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Mechanism of inhibition in neutral solutions
CorrosionScience,Vol.35, Nos5-8, pp. 1471-1476, 1993
0010-938X/93$6.00+ 0.00 (~) 1993PergamonPressLtd
Printed in Great Britain.
MECHANISM
OF
INHIBITION
IN NEUTRAL
SOLUTIONS
E. KALMXNand G. PXLINK.~S Department of Solution Chemistryand Corrosion Research, Central Research Institute for Chemistry, Hungarian Academyof Sciences, P.O. Box 17, H-1525 Budapest, Hungary Abstract--A stochastic mathematical model has been developed for a statistical description of corrosion process of metals and inhibition of corrosion by an adsorption mechanism. Based on the model, the dissolution of metals and the efficiencyof inhibitors can be studied by computer simulation. INTRODUCTION THE CHEMICALSused in the inhibition of metal corrosion in nearly-neutral aqueous solutions can be classified as film-forming inhibitors. These chemicals are capable of depositing on metal surfaces, thus forming a three-dimensional protective-layer. 1 During the past decade, a number of phosphonates have been used in different inhibitor compositions in neutral aqueous solutions. 2 A typical example is 1-hydroxy-ethane-1,1-diphosphonicacid ( H E D P ) . It is well known that the presence of some double charged cations in aqueous solution synergistically increases the inhibitor efficiency of phosphonic acids. 3'4 It has also been shown by radiotracer method, that H E D P by itself form a loosely bound adsorption layer on the iron surface and that the presence of zinc or calcium ions in solution leads to an increased adsorption of H E D P molecules. 5 The relationship between the amount of substance adsorbed on unit area of the metal surface and the concentration of inhibitor molecules in the solution at a given temperature is given by an adsorption isotherm. In the simplest case, assuming that there is no interaction between the adsorbed species on the metal surface and the adsorbate which forms a monolayer, the fractional coverage of the surface 0 is described by the Langmuir isotherm,, 0
boc - 1 - 0
(1)
where c is the concentration of the adsorbate in the bulk solution and the b0 parameter is the ratio of adsorption and desorption rate constants. One of the simplest isotherms which includes the possibility of interaction between the adsorbed species, and describes an enhanced adsorption is the Frumkin isotherm, 0
blC -- 1 - 0 exp (-alO)
(2)
where ai is an interaction parameter. The two different types of isotherms can be seen on Fig. 1, where experimental data on inhibitor efficiencies IE (IE = 0) of H E D P are shown for 0.5 tool l - 1NaC104 1471
1472
E.K./~LMANand G. PJ,LINK~S 1.0 0.8
(B) d
, n)~~"-~,
~
I 3
5
0.6 0.4 0.2
J
I 1
I 2
I 4
¢ x 1 0 4 t o o l 1"1
Fro. 1. Fractional coverage of carbon steel in NaCIO4 solutions as a function of HEDP inhibitor concentration in the absence (A) and in the presence (B) of Ca ions. Stars and triangles stand for experimental data (A and B, respectively), full lines represent Langmuir and Frumkin isotherms fitted to experimental data (A) and (B), respectively. Open circles are the results of computer simulations. solution (A) without and (B) with the presence of Ca ions. The experiments were carried out in our laboratory and the inhibitor efficiencies were determined by the weight loss method. The fit of (A) Langmuir form, and (B) Frumkin form against the experimental data are shown by the full curves in Fig. 1. with parameters b0 = 1.27 × 104 dm 3 tool -1, b I = 0.2 x 10 4 dm 3 tool -1 and a I = 4.2, respectively. The aim of our model calculations was to distinguish these isotherms from each other by computer simulations. 6 THE MODEL The total volume of the metal is divided into volume elements. The dissolution probability of each volume element depends on the number of free surface sites, the type of the metal and aggressiveness of the environment. In discrete time intervals the computer algorithm scans the whole surface of the metal and based on the given probability, a random number generator decides on the dissolution of each volume element with at least one surface site. During the dissolution in a volume element the number of free surface sites for neighboring volume elements increases, which raises the probability of dissolution for those in the next time step. The probability of dissolution in a volume element through one of its free surface sites is a function of solution parameters (c i, T i, etc.), pc = p(ci,
~,
. . .).
(3)
The number of dissolved volume elements ki is proportional to the number of free surface sites and to the probability of dissolution at the given surface site Pc, ki - N i - ni Ai Ni P C - A o o P c
(4)
where N i is the number of total and ni is the number of blocked surface sites. A i and A0 are free and total areas of the surface, respectively.
