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Molecular organization of water-detergent systems at low water content
Volume 107A, number 3
PHYSICS LETTERS
21 January 1985
MOLECULAR ORGANIZATION OF WATER-DETERGENT SYSTEMS AT LOW WATER CONTENT A. DERZHANSKI, A. ZHELIASKOVA and PHAM VIET NHU Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Lenin Boulevard, 1184 Sofia, Bulgaria Received 25 May 1984 Revised manuscript received 26 November 1984
The binary systemp-nonylphenolpolyethyleneoxide with 10 mole ethylene oxide, heavy water in the concentration range 0-10wt%, was investigated by means of broad line NMR spectroscopy.The NMR spectra broaden when the water concentration increases. This phenomenon is probably based on hindered molecular molaon because of the hydrogen bonds.
The object of the present investigations was the system p-nonylphenolpolyethylene oxide with 10 mole ethylene oxide (Arkopal 10 C g H 1 9 - ~ - (OCH2fH2)10OH)-heavy water. The concentration ot the detergent in the mixture was 100, 97.5, 95 and 92.5 wt%. The broad line H 1 NMR spectra of these probes were recorded. For this purpose, a home-made NMR spectrometer, with hight frequency v = 13 MHz was used at temperature T = 303 K. The nature of the spectra leads us to accept that each of them is the sum of at least two gaussian curves, A and B. Using the least-squares method, the parameters of the two gaussian functions were determined in such a way that their sum be as close as possible to the experimentally obtained spectrum. A proper computer programme was written, by means of which the spectra were processed. The half-widths b A and b B of the constituent curves A and B, and
their statistical weights PA and PB are given in table I. Curve A with the greater half-width is connected with the reorientation and the movement of the molecule as a whole, while curve B reflects the intramolecular movements. Curve B does not show any change when there are changes in the concentration of the water, which supports this supposition. The presence of water and the increase of the water content changes the component A by broadening it (table 1). The relatively low water content does not allow the formation of isolated aggregates or phases, which could widen the spectrum. The samples are optically isotropic under a polarizing microscope. We assume that the water molecules in the sample, as well as the presence of an OH group at the end of each ethylene glycol chain, promote the formation of hydrogen bonds. As the water concentration increases, so does their number. The detergent molecules con-
Table 1 Concentration
bA
bB
PA
PB
1"c
u
/.to
of A-10 (%)
(G)
(G)
(%)
(%)
(s)
(s-I )
(cm/dyn s)
100 97.5
2.45 2.71
1.79 1.46
52 52
48 48
95.0 92.5
3.38 3.47
1.56 1.70
52 52
48 48
5.8 x 6.4 x 7.9 x 8.2 x
2.76 x l0 s 4.29 x l0 s 4.82 x l0 s 5.69 × l0 s
1.97 x 106 2.39 x 106 2.41 × 106 2.67 × 106
0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
10-6 10-6-6 10-6 10-6
139
Volume 107A, number 3
PHYSICS LETTERS
21 January 1985
nected via hydrogen bonds are lesss mobile. According to Abragam [ 1], the second moment of the absorption NMR spectrum in the presence of molecular movements is given by the expressxon
Pt~ = P*/al/[/al+ (M - 1) p*] .
5 co2 = 5 ~o2 (2/1r) arctg(t~8 ~orc),
( M - 1)p* < / a l ,
(1)
where 5 ~ 2 is the second moment, 5¢0 is the half-width of the spectrum of the measured sample, 5COo 2 is the second moment for the corresponding solid lattice, r c is the correlation time characterising the molecular reorientation, ct is a coefficient of the order of unity. According to ref. [2], the second moment for immobile CH 2 groups is 6oo2 = 1.79 × 10 -10 s -1 . By means of (1), an estimation is made for the correlation time r c of each of the examples under investigation, using the experimental data for 56o. The results obtained are given in table 1. The prolongated form and the flexibility of the molecules of Arkopal 10 permit us to consider them as polymer chains with intermediate length in a melt. We apply to our system the theory given by de Gennes [3] for the dynamics of melts or concentrated solutions of polymers, thus the diffusion of the molecule is considered as a translation in a tube, the so-called reptation. The resistance force F, supported by the molecule, is proportional to the velocity o of the reptation F
=
olut~,
(2)
where Ptr is the mobility of the molecules. The total force acting in the sample is the sum of all atomic groups comprising the molecules. We denote the number of these groups by M. For simplicity we assume the CH 2 groups, the CH 3 groups and the oxygen atoms to be equal. M
M
F = ~ F i = ~ o[pi, i=1 i=1
where Pi is the mobility of the ith group. In the case of all tai equal (pq =/al) we obviously shall have Pt~ = l a l l M .
