a l effect o f t h e c a r b o x y l a n d - - C = O groups in the copolymer. With
I
OCH.
Adhesion and properties of acrylic polymers
1923
small concentrations of MAA in the copolymers and at low temperatures, t h e component Ii~(v ) can be neglected. Hence:
Ii(v)=I(v)-12(v).
(6),
For the copolymers investigated, I2 (v) was found by introducing the same amounts of the luminor 2z into equal volumes of MAA, PMA and MA-MAA copolymers. The values of 11 (v) having been obtained from eqn. (6), the density .~0C7•par•$
.I 02
;00
+3
It i
1.oo
+_.+
+
0
~N 2
g'08
0"8
8 FiG. 1
80 ~,,/,rn
I -
*F 0.08
0.8
2/~"
8 FIG. 2
FIG. 1. Dependence of the density of acrylic polymers on the thickness, 5, of the polymer. layer deposited on glass (1, 2, 3, 4) a n d aluminium (1') for: 1 and I ' ' P M A ; 2 - - 5 MAA;: 3-- 10 MAA and 4-- 30 MAA. FIG. 2. Dependence of the parameters El, E= and Ttrans in eqn. (10) on the thickness of t h e layer deposited on glas s(1, 2, 3, 4) and aluminium (1') for: 1 and I ' - - P M A ; 2 - - 5 M A A ; 3--10 MAA and 4 - - 3 0 MAA. I - - E l and I I - - E v
1 of the copolymers in the layers bounding the substrate were then found from the generalized curve. Figure 1 shows how the density of the polymers depends. on the thickness of the polymer layer. For the flexible chain polymer PMA, the interaction with the substrate surface led to a non-monotonic change in the density with the polymer thickness. The densities close to the surface are thus greater than in the volume. As t h e rigidity of the polymer chain was increased with the introduction of strongly polar carboxyl groups, this relationship was converted into a monotonic one and the density of the layer close to the substrate surface gradually became less and, for the strongly polar polymer, 30 M_dA, it became less than that in the volume. For deposition of the polymers on to an inactive surface (the fluoroplastic), no change in density was obsorvedL with the thickness.
]924
I . V . VORON*~ and V. V. LAVRENT'EV
The local viscosity of the polymers was found from the relationship [5]
IT----~IT[~+fl(~II)]-~,
(7)
where IT is the fluorescence intensity at the maximum of the spectrum; T is the temperature, °K, and ~ and fl are constants. In investigations of the thermal -extinction of luminor 2z in MAA it has been found that the complexes formed between the luminor and the carboxyl groups are not subject to thermal extinction. The energy intensity of the fluorescence of the luminor 2z in the copolymers can therefore be represented b y an equation similar to eqn. (6):
I (v)=Io (v)+IT (v),
(8)
w h e r e Io(v ) is the component which does not undergo thermal extinction and is equal to the intensity of the luminescence from the complex formed b y the luminor and the carboxyl group; IT(r) is the component which does undergo t h e r m a l extinction and is equal to the intensity of the luminescence from the ~eomplex formed b y the luminor and the --C----O. Thus the thermal extinction
I
OCH8
in the copolymers is determined b y the mobility of the same groups as in PMA. Thus: IT(v)-----I (v)--Io(v ) (9) I0 (v) was found b y introducing the same quantities of the luminor 2z into equal volumes of MAA, PMA and the MA-MAA copolymers. The constants a and fl were found b y investigating the thermal extinction of luminor 2z in MA and in acetone. The temperature dependence of the local viscosities t/ of the polymers investigated was described well b y the equation: th:~/o ~ exp
(E1/RT)
,
(10)
where E1 is the activation energy for the process, R the universal gas constant, T the temperature, °K, and ~/o, is a constant. In semilogarithmic coordinates, In ~/and 1/T, this relationship was expressed b y two straight lines with different slopes with respect to the abscissa axis. The high temperature branch was found to depend on the concentration of the luminor in the polymer. This points to a cooperative mechanism in the vibrational process caused b y a joint effect of the vibrating --C----O groups.As the concentration c of the luminor 2z approaches
I
OCH3 zero, the relationship described b y eqn. (10) undergoes a change at the point T----Ttrans into a similar relationship with the constants ~]0~and E~; E~ is found to be greater than E 2. The w a y in which the parameters E 1, E 2 and Ttran, depend on the thickness of the polymer layer deposited on to the active substrate is shown in Fig. 2. •
Adhesion and properties of acrylic polymers
1925
