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A study of the behaviour of ampicillin in aqueous solution and thermodynamic characterization of its aggregation

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M
OLECULAR
P
HYSICS
, 2001, V
OL.
99, N
O.
24, 2003±2009
A study of the behaviour of ampicillin in aqueous solution andthermodynamic characterization of its aggregation
LINA BESADA, PABLO MARTINEZ-LANDEIRA, LAURA SEOANE,GERARDO PRIETO, FELIX SARMIENTO and JUAN M. RUSO*Biophysics and Interfaces Group, Department of Applied Physics,Faculty of Physics, University of Santiago de Compostela,E-15782 Santiago de Compostela, Spain
(
Received 5 June 2001; revised version accepted 9 August 2001
)The aggregationof ampicillin in water has been examined by conductivitymeasurementsoverthe temperature range 288.15±313.15K and light scattering.These measurements indicate theformationof two critical concentrationsover the range0±0.35 mol kg
¡
1
. Aggregationnumberand eectiveaggregatechargewere calculatedfromthestaticlight scatteringdataaccordingtothe Anacker and Westwell treatment. Thermodynamic parameters of aggregate formationwere obtained from a form of the mass action model applicable to systems of low aggregationnumber. This method was applied at both critical concentrations.A valence of one was usedfor the monomers presentin the ®rst equilibrium.The second equilibrium was between aggre-gates of two dierent sizes, in this case, the valenceof the aggregatesbeing the eective chargecalculated from the Anacker and Westwell treatment. Experimental results show that freeenergies of micellization for ampicillin are higher for the ®rst critical concentration and inthe same range, but lower than for other penicillins. The enthalpies of micellization becomenegativewhen the temperatureis increased,but the variationis three times greaterfor the ®rstcritical concentration than for the second.
1. Introduction
It is well known that amphiphilic molecules have spa-tially distinct polar and non-polar parts. The number of amphiphilic molecules is very wide, including dierentstructures, sizes and shapes. Aqueous solutions of these molecules show completely normal physical-chemical properties when they are suciently dilute.When the concentration increases, a rapid change inphysical-chemical properties is observed. This changeoccurs in all properties over the same range of concen-trations, which is narrow enough to be called criticaland is interpretable as an aggregation of the monomersinto aggregates called micelles. Therefore this is desig-nated the critical micellization concentration, (cmc).This aggregation depends primarily on the moleculearchitecture, the solvent, the presence of added compon-ents (such as salt, ions) and the temperature. Themicelles are in rapid equilibrium with single molecules.A very important parameter of micelles is aggregationnumber, which is the average number of monomers inone micelle [1±3].Micelles formed in an aqueous environment can havea variety of shapes (depending on the geometry of themolecules comprising the aggregate), having a hydro-philic exterior and hydrophobic core. Micellar solutionsare important for a variety of applications, includingdetergency, catalysis, pharmaceuticals, food and cos-metics. Recently, micelles have become more relevantdue to their being useful physical models for more com-plicated biological systems such as biomembranes [4±9].From a thermodynamic point of view, two classicalapproaches have been used to analyse the process of micellization: the phase separation model, wheremicelles are considered to form a separate phase at thecmc, and the mass action model, where micelles aretreated as solution species.We have studied the self-association in aqueoussolutions of several penicillins such as penicillin V [10],nafcillin, cloxacillin, dicloxacillin and ¯ucoxacillin [11± 13] and other pharmacologically interesting drugs [14,15] using dierent physical techniques such as electricalconductivity, microcalorimetry, surface tension, staticand dynamic light scattering and nuclear magneticresonance. These have given us a solid base to undertakeon a systematic investigation of new substances. In thepresent study we have examined the aqueous behaviourof ampicillin as a function of temperature and have
Molecular Physics
ISSN 0026±8976 print/ISSN 1362±3028 online
#
2001 Taylor & Francis Ltdhttp://www.tandf.co.uk/journalsDOI: 10.1080/00268970110089126
*Authorforcorrespondence.e-mail:faruso@uscmail.usc.es
characterized thermodynamically the aggregationprocess.Ampicillin (
1
) is an antibiotic in the class of drugscalled penicillins. Ampicillin ®ghts bacteria in thehuman body; it is used to treat many dierent types of infection, such as tonsillitis, pneumonia, bronchitis,urinary tract infections, gonorrhea, and infections of the intestines such as
Salmonella
(food poisoning).Electrical conductivities for a range of temperatures(from 288.15 K to 313.15K) were measured, showingthe typical slope change in the aggregation process.With static and dynamic light scattering the formationand presence of micelles is corroborated. Also, theaggregation number and micellar charge are determinedby these techniques, which are necessary for calculatingthe free energies of micellization on the basis of massaction model. Enthalpies and entropies of micellizationwere calculated from the application of the Gibbs± Helmholtz equation. All these events are typical of aggregation studies. However, here we show how theaggregation of ampicillin results in two critical concen-trations and the mass action model is applied at both.The ®rst is considered an equilibrium between mono-mers and micelles, and in the second the micelles areconsidered more like monomers possessing the netcharge of the micelle.