Inhibition in neutral solutions
1473
The adsorption of the inhibitor c o m p o u n d on the free surface sites of a metal is characterized also by probability functions, depending on the inhibitor and the solution as in the case of the dissolution processes. The probability of adsorption Pa is also a function of solution parameters. At equilibrium at any t e m p e r a t u r e and concentration a fraction 0 of the sites is occupied by adsorbed molecules and a fraction 1 - 0 is not occupied. The probability of adsorption is the same for all sites and does not or does depend on the fraction covered for the Langmuir and Frumkin cases, respectively. The algorithm determines at each time step the n u m b e r of blocked sites elements by means of a r a n d o m n u m b e r generator, which results in a decrease of the probability for the dissolution in the next time step. The time evaluation of the processes can be calculated by repeating each step. If the n u m b e r of dissolved volume elements is ki at the ith time step, the corrosion rate Cv results in
Cv -
6M At
• kip Ov
~
ki
i A ~ , i 6t
i Z
i
i
(5)
i
where 6 M is the loss of mass, 6v is the volume of elementary cubes, A is the area and p is the density of the metal. Thus the corrosion rate at the ith time step is proportional to the n u m b e r of dissolved volume elements, i.e. Cvia ~ kg. If the n u m b e r of blocked surface sites is n i and the n u m b e r of free surface sites is N i - n i at each time step the fractional coverage is, simply, 0 = ~ / / = Pa.
(6)
The probability of the adsorption is equal to the fractional coverage in the model. Thus, the corrosion rate in the presence of adsorption is expressed by the equation, Cv,- 1 -
Pc = (1 - O)p c = (1 - P a ) P c .
(7)
As a result of the above equation the efficiency due to adsorption is, IE - Cv,,- cv,_ 0 = Pa.
(8)
Cvo
COMPUTER SIMULATION Two kinds of c o m p u t e r simulations have been carried out. In the first one the interaction between the blocked surface sites was excluded (Langmuir case). In the second one the interaction between the adsorbant with the already blocked nearest neighbor sites was taken into account by an simple algorithm (Frumkin case). The coordinates of all volume elements are stored in each time step (cycle). Originally the surface is smooth and the n u m b e r of surface sites is actually 10 6. There is initially no blocked surface site (no = 0). The calculation consists of cycles, with each cycle having a dissolution and an adsorption step. The program scans through all free surface sites and removes at r a n d o m kg volume elements with Pc probability. In the
1474
E. K~LM~N and G, PALINK~S i n i t i a l m e t a l s u r f a c e at t = 0
k
~-)
602 "~ 40 2
pc = 0.4 pa = 0 no i n h i b i t o r c o r r o s i o n rate 0.6 mm y~
60 " ~ 4 0._~ 20? 0
FIG. 2.
Part of a metal surface at the beginning and at the end of the simulation with the probability of dissolution Pc = 0.4 without an adsorption process.
second adsorption step, the algorithm blocks ni surface sites with Pa or p * probability for Langmuir or Frumkin type of adsorption, respectively. The input probabilities for the simulations are Pc, Pa or Pa0. Pc is estimated from experimental corrosion rate without any inhibitor, i.e. Pc = constant x Cvo. The probability of adsorption pa(C) for the Langmuir case is determined from the experimental efficiency as a function of inhibitor concentration for solution (A) (Pa = IE). The probability of adsorption p* for the simulation with interaction between the adsorbants is determined as follows. Substituting a~ = 0 in the Frumkin isotherm (equation 2) fitted to experimental data (B) one can approximate the probability of adsorption in a free surface site Pa0 if there are no blocked sites in the nearest neighborhood,
I n h i b i t i o n in n e u t r a l s o l u t i o n s
1475
pc = 0.4 pa = 0.4 c o r r o s i o n r a t e 0 . 2 4 m m y-l
60"7~ 4 0 -
p c = 0 . 4 p a -- 0 . 8 -I c o r r o s i o n r a t e 0 . 1 turn y
8o 60
~ 40 20 0
FIG. 3.