The interaction of polymers with substrate surfaces did not affect the values of E1 and E2. Neither did the concentration of carboxyl groups in the copolymers affect these quantities. On the other hand, Ttrans depended essentially both on the concentration of carboxyl groups and also on the thickness of the polymer layer on the substrate surface. In sufficiently thick layers, as the chain rigidity increased with the introduction of carboxyl groups, Ttrans rose monotonically. The interaction with the surface of an active substrate led to different changes in Ttrans for the different polymers. A monotonic increase in Ttrans was observed for PMA as the layer thickness was decreased. With the introduction of carboxyl groups into the chain, the dependence of Ttrans on layer thickness became nonmonotonic. Primarily Ttrans was greater close to the substrate surface than in the volume. When the polymers were deposited on to the inactive surface of the fluoroplastic, no changes in El, E2 and Ttrans were observed with a change in the thickness of the polymer layer. The adhesive properties of the polymers selected were determined by the straight tensile method with a constant rate of loading. The temperature dependence of the adhesive strength was investigated in three conditions of testing; 1) at a constant temperature of rupture, Tr; 2) with a constant temperature of contact, To; and 3) with T r = T c . With this type of test, the adhesive strength is determined by the expression a=nafav,
(11)
where n3
n3=nl(1--Ava) ,
(12)
where A is a constant. The frequency v was expressed by an equation similar to the ~Vogel-Fulcher-Tamman eqn. [6] since it was considered that it takes t h e nature of the polymer into account better than does eqn. (4):
v~----Vo~exp [-- U~/R (T--T~)],
(13)
where T~ is a characteristic temperature related to the glass temperature of the polymer and U'~ is a temperature coefficient related to the activation energy for the process. By taking account of eqn. (3), (12) and (13) and making the approximation TI=T~=Ta, eqn. (11) m a y be written in the following way 0"=
av no
l + e x p [A U'/R (To--T,)]
{1--B exp [--U~/R(Ttrans--T3)]},
<14)
I. V. VORONINand V. V. I~VRENT'~.V
1926
where AU'-=-U~--U~ and B is a constant. Figure 3 shows the measurements of t h e way in which the adhesive strength depends on temperature in experiments u n d er the three conditions for the system PMA-glass.
~o, kS/cm~
~cal/mole f
I~
c..3
~
qO
60
30
(,, I
ro
I
~o0 ~°C
60
\
~I 3 20 " ~ ' l ~ < - " ~ i O
l~m. 3
10
% I
20
2O
30 MAA,w~.%
Fro. 4
1~io. 3. Temperaturedependence of the adhesive strength for the system PMA-glass for the following conditions: 1-- Tc ~ const = 80°C; 2-- Trupt~ const = 25°C and] 3-- Tc= Trupt. The curves correspond to the theory and the points are experimental. FIG. 4. The effect of MAA concentration in acrylic polymers on their adhesive strength (in accordemce with eqn. (14)) for the interaction between the polymers and the following: 1, 2 and 3--glass; l'--aluminium. 1 and 1' refer to ~0, 2 to T1 and 3 to U.
Figure 4 shows the effect of the MAA concentration in the polymers on t h e parameters Us, T 1 and ao-~favno/{1-~exp[AU/R(Tc--T1)]}. These parameters were found from the determination of the adhesive strength under t he three conditions testing. The increase in T1 with an increase in the MAA concentration is in agreement with the change in Ttrans (Fig. 2) and is connected with the increase in the rigidity of the polymer chains when carboxyl groups are introduced. The fact t h a t A U' (Fig. 4) and E1 and E2 (Fig. 2) are constant as t he MAA concentration is increased is clearly not a chance result. T hi s can be explained b y the fact t h a t the kinetics of forming and breaking adhesive bonds between the polymer and the substrate and the characteristics of the temperat u r e dependence of the ~adhesive strength are determined by the most mobile groups in the polymers, in this case, b y --C----O groups. These groups first
I
OCH3 form bonds with active centres on the substrate surface. Thus the number of eonformational possibilities open to t h e molecules decreases and this, according t o Eyring [1], entails an increase in the probability of the transfer of the re-
Adhesion and properties of acrylic polymers
1927
quired amount of energy in the one direction and, as a consequence, an increase in the probability of forming adhesive bonds by other groups of the polymers. The process is accompanied by lower energy losses and, during the formation of bonds by carboxyl groups thereafter, approximately the same barrier is overcome as in the formation of bonds by the - - C = O groups. The breakdown
I
OCH8 of bonds at the surface also occurs in the first instance at the location of - - C = O
I