(3)
Let us denote the mobility of an atomic group as p* (in our case an oxygen atom) in the case of a hydrogen bond, which makes movement difficult. The mobility of the other groups without hydrogen bonds can be assumed to be equal. It is again denoted by Pl. Then F = v ~1 + (M - 1)]/#*Pl • 140
(4)
Comparing (2) and (4), we can note that (5)
We suppose that (6)
then (7)
Pt~ = P* .
By analogy in the case of S hydrogen bonds we obtain Utr = ~* / s .
(8)
According to the theory of the reptation of one long and flexible molecule, the diffusion coefficient is equal to Dtr =latr k T ,
(9)
and in our case Dtr = p* k T / S .
(10)
The correlation time of this diffusion, which is also the correlation time of molecular reorientation, is given by rtx = L 2 / D t r = L 2S/p * k T .
(11)
and the velocity of reorientation by v = 1/ztx = p* k T / S L 2 .
(12)
According to the statistics, the probability for the P 1 hydrogen bond to be realized is ~l/Pl
1
where Pl
Pl ! ( , P - P l ) !"
p is the number of possible hydrogen bonds for one molecule Arkopal 10 and Pl is the number of the realized ones. Hydrogen bonds can be formed by the hydrogen nuclei of the water molecules (fig. 1B) and besides the hydrogen nuclei of the OH groups situated at the ends of each polyethylene glycol chain (fig. IA). m is the part of these hydrogen nuclei which form bridges between two detergent molecules by means of hydrogen bonds. The rest of the hydrogen nuclei form bonds between two or more water molecules
(fig. 1c). m = Nam/3 + 2 N D 2 0 ~ 2 ,
Volume 107A, number 3
C,H,,-(~-(OCH:CH,I
PHYSICS LETTERS
(OC,,CH,)(OC,,C,,)~OCJ~,CH,I(OC,,CH, IO
21 January 1985
can be expressed by the coefficient
7 = (Nam +No20/3)/(Nam + 0.5/3ND20). \H
C,H,, -(~-(OCH2CH,}
H
[OCH,CHz)(OCt4=CH,)(iCCH,}(OCh£Hz) H, 0H
Thus, let/S* be the effective mobility depending on the water concentration /S* = "//s o •
Fig. 1.
(16)
(17)
Nam and ND20 are the number of amphiphilic and water molecules in 1 gram of the system,
For all the concentrations used, the calculated values of/s 0 are the same within the limits of error (see table 1). We accept as the most probable value for/sO
13= llNam/(llNam +ND20).
/so = 2.4 X 106 .
The multiplier shows the number of oxygen atoms in one molecule Arkopal 10,
n= l lNam . The probability of formation of an arbitrary number (from 0 to p) of hydrogen bonds is x--~l p p \ W= p % t P l ) (m/n)Pl ( 1 - m / n ) P - P l = l .