2. Experimental
2.1.
Materials
Ampicillin (
d
(
7
)-
¬
-aminobenzylpenicillin, sodiumsalt, molecular weight 371.4), product No. A-9518,was purchased from Sigma Chemical Co. Solutionswere prepared with doubly distilled and degassed water.2.2.
Instrumentation
Conductance was measured by using a conductivitymeter (Kyoto Electronics type C-117) the cell of which(Kyoto, type K-121) was calibrated with KCl solutionsin the appropriate concentration range. The cellconstant was calculated using molar conductivity datapublished by Shedlovsky [16] and Chambers
et al.
[17].Concentrated solutions of surfactant systems of known concentration were progressively added tobuer solution using an automatic pump (Dosimat 665method). The measuring cell was immersed in a thermo-statted bath, maintaining the temperature constant towithin 0
:
01K.Static light-scattering measurements were made at298 0
:
1K using a Coherent DPSS 532 laser light-scattering instrument equipped with a 0.5W solid statelaser, operating at 532nm with vertically polarized light.Solutions were clari®ed by ultra®ltration through 0.1
m
m®lters with the ratio of light scattering at angles of 45
8
and 135
8
not exceeding 1.10.The refractive index increments of the ampicillinaggregates were measured at 298 0
:
1K using an RA-510M (Mettler Toledo) refractometer. These values werecalculated for 589.3nm (line D of sodium), giving a vari-ation with concentration of 0
:
07004 0
:
00037kgmol
¡
1
.Dynamic light scattering measurements were made at298 0
:
1K and at a scattering angle of 90
8
. Timecorrelation was analysed by an ALV-5000 multiple-taucorrelator (ALV, Langen, Germany). Solutions wereclari®ed as described above. Diusion coecients weredetermined from a single exponential ®t to the correla-tion curve. Hydrodynamic radii were calculated frommeasured diusion coecients by means of theStokes±Einstein equation.
3. Results and discussion
Figure 1 shows the speci®c conductivities
µ
of peni-cillin in aqueous solution for dierent temperatures:288.15, 293.15, 298.15, 303.15, 308.15 and 313.15K. Itis common for a break to appear in this kind of plot. Atthe break point, the critical micellization concentration2004 L. Besada
et al.
(
1
)Figure 1. Speci®c conductivity
µ
of ampicillin in water as afunction of molality at dierent temperatures:
&
, 288.15;
*
, 293.15;
~
, 298.15;
!
, 303.15;
^
, 308.15; and
‡
,313.15K.