OCH, groups. This process increases the stress applied to the remaining bonds aud this, according to Zhurkov [7], should reduce t h e activation barrier to their rupture. Let us now consider how the values of nl and fay affect a0, according to eqn. (1). The value of a0 m a y be represented as: O'O-----nllfav 1(1--c)%nlJav ~c,
(15)
where n l l and fay, are the parameters in oqn. (1) for bonds formed by --C-----O
I
OOHs groups; n12 and fay 2 are the same quantities for bonds formed by carboxyl groups and c is the molar fraction of carboxyl groups. Since nl is proportional to the density of the boundary layer pb, eqn. (15) m a y be rearranged in the form: ao ~- apbfav l ( 1 - - c ) = apcfav zc,
(16 )
where a is a coefficient of proportionality. On t h e basis of the values obtained for ao (Fig. 4) and pb (Fig. 1), afav 1 and afav ~ were calculated. The results of t h e calculation are shown in the Table. I t follows from the Table and Fig. 1 that, when a polymer having active groups of only one type (PMA) interacts with different substrates, changes in t h e adhesive strength involve •1 and also fay. When polymers having two types of active groups (5 MAA, 10 MAA) interact with a substrate of a particular nature, the predominant formation of bonds by one type of group was not observed. Bonds with the substrate surface were distributed in proportion to the n u m b e r of groups existing in the polymer. The fact t h a t the calculated values of fay Jfav 1 were approximately the same for 5 MAA and 10 MAA points to this conclusion. Thus the specific force pertaining to one carboxyl group of the polymer is approximately 6 times as great as t h a t pertaining to one - - C = O group. When a rigid
I
OCHs chain polymer with a high concentration of carboxyl groups (30 MAA) interacted with the substrate surface, the complete possible number of contacts b e t w e e n the polymer and the substrate was not realized. The low calculated
I. V. VoRo~rn~ and V. V. LAVRENT'EV
1928
value of afar j for 30 MAA indicates this. If all possible contacts between thia polymer and the substrate were formed, by taking account of the values of pb (Fig. 1) and the calculated values afar 1 and afar 2 for complete contact (see Table), the adhesive strength a0 would be approximately 60 kg/cm 2 according to eqn. (16). C H A R A C T E R I S T I C S OF T H E A V A R A G E S T R E N G T H OF T H E A D H E S I V E B O N D F O R V A R I O U S G R O U P S OF A C R Y L I C P O L Y M E R S
Polymer
PMA
Substrate
Aluminium Glass
afay,,
I a/av2 kg" cm/g
5 MAA
20"5 28"5 28"5
170
10 MAA 30 MAA
28.5 28.5
180 7.7*
• Adhesive contact
~e&V2/faV I
6 6-4
incomplete.
In considering, in conjunction, the results from the investigation of the adhesive properties and the boundary properties of the polymers, we may note the following. When there is high adhesion of the polymer to the substrate, ~here is characteristically non-uniformity in the properties of the polymer through the thickness in the part of the polymer bounding the substrate surface. In this case, it is possible to distinguish two layers differing in their properties from the volume: a layer lying directly adjacent to the substrate surface and an intermediate layer. The first layer is thus about one-tenth the thickness of the second. For polymers with flexible chains (PMA), non-uniformity of the layer with respect to density is characteristic (Fig. 1), a fact which is evidently related to the high number of bonds between the polymer and the substrate (in accordance with eqn. (16)). In the case of a more rigid chain polymer containing highly polar carboxyl groups (5 MAA, 10 MAA, 30 MAA), a non-monotonic change ~n the mobility of the polymer chains through the thickness of the layer is observed (Fig, 2), a fact which is evidently connected with the high average bond energy (see Table). Possible structures of the boundary layers for polymers with flexible chains (PMA) and for polymers with highly polar carboxyl groups (5 MAA, 10 MAA, 30 MAA) are shown in Figures 5 and 6 respectively. The first layer of a flexible chain polymer lying directly adjacent to the substrate surface (thickness, ~1) has a dense folded structure with a fold length of approximately 3-4 segments. The second layer (thickness, ~2) has an open structure of approximately the same thickness as the length of a macromolecule. The extended macromolecules linked to t h e substrate surface impede dense packing of the macromo!ecu!es in this layer. The more rigid chains of macromolecules (copolymers 5 MAA, 10 MAA,
Adhesion and properties of acrylic polymers
1929~
30 MAA) with a high bond energy do not form a folded structure and the bounda r y layer J1, which is approximately 10-20 segments thick and has an ordered structure, gradually merges into the volume. The increase in bond energy leads.