P a r t o f t h e m e t a l s u r f a c e at t h e e n d o f s i m u l a t i o n w i t h d i s s o l u t i o n p r o b a b i l i t y Pc = 0 . 4 a n d p r o b a b i l i t i e s o f a d s o r p t i o n Pa = 0.4 a n d P a = 0 . 8 , r e s p e c t i v e l y .
bic =
Pao 1 -
(9)
Pao
It corresponds to an adsorption event with no interactions. However, the probability of adsorption is increased to P*a if there are already blocked sites in the nearest neighborhood. The p*~ is then determined as p*~ = n x a x Pa0
(10)
ifp~ -< 1, and p~ = 1 for the cases when p* > 1, where n is the number of already blocked neighboring surface sites (maximum 4) and a is an adjustable parameter (a = 1.4 for (B) solution).
1476
E. KALM,~Nand G. PALINK~S
As a result of the simulation, the average thickness of the model metal decreases and surface coverage changes. The corrosion rate of mild steel in solution A (without Ca) was 0.6 mm y-i. Pc was chosen so as to reduce the height by 60% in 1 year which means 90,000 cycles (1 cycle = 0.1 h, Pc = 0.4). RESULTS
Figure 2 shows the model metal surface at the beginning of the simulation and after 90,000 cycles without an adsorption process. The results of simulations for Langmuir type of adsorption with p~ = 0.4 and Pc = 0.6 can be seen in Fig. 3. The reproduction of fractional coverages as a function of inhibitor concentration by simulating adsorption both without and with interaction of adsorbants for experimental data (A) and (B) is shown by circles in Fig. 1. Comparing simulated and experimentally determined fractional coverages in Fig. 1, one can see that a very simple model for interaction between the adsorbed species (equation 10) is able to distinguish between the Langmuir and Frumkin type of adsorption mechanisms. Acknowledgements--This work has been supported by the National Scientific Research Foundation (OTKA No. 1808). REFERENCES 1. G. TRABANELLI, Corrosion Mechanisms (ed. F. MANSFELD), p. 119. Marcel Dekker, New York (1987). 2. A. J. FREEDMAN,Mater. Perform. 33, 9 (1984). 3. R. H. ASHCRAFT,G. BOHNSACK,R. KLEINSTUECKand S. STORP, Corrosion 86, Houston (1986). 4. W. NEAGLEand P. HAMMONDS,Proc. U.K. Corrosion (1988). 5. F. H. K~.RMAN,E. K~LM~N, L. V~,RALLYAIand J. K6NYA, Z. Naturforsch. 46a, 183 (1991). 6. E. KALM/,N and G. P/~LINK~,S,33rd IUPAC Congr. Coll. Abstr. 3048 (1991).
0010-938X/93$6.00+ 0.00 (~) 1993PergamonPressLtd
Printed in Great Britain.
MECHANISM
OF
INHIBITION
IN NEUTRAL
SOLUTIONS
E. KALMXNand G. PXLINK.~S Department of Solution Chemistryand Corrosion Research, Central Research Institute for Chemistry, Hungarian Academyof Sciences, P.O. Box 17, H-1525 Budapest, Hungary Abstract--A stochastic mathematical model has been developed for a statistical description of corrosion process of metals and inhibition of corrosion by an adsorption mechanism. Based on the model, the dissolution of metals and the efficiencyof inhibitors can be studied by computer simulation. INTRODUCTION THE CHEMICALSused in the inhibition of metal corrosion in nearly-neutral aqueous solutions can be classified as film-forming inhibitors. These chemicals are capable of depositing on metal surfaces, thus forming a three-dimensional protective-layer. 1 During the past decade, a number of phosphonates have been used in different inhibitor compositions in neutral aqueous solutions. 2 A typical example is 1-hydroxy-ethane-1,1-diphosphonicacid ( H E D P ) . It is well known that the presence of some double charged cations in aqueous solution synergistically increases the inhibitor efficiency of phosphonic acids. 3'4 It has also been shown by radiotracer method, that H E D P by itself form a loosely bound adsorption layer on the iron surface and that the presence of zinc or calcium ions in solution leads to an increased adsorption of H E D P molecules. 5 The relationship between the amount of substance adsorbed on unit area of the metal surface and the concentration of inhibitor molecules in the solution at a given temperature is given by an adsorption isotherm. In the simplest case, assuming that there is no interaction between the adsorbed species on the metal surface and the adsorbate which forms a monolayer, the fractional coverage of the surface 0 is described by the Langmuir isotherm,, 0
boc - 1 - 0
(1)
where c is the concentration of the adsorbate in the bulk solution and the b0 parameter is the ratio of adsorption and desorption rate constants. One of the simplest isotherms which includes the possibility of interaction between the adsorbed species, and describes an enhanced adsorption is the Frumkin isotherm, 0