(cmc) represents the surfactant concentration beyondwhich all further surfactant added forms micelles. Theduration of the dynamic processes may vary from 10
¡
8
s(which is the time it takes a surfactant to leave or enter amicelle), to 10
¡
2
s (the timescale of the fusion of micelles)[18], so the equilibrium process occurs in just a fewseconds after dilution when the measurement is made.Although the gradual decrease in the slope of ®gure 1seems to indicate an aggregation process, if does notallow us to calculate exactly what kind of behaviourthe penicillin exhibits. For this purpose we carried outstatic light-scattering measurements at the same tem-perature and for the same range of concentrations.The results are given in ®gure 2, where the concentrationdependence of the light-scattering ratio
S
90
(intensity of light scattered by the solution relative to that obtainedfrom toluene) shows abrupt discontinuities at wellde®ned critical concentrations. The ®rst critical concen-tration is determined from the intersection of the scat-tering curves and the theoretical line of monomers(represented by a dashed line in ®gure 2). This linewas obtained by application of the Anacker andWestwell treatment [19], which is explained in the nextparagraph, considering aggregation number 1 and nomonomer±monomer interactions so the second virialcoecients are zero. This concentration represents the®rst step in the aggregation process, when there aremicelles in the solution. When the higher concentrationis reached a second break point is shown. This kind of behaviour was observed for a wide range of ionic sur-factants, and generally has been interpreted in terms of atransition from spherical to cylindrical micelles [20].Amphiphilic drugs with the phenothiazine ring systemalso have two or three critical concentrations [11, 21± 23], although with these kinds of molecule the additionalbreak point is attributed to a restructuring of the aggre-gate rather than to a sphere-to-rod transition, due totheir low aggregation numbers.The aggregation numbers
N
1
, and eective aggregatecharges
z
1
, corresponding to the ®rst critical concentra-tion were calculated according to the Anacker andWestwell treatment [19], in which the light-scatteringfrom solutions of ionic aggregates is represented by
K
0
m
2
¢
R
90
ˆ
2
m
3
‡
N
¡
11
…
z
1
‡
z
21
†
m
2
‰
2
N
1
‡ …
2
N
1
†
¡
1
…
z
1
‡
z
21
†
f
2
¡
2
fz
1
Š
m
3
‡
z
1
m
2
;
…
1
†
where
¢
R
90
is the Rayleigh ratio of the solution inexcess of the solution at the critical concentration,
m
2
is the molality of the aggregated species in terms of monomer,
m
3
is the molality of the supporting electro-lyte, and
f
ˆ …
d
n
=
d
m
3
†
m
2
=
…
d
n
=
d
m
2
†
m
3
.
K
0
for verticallypolarized incident light is de®ned by
K
0
ˆ
4
º
2
n
20
…
d
n
=
d
m
2
†
2
m
3
V
0
=
L
¶
4
;
…
2
†
with
n
0
being the refractive index of the solvent,
V
0
the volume of solution containing 1kg of water,
L
Avogadro’s number, and
¶
the wavelength of the inci-dent light (532nm). Expansion of equation (1) in powersof
m
2
leads to
K
0
m
2
¢
R
90
ˆ
A
‡
Bm
2
‡
. . .
;
…
3
†
where
A
ˆ
4
N
1
‰…
2
N
1
¡
fz
1
†
2
‡
z
1
f
2
Š
¡
1
…
4
†
and
B
ˆ
z
1
A
…
2
m
3
†
¡
1
‰…
1
‡
z
1
†
N
¡
11
¡
A
Š
:
…
5
†
The results obtained for this ®rst point were
N
1
ˆ
3 and
z
1
ˆ
1
:
11.Estimation of the size of the aggregates formed at thesecond critical concentration is more speculative. Weassume that these aggregates are formed by the single-step association of the aggregates present at the ®rstcritical concentration, treated like monomers withcharge
z
1
, and are in equilibrium with these primaryaggregates. The properties of the aggregates formed atthe second critical concentration were determined byapplication of the general ¯uctuation theory of lightscattering by multicomponent systems to surfactantsolutions, following the method of Anacker andJacobs [24]. This method of treatment of the staticlight scattering data gives only an approximate indica-tion of the size of the micelles formed at the secondcritical concentration, assuming that the aggregates
Aggregation of ampicillin in aqueous solution
2005
Figure 2. Variation of the scattering ratio
S
90
with molality
m
for ampicillin in water at 298.15K. The dashed lineindicates the theoretical line for unassociated monomers.Arrows denote the critical concentrations.