(14)
One molecule occupies each of the states, expressed by (13) with probability ICpl. v, as mentioned above (12), is the frequency of reorientation of one molecule Arkopal 10 with S hydrogen bonds. The average frequency of reorientation is the sum of all p multiplied by their corresponding statistical weights (13). p
P pl=O Pl
(m/n)Pl (I - m / n ) P - P l Pl +-"'~I r c "
A similar equation can be written for each of the concentrations used by us. So, four equations can be written, from which v can be calculated for each of the concentrations (see table 1). As was mentioned above,/S* gives the mobility of a molecule of Arkopal 10 with one hydrogen bond. The hydrogen bonds under consideration can be divided into two groups: (1) single - realizing bridges between the OH group of one molecule Arkopal 10 with an oxygen atom of a neighbouring amphiphilic molecule; (2) hydrogen bonds by which one water molecule connects two neighbouring molecules of Arkopal 10 with the help of its two hydrogen atoms. Destruction of the second type of hydrogen bonds is twice as probable because of the participation of two consecutively connected hydrogen bonds. Due to this, if the mobility in the first case is/So, it will be 2/S0 in the second case. This difference in the two types of hydrogen bonds
(18)
The following value can be extracted, DpE = 4 X 10 -7 cm2/s,
(19)
from the paper of McCall and coauthors [4], through a graphic extrapolation and using the relation obtained in ref. [4] between the number of atomic groups and the diffusion of the polyoxyethylene chain, for the diffusion coefficient of a polyethylene chain with the same lenght L of the molecule Arkopal 10 at temperature T = 303 K. From (3) and (9) we obtain for the mobility of one CH2 group (the mobility of one atomic group without hydrogen bond) #IPE = 4 X 108 . The ratio/SlPE//S0 is then 170, which is in agreement with our supposition in (6). From the relation
la l / IsO = exp( AE/R T)
(20)
the value of one hydrogen bond in the system under investigation can be found: AE = 3 kcal/mole. This value is of the same order as the values known from the literature [5,6]. [1] A. Abragam, The principles of nuclear magnetism (Pergamon, London, 1961). [2] l.Ya. Slonim, Vysokomol. Soedin. 6 (1964) 1371. [3] P.-G. de Gennes, Scaling concepts in polymer physics (Cornell Univ. Press, Ithaca, 1979). [4] D.W. McCall,D.C. Douglass and E.W. Anderson, J. Chem. Phys. 30 (1959) 771. [5 ] G.C. Pimentel and A.L. McClellan,The hydrogen bond (Freeman, San Francisco, 1960). [6] P. Schuster, ed., The hydrogen bond, recent developments
in theory and experiments, Vols. 1, 2 (North-Holland, Amsterdam, 1976). 141
PHYSICS LETTERS
21 January 1985
MOLECULAR ORGANIZATION OF WATER-DETERGENT SYSTEMS AT LOW WATER CONTENT A. DERZHANSKI, A. ZHELIASKOVA and PHAM VIET NHU Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Lenin Boulevard, 1184 Sofia, Bulgaria Received 25 May 1984 Revised manuscript received 26 November 1984
The binary systemp-nonylphenolpolyethyleneoxide with 10 mole ethylene oxide, heavy water in the concentration range 0-10wt%, was investigated by means of broad line NMR spectroscopy.The NMR spectra broaden when the water concentration increases. This phenomenon is probably based on hindered molecular molaon because of the hydrogen bonds.
The object of the present investigations was the system p-nonylphenolpolyethylene oxide with 10 mole ethylene oxide (Arkopal 10 C g H 1 9 - ~ - (OCH2fH2)10OH)-heavy water. The concentration ot the detergent in the mixture was 100, 97.5, 95 and 92.5 wt%. The broad line H 1 NMR spectra of these probes were recorded. For this purpose, a home-made NMR spectrometer, with hight frequency v = 13 MHz was used at temperature T = 303 K. The nature of the spectra leads us to accept that each of them is the sum of at least two gaussian curves, A and B. Using the least-squares method, the parameters of the two gaussian functions were determined in such a way that their sum be as close as possible to the experimentally obtained spectrum. A proper computer programme was written, by means of which the spectra were processed. The half-widths b A and b B of the constituent curves A and B, and
their statistical weights PA and PB are given in table I. Curve A with the greater half-width is connected with the reorientation and the movement of the molecule as a whole, while curve B reflects the intramolecular movements. Curve B does not show any change when there are changes in the concentration of the water, which supports this supposition. The presence of water and the increase of the water content changes the component A by broadening it (table 1). The relatively low water content does not allow the formation of isolated aggregates or phases, which could widen the spectrum. The samples are optically isotropic under a polarizing microscope. We assume that the water molecules in the sample, as well as the presence of an OH group at the end of each ethylene glycol chain, promote the formation of hydrogen bonds. As the water concentration increases, so does their number. The detergent molecules con-
Table 1 Concentration
bA
bB
PA
PB
1"c
u
/.to
of A-10 (%)
(G)
(G)
(%)
(%)
(s)
(s-I )
(cm/dyn s)
100 97.5
2.45 2.71
1.79 1.46
52 52
48 48
95.0 92.5
3.38 3.47
1.56 1.70
52 52
48 48
5.8 x 6.4 x 7.9 x 8.2 x
2.76 x l0 s 4.29 x l0 s 4.82 x l0 s 5.69 × l0 s
1.97 x 106 2.39 x 106 2.41 × 106 2.67 × 106
0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
10-6 10-6-6 10-6 10-6
139
Volume 107A, number 3
PHYSICS LETTERS
21 January 1985
nected via hydrogen bonds are lesss mobile. According to Abragam [ 1], the second moment of the absorption NMR spectrum in the presence of molecular movements is given by the expressxon
Pt~ = P*/al/[/al+ (M - 1) p*] .