blC -- 1 - 0 exp (-alO)
(2)
where ai is an interaction parameter. The two different types of isotherms can be seen on Fig. 1, where experimental data on inhibitor efficiencies IE (IE = 0) of H E D P are shown for 0.5 tool l - 1NaC104 1471
1472
E.K./~LMANand G. PJ,LINK~S 1.0 0.8
(B) d
, n)~~"-~,
~
I 3
5
0.6 0.4 0.2
J
I 1
I 2
I 4
¢ x 1 0 4 t o o l 1"1
Fro. 1. Fractional coverage of carbon steel in NaCIO4 solutions as a function of HEDP inhibitor concentration in the absence (A) and in the presence (B) of Ca ions. Stars and triangles stand for experimental data (A and B, respectively), full lines represent Langmuir and Frumkin isotherms fitted to experimental data (A) and (B), respectively. Open circles are the results of computer simulations. solution (A) without and (B) with the presence of Ca ions. The experiments were carried out in our laboratory and the inhibitor efficiencies were determined by the weight loss method. The fit of (A) Langmuir form, and (B) Frumkin form against the experimental data are shown by the full curves in Fig. 1. with parameters b0 = 1.27 × 104 dm 3 tool -1, b I = 0.2 x 10 4 dm 3 tool -1 and a I = 4.2, respectively. The aim of our model calculations was to distinguish these isotherms from each other by computer simulations. 6 THE MODEL The total volume of the metal is divided into volume elements. The dissolution probability of each volume element depends on the number of free surface sites, the type of the metal and aggressiveness of the environment. In discrete time intervals the computer algorithm scans the whole surface of the metal and based on the given probability, a random number generator decides on the dissolution of each volume element with at least one surface site. During the dissolution in a volume element the number of free surface sites for neighboring volume elements increases, which raises the probability of dissolution for those in the next time step. The probability of dissolution in a volume element through one of its free surface sites is a function of solution parameters (c i, T i, etc.), pc = p(ci,
~,
. . .).
(3)
The number of dissolved volume elements ki is proportional to the number of free surface sites and to the probability of dissolution at the given surface site Pc, ki - N i - ni Ai Ni P C - A o o P c
(4)
where N i is the number of total and ni is the number of blocked surface sites. A i and A0 are free and total areas of the surface, respectively.
Inhibition in neutral solutions
1473
The adsorption of the inhibitor c o m p o u n d on the free surface sites of a metal is characterized also by probability functions, depending on the inhibitor and the solution as in the case of the dissolution processes. The probability of adsorption Pa is also a function of solution parameters. At equilibrium at any t e m p e r a t u r e and concentration a fraction 0 of the sites is occupied by adsorbed molecules and a fraction 1 - 0 is not occupied. The probability of adsorption is the same for all sites and does not or does depend on the fraction covered for the Langmuir and Frumkin cases, respectively. The algorithm determines at each time step the n u m b e r of blocked sites elements by means of a r a n d o m n u m b e r generator, which results in a decrease of the probability for the dissolution in the next time step. The time evaluation of the processes can be calculated by repeating each step. If the n u m b e r of dissolved volume elements is ki at the ith time step, the corrosion rate Cv results in
Cv -
6M At
• kip Ov
~
ki
i A ~ , i 6t
i Z
i
i
(5)
i
where 6 M is the loss of mass, 6v is the volume of elementary cubes, A is the area and p is the density of the metal. Thus the corrosion rate at the ith time step is proportional to the n u m b e r of dissolved volume elements, i.e. Cvia ~ kg. If the n u m b e r of blocked surface sites is n i and the n u m b e r of free surface sites is N i - n i at each time step the fractional coverage is, simply, 0 = ~ / / = Pa.
(6)
The probability of the adsorption is equal to the fractional coverage in the model. Thus, the corrosion rate in the presence of adsorption is expressed by the equation, Cv,- 1 -
Pc = (1 - O)p c = (1 - P a ) P c .
(7)
As a result of the above equation the efficiency due to adsorption is, IE - Cv,,- cv,_ 0 = Pa.