formed at the ®rst one are particles with charge
z
1
,which aggregate at the ®rst critical concentration withan aggregation number
N
2
. We have previously appliedthe method to other systems exhibiting this type of as-sociation process, such as dicloxacillin and ¯ucloxacillin[11] and penicillin V [10]. The excess turbidity due to amicellar component of a 3-component system withregard to the solvent is given by [25]
½
ˆ
C
3
‡
C
4
m
0
2
C
1
‡
C
2
m
0
2
…
Hn
0
22
V
0
m
0
2
†
;
…
8
†
where
H
ˆ
16
º
K
0
=
3, and
m
0
2
is the molality of themicellar species at concentrations above the second cri-tical concentration,
n
0
2
ˆ…
@
n
=@
m
0
2
†
T
;
P
;
w
1
;
w
3
;
C
1
ˆ
…
‡
¿
†
m
3
;
C
2
ˆb
…
‡
¿
†
N
2
‡
z
2
…
z
2
‡
1
†…
f
2
=
N
2
†…
=
…
‡
¿
††¡
2
fz
2
c
m
3
;
C
3
ˆb
…
‡
¿
†
N
2
‡
z
2
…
z
2
‡
1
†…
f
21
=
N
2
†…
=
…
‡
¿
††¡
2
f
1
z
2
c
m
3
;
C
4
ˆ
z
2
¿:
T
is the absolute temperature,
P
is the pressure,
w
1
is thenumber of water molecules,
w
2
is the number of micelles,
…
z
2
w
2
‡
w
3
†
is the number of counterions,
¿
w
3
is thenumber of drug ions and co-ions,
f
ˆ
N
2
n
3
=
n
2
, and
z
2
isthe charge of the micelle. Expansion of equation (8) inpowers of
m
0
2
leads to
Hn
0
22
V
0
m
0
2
½
ˆ
A
‡
Bm
0
2
‡
. . .
;
…
9
†
where
A
ˆ
C
1
C
3
ˆ
…
‡
¿
†
2
N
2
…
‡
¿
†
2
N
2
‡
…
z
2
‡
z
22
†
f
21
¡
2
…
‡
¿
†
z
2
f
1
N
2
;
…
10
†
B
ˆ …
C
2
¡
C
4
A
†
AC
1
ˆ
¿
A
…
z
2
‡
z
22
¡
z
2
AN
2
†
…
‡
¿
†
m
3
N
2
:
…
11
†
A
and
B
can be determined experimentally as the inter-cept and limiting slope, respectively, of the plot of
Hn
0
22
V
0
m
0
2
=½
versus
m
0
2
. By solving equations (10) and(11) simultaneously, the following expressions for
z
2
and
N
2
are obtained:
z
2
ˆ ‰
¿
…
‡
¿
†
3
m
3
B
Š
1
=
2
‡
…
‡
¿
†
f
1
m
3
B
…
‡
¿
¡
f
1
A
†
¿
A
;
…
12
†
N
2
ˆ …
z
2
‡
z
22
†
¿
A
…
‡
¿
†
m
3
B
‡
z
2
¿
A
2
;
…
13
†
which lead to a global aggregation number
…
N
ˆ
N
1
N
2
†
of 6.As an example and to con®rm the existence of aggre-gates we use a measurement of dynamic light-scatteringto obtain a size distribution. We have chosen the highestconcentration, 0.35molkg
¡
1
, far away from the twobreak points, and consequently, where aggregates arepresent. The correlation functions from dynamic light-scattering were single exponentials and were analysed bythe Contin method. Polydispersity indices generated bythis analytical method were less than 0.1, indicative of areasonable degree of monodispersity of size. Figure 3shows the size distribution obtained. It is a single peakcentred at 2.94nm.With the presence of an aggregation process guaran-teed we can return to conductivity data. These resultswere analysed to detect precise values of critical micellarconcentrations (cmcs) by two methods, the ®rst usingthe Phillips [26] de®nition of the critical micelle concen-tration, which de®nes it as the concentration corre-sponding to the maximum change in gradient in plotsof the solution conductivity versus concentration:
¯
3
µ¯
m
3
Á !
c
ˆ
cmc
ˆ
0
:
…
14
†
A numerical analysis of the data was made by meansof a recently developed algorithm [27]. The methodallows the determination of precise values of the criticalconcentrations of drugs and surfactants of low aggrega-tion number, and it consists of a Gaussian approxima-tion of the second derivative of the conductivity/concentration data, followed by two consecutive numer-ical integrations by the Runge±Kutta [28] method andthe Levenverg±Marquardt least-squares ®tting algor-ithm [29]. Figure 4 shows the existence of two minimaof the second derivative and therefore two critical con-2006 L. Besada
et al.