5 co2 = 5 ~o2 (2/1r) arctg(t~8 ~orc),
( M - 1)p* < / a l ,
(1)
where 5 ~ 2 is the second moment, 5¢0 is the half-width of the spectrum of the measured sample, 5COo 2 is the second moment for the corresponding solid lattice, r c is the correlation time characterising the molecular reorientation, ct is a coefficient of the order of unity. According to ref. [2], the second moment for immobile CH 2 groups is 6oo2 = 1.79 × 10 -10 s -1 . By means of (1), an estimation is made for the correlation time r c of each of the examples under investigation, using the experimental data for 56o. The results obtained are given in table 1. The prolongated form and the flexibility of the molecules of Arkopal 10 permit us to consider them as polymer chains with intermediate length in a melt. We apply to our system the theory given by de Gennes [3] for the dynamics of melts or concentrated solutions of polymers, thus the diffusion of the molecule is considered as a translation in a tube, the so-called reptation. The resistance force F, supported by the molecule, is proportional to the velocity o of the reptation F
=
olut~,
(2)
where Ptr is the mobility of the molecules. The total force acting in the sample is the sum of all atomic groups comprising the molecules. We denote the number of these groups by M. For simplicity we assume the CH 2 groups, the CH 3 groups and the oxygen atoms to be equal. M
M
F = ~ F i = ~ o[pi, i=1 i=1
where Pi is the mobility of the ith group. In the case of all tai equal (pq =/al) we obviously shall have Pt~ = l a l l M .
(3)
Let us denote the mobility of an atomic group as p* (in our case an oxygen atom) in the case of a hydrogen bond, which makes movement difficult. The mobility of the other groups without hydrogen bonds can be assumed to be equal. It is again denoted by Pl. Then F = v ~1 + (M - 1)]/#*Pl • 140
(4)
Comparing (2) and (4), we can note that (5)
We suppose that (6)
then (7)
Pt~ = P* .
By analogy in the case of S hydrogen bonds we obtain Utr = ~* / s .
(8)
According to the theory of the reptation of one long and flexible molecule, the diffusion coefficient is equal to Dtr =latr k T ,
(9)
and in our case Dtr = p* k T / S .
(10)
The correlation time of this diffusion, which is also the correlation time of molecular reorientation, is given by rtx = L 2 / D t r = L 2S/p * k T .
(11)
and the velocity of reorientation by v = 1/ztx = p* k T / S L 2 .