/,,~/flflf/~
,,.,/l',lfJflflf/l'l/fl/fff/Tffl'l'~.
FIG. 5
FIG. 6
FxG. 5. Structure of the boundary layer of a flexible-chain polymer (PMA) for a high ad-hesion interaction with the substrat~ surface. Fie. 6. Structure of the boundary layer of a polymer having highly polar oarboxyl groups~ (5 MAA, 10 MAA and 30 MAA) in the case of a high adhesion interaction with the substrato surface. to a reduction in the possibility of the bonds migrating along the surface of the~ solid body and, as a consequence, to an increase in the number of contacting macromolecules. The mobility of --C----O groups of a flexible chain polymer (PMA) decreases.
I
OCH 3 monotonically as the thickness decreases but for polymers with carboxyl groups, the change follows a curve with a maximum. This is connected with the f a c t that, although the intermediate layer of the latter polymers is more ordered, its density is equal to the volume density; t h a t is, its density is less than t h a t characteristic of more ordered structures. Greater freedom is therefore created for the groups under consideration. I t should be noted t h a t the change in mobility is related to a change in the glass temperature of the polymer and is not related to any change in the potential barrier to vibrations. The fact t h a t Ttrans changes whereas E1 and E 2 remain unchanged as the thickness J is decreased is evidence of this (Fig. 2). In particular, vibrations appear feebly or are "frozen" in d i r e c t proximity to the substrate surface. In connection with this, the actual contact between the polymer and the substrate begins to be diminished, which is especially appreciable in the case of 30 MAA. I n order to increase the mobility of the active groups of the polymers and toincrease the real contact between the polymer and the substrate, elevated tern-
1930
I.V. VoBo~n~ and V. V. LAV~I~T'EV
peratures are generally used, lying above the transition temperatures of the pure tIolymers. I n certain eases, however, it is impossible in principle to achieve complete contact if the decomposition temperature of the polymer lies below these temperatures. This is found to be the case for the system 30 MAA-glass. Another method of increasing the area of real contact is to reduce the activation barrier to interaction between the polymer and the substrate. This is achieved by selecting an appropriate mixture of "poor" and "good" solvents or by intro~dueing highly mobile functional groups into the macromolecular chain. I n our •case, an acetone-benzene mixture was selected as a mixture of this type and - - C ~ O groups were selected as the appropriate functional groups. A negative
I
OCH3 factor in reducing the activation barrier by these methods is, in the first ease, the difficulty of removing the solvents adsorbed on to the substrate surface, a n d in the second case, the lowering of the activation barrier for rupture of the -adhesive bonds. Thus the characteristics of the adhesive interaction of acrylic polymers are also determined by their boundary properties. A change in the chemical composition of the polymers leads to a corresponding change in their adhesive and b o u n d a r y properties. Thus the most mobile groups of the polymers determine t h e characteristics of the temperature dependence both of the adhesive strength a n d also of the mobility of the polymers' maeromolecules in the boundary layer. The authors wish to t h a n k Yu. M. Malinskii for his interest in the work and f o r a number of valuable comments on the manuscript. Translated by G. F. MODLE~ REFERENCES
1. S. CLASSTONE, K. LAIDLER and G. EYRING, Teoriya absolyutnykh skorostei reaktsii (Theory of Absolute Reaction Rates). Izd-vo inostr, lit., 1948 (Russian translation) :2. L. F. PLISKO, K. K. OSTREIKO, V. V. LAVRENT'YEV, V. L. VAKULA and S. S. VOYUTSI{II~ Vysokomol. soyed. 15: 2529, 1974 (Not translated in Polymer Sci. U.S.S.R.) 3. V. V. LAVRENT'YEV and I. V. VORONIN, Kolloidn. zh. 36: 163, 1974 -4. I. V. VORONIN and V. V. LAVRENT'YEV, V kn. Termodinanicheskiye i strukturnyye svoistva granichnykh sloyev polimerov (In the book: Thermodynamic and Structural Properties of Boundary Layers in Polymers). p. 53, Izd. "Naukova dumka", 1976 -5. {~. OSTER and C. NISHIJIMA, J. Amer. Chem. Soc. 78: 1581, 1956 6. H. VOGEL, Phys. Z., 22: 645, 1921 "7. S. N. ZHURKOV and S. A. ABASOV, Vysokomol. soyed. 3: 439, 1961 (Not translated in Polymer Sci. U.S.S.R.)