Figure 3. Size distributionof a solution of ampicillin in waterwith
m
ˆ
0
:
35molkg
¡
1
at 298.15K
centrations for ampicillin, as might be expected fromlight-scattering data.In the second method each break is at the point of intersection of the straight line ®ts to the high and lowconcentration regions. In order to settle the ambiguity inselecting the linear regimes in the high concentrationand low concentration parts of the curve, the followingmethod was adopted. The data were split into twogroups, for each point, with varying number of pointsin each group. Both groups were ®tted by linear regres-sions and the average value of the correlation coecientwas noted down. The maximum of the correlation coef-®cient would correspond to that grouping of the datawhich would have the best linear ®t in both low and highconcentration regimes. The break point was determinedby grouping the data as per this correlation coecientvalue. Values obtained from the two methods are shownin table 1.The variation in critical concentrations with tempera-ture passes through a minimum close to 294K for both,and the concentrations were ®tted to the equationln
X
cmc
ˆ
a
‡
bT
‡
cT
2
;
…
15
†
for the values of the coecients refer to table 2.The thermodynamic properties of aggregation werederived by application of the mass action model [30]as follows. If the equilibrium between ions and aggre-gates is represented by the equation
n
D
v
‡
‡ …
nv
¡
p
†
X
¡
,
A
p
‡
;
…
16
†
where D
v
‡
denotes the drug ion, A
p
‡
the aggregate witheective charge
p
, X
¡
the counterion,
v
the valence of the monomer and
n
the aggregation number, then it ispossible to determine the thermodynamic properties of aggregation using a modi®cation of the mass actionmodel for application to systems of low aggregationnumber [31]. The equilibrium constant for the aggre-gation process is expressed as1
K
m
ˆ
nv
…
nv
¡
p
†
‰
n
…
v
‡
1
†¡
p
Š‰
2
n
…
v
‡
1
†¡
2
p
¡
1
Š
n
…
v
‡
1
†¡
p
¡
2
‰
n
…
v
‡
1
†¡
p
Š‰
2
n
…
v
‡
1
†¡
2
p
¡
1
Š‰
n
…
v
‡
1
†¡
p
¡
1
Š‰
2
n
…
v
‡
1
†¡
2
p
‡
2
Š
X
cmc
µ ¶
n
…
v
‡
1
†¡
p
¡
1
;
…
17
†
where
v
is the valence of the monomer.
Aggregation of ampicillin in aqueous solution
2007
Figure 4. Speci®c conductivity
µ
of ampicillin in water as afunction of molality at 298.15K. The dashed lines repre-sent the two Gaussian ®ts of the second derivative of theconductivity±concentration curve. Arrows denote theminimum of the Gaussian.Table 1. First and second critical concentrations of ampicil-lin in water at dierent temperatures. The methods of determination are explained in the text.cmc
1
/molkg
¡
1
cmc
2
/molkg
¡
1
First Second First SecondTemperature/K method method method method288.15 0.075 0.073 0.234 0.230293.15 0.068 0.068 0.230 0.221298.15 0.071 0.070 0.229 0.231303.15 0.074 0.072 0.236 0.240313.15 0.081 0.080 0.243 0.246318.15 0.084 0.081 0.245 0.246Table 2. Coecients
a
,
b
and
c
for ®ts of equation (15).
a b c
For the ln
X
cnc
against
T
®tFirst cmc 47 23
¡
0
:
36 0
:
16 6
:
1 10
¡
4
2
:
6 10
¡
4
Second cmc 10
:
7 7
:
6
¡
0
:
110 0
:
051 1
:
86 10
¡
4
0
:
84 10
¡
4
For the ln
K
m
against
T
®tFirst cmc
¡
191 89 1
:
45 0
:
59
7
24
:
6 10
¡
4
9
:
8 10
¡
4
Second cmc
¡
33 22 0
:
32 0
:
15
7
5
:
4 10
¡
4
2
:
4 10
¡
4

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