(12)
According to the statistics, the probability for the P 1 hydrogen bond to be realized is ~l/Pl
1
where Pl
Pl ! ( , P - P l ) !"
p is the number of possible hydrogen bonds for one molecule Arkopal 10 and Pl is the number of the realized ones. Hydrogen bonds can be formed by the hydrogen nuclei of the water molecules (fig. 1B) and besides the hydrogen nuclei of the OH groups situated at the ends of each polyethylene glycol chain (fig. IA). m is the part of these hydrogen nuclei which form bridges between two detergent molecules by means of hydrogen bonds. The rest of the hydrogen nuclei form bonds between two or more water molecules
(fig. 1c). m = Nam/3 + 2 N D 2 0 ~ 2 ,
Volume 107A, number 3
C,H,,-(~-(OCH:CH,I
PHYSICS LETTERS
(OC,,CH,)(OC,,C,,)~OCJ~,CH,I(OC,,CH, IO
21 January 1985
can be expressed by the coefficient
7 = (Nam +No20/3)/(Nam + 0.5/3ND20). \H
C,H,, -(~-(OCH2CH,}
H
[OCH,CHz)(OCt4=CH,)(iCCH,}(OCh£Hz) H, 0H
Thus, let/S* be the effective mobility depending on the water concentration /S* = "//s o •
Fig. 1.
(16)
(17)
Nam and ND20 are the number of amphiphilic and water molecules in 1 gram of the system,
For all the concentrations used, the calculated values of/s 0 are the same within the limits of error (see table 1). We accept as the most probable value for/sO
13= llNam/(llNam +ND20).
/so = 2.4 X 106 .
The multiplier shows the number of oxygen atoms in one molecule Arkopal 10,
n= l lNam . The probability of formation of an arbitrary number (from 0 to p) of hydrogen bonds is x--~l p p \ W= p % t P l ) (m/n)Pl ( 1 - m / n ) P - P l = l .
(14)
One molecule occupies each of the states, expressed by (13) with probability ICpl. v, as mentioned above (12), is the frequency of reorientation of one molecule Arkopal 10 with S hydrogen bonds. The average frequency of reorientation is the sum of all p multiplied by their corresponding statistical weights (13). p
P pl=O Pl
(m/n)Pl (I - m / n ) P - P l Pl +-"'~I r c "
A similar equation can be written for each of the concentrations used by us. So, four equations can be written, from which v can be calculated for each of the concentrations (see table 1). As was mentioned above,/S* gives the mobility of a molecule of Arkopal 10 with one hydrogen bond. The hydrogen bonds under consideration can be divided into two groups: (1) single - realizing bridges between the OH group of one molecule Arkopal 10 with an oxygen atom of a neighbouring amphiphilic molecule; (2) hydrogen bonds by which one water molecule connects two neighbouring molecules of Arkopal 10 with the help of its two hydrogen atoms. Destruction of the second type of hydrogen bonds is twice as probable because of the participation of two consecutively connected hydrogen bonds. Due to this, if the mobility in the first case is/So, it will be 2/S0 in the second case. This difference in the two types of hydrogen bonds
(18)
The following value can be extracted, DpE = 4 X 10 -7 cm2/s,
(19)
from the paper of McCall and coauthors [4], through a graphic extrapolation and using the relation obtained in ref. [4] between the number of atomic groups and the diffusion of the polyoxyethylene chain, for the diffusion coefficient of a polyethylene chain with the same lenght L of the molecule Arkopal 10 at temperature T = 303 K. From (3) and (9) we obtain for the mobility of one CH2 group (the mobility of one atomic group without hydrogen bond) #IPE = 4 X 108 . The ratio/SlPE//S0 is then 170, which is in agreement with our supposition in (6). From the relation
la l / IsO = exp( AE/R T)
(20)
the value of one hydrogen bond in the system under investigation can be found: AE = 3 kcal/mole. This value is of the same order as the values known from the literature [5,6]. [1] A. Abragam, The principles of nuclear magnetism (Pergamon, London, 1961). [2] l.Ya. Slonim, Vysokomol. Soedin. 6 (1964) 1371. [3] P.-G. de Gennes, Scaling concepts in polymer physics (Cornell Univ. Press, Ithaca, 1979). [4] D.W. McCall,D.C. Douglass and E.W. Anderson, J. Chem. Phys. 30 (1959) 771. [5 ] G.C. Pimentel and A.L. McClellan,The hydrogen bond (Freeman, San Francisco, 1960). [6] P. Schuster, ed., The hydrogen bond, recent developments
in theory and experiments, Vols. 1, 2 (North-Holland, Amsterdam, 1976). 141