(8)
Cvo
COMPUTER SIMULATION Two kinds of c o m p u t e r simulations have been carried out. In the first one the interaction between the blocked surface sites was excluded (Langmuir case). In the second one the interaction between the adsorbant with the already blocked nearest neighbor sites was taken into account by an simple algorithm (Frumkin case). The coordinates of all volume elements are stored in each time step (cycle). Originally the surface is smooth and the n u m b e r of surface sites is actually 10 6. There is initially no blocked surface site (no = 0). The calculation consists of cycles, with each cycle having a dissolution and an adsorption step. The program scans through all free surface sites and removes at r a n d o m kg volume elements with Pc probability. In the
1474
E. K~LM~N and G, PALINK~S i n i t i a l m e t a l s u r f a c e at t = 0
k
~-)
602 "~ 40 2
pc = 0.4 pa = 0 no i n h i b i t o r c o r r o s i o n rate 0.6 mm y~
60 " ~ 4 0._~ 20? 0
FIG. 2.
Part of a metal surface at the beginning and at the end of the simulation with the probability of dissolution Pc = 0.4 without an adsorption process.
second adsorption step, the algorithm blocks ni surface sites with Pa or p * probability for Langmuir or Frumkin type of adsorption, respectively. The input probabilities for the simulations are Pc, Pa or Pa0. Pc is estimated from experimental corrosion rate without any inhibitor, i.e. Pc = constant x Cvo. The probability of adsorption pa(C) for the Langmuir case is determined from the experimental efficiency as a function of inhibitor concentration for solution (A) (Pa = IE). The probability of adsorption p* for the simulation with interaction between the adsorbants is determined as follows. Substituting a~ = 0 in the Frumkin isotherm (equation 2) fitted to experimental data (B) one can approximate the probability of adsorption in a free surface site Pa0 if there are no blocked sites in the nearest neighborhood,
I n h i b i t i o n in n e u t r a l s o l u t i o n s
1475
pc = 0.4 pa = 0.4 c o r r o s i o n r a t e 0 . 2 4 m m y-l
60"7~ 4 0 -
p c = 0 . 4 p a -- 0 . 8 -I c o r r o s i o n r a t e 0 . 1 turn y
8o 60
~ 40 20 0
FIG. 3.
P a r t o f t h e m e t a l s u r f a c e at t h e e n d o f s i m u l a t i o n w i t h d i s s o l u t i o n p r o b a b i l i t y Pc = 0 . 4 a n d p r o b a b i l i t i e s o f a d s o r p t i o n Pa = 0.4 a n d P a = 0 . 8 , r e s p e c t i v e l y .
bic =
Pao 1 -
(9)
Pao
It corresponds to an adsorption event with no interactions. However, the probability of adsorption is increased to P*a if there are already blocked sites in the nearest neighborhood. The p*~ is then determined as p*~ = n x a x Pa0
(10)
ifp~ -< 1, and p~ = 1 for the cases when p* > 1, where n is the number of already blocked neighboring surface sites (maximum 4) and a is an adjustable parameter (a = 1.4 for (B) solution).
1476
E. KALM,~Nand G. PALINK~S
As a result of the simulation, the average thickness of the model metal decreases and surface coverage changes. The corrosion rate of mild steel in solution A (without Ca) was 0.6 mm y-i. Pc was chosen so as to reduce the height by 60% in 1 year which means 90,000 cycles (1 cycle = 0.1 h, Pc = 0.4). RESULTS
Figure 2 shows the model metal surface at the beginning of the simulation and after 90,000 cycles without an adsorption process. The results of simulations for Langmuir type of adsorption with p~ = 0.4 and Pc = 0.6 can be seen in Fig. 3. The reproduction of fractional coverages as a function of inhibitor concentration by simulating adsorption both without and with interaction of adsorbants for experimental data (A) and (B) is shown by circles in Fig. 1. Comparing simulated and experimentally determined fractional coverages in Fig. 1, one can see that a very simple model for interaction between the adsorbed species (equation 10) is able to distinguish between the Langmuir and Frumkin type of adsorption mechanisms. Acknowledgements--This work has been supported by the National Scientific Research Foundation (OTKA No. 1808). REFERENCES 1. G. TRABANELLI, Corrosion Mechanisms (ed. F. MANSFELD), p. 119. Marcel Dekker, New York (1987). 2. A. J. FREEDMAN,Mater. Perform. 33, 9 (1984). 3. R. H. ASHCRAFT,G. BOHNSACK,R. KLEINSTUECKand S. STORP, Corrosion 86, Houston (1986). 4. W. NEAGLEand P. HAMMONDS,Proc. U.K. Corrosion (1988). 5. F. H. K~.RMAN,E. K~LM~N, L. V~,RALLYAIand J. K6NYA, Z. Naturforsch. 46a, 183 (1991). 6. E. KALM/,N and G. P/~LINK~,S,33rd IUPAC Congr. Coll. Abstr. 3048 (1991).