Makromol. Chem. 182,113 - I18 (1981) 113

The Partial Specific Volume of Lysozyme Chloride in Water under Pressure

Rose-Marie Chiri, Frangois AbPtino, Jean-Frangois Baret, Robert Catella

Universite de Provence, Departement de Physique des Liquides, Place Victor-Hugo, 13003 Marseille,

Jeanne Frangois, Jean Dayantis*

Centre de Recherches sur les Macromolecules, 6, rue Boussingault, F-67083 Strasbourg Cedex

(Date of receipt: August 1 , 1979)

SUMMARY: The apparent specific volume f;pp of lysozyme chloride dissolved in pure water has been

measured from 1 to 4000 bar using the Adams-Gibson-Anderson method of trapped mercury. A parametric expression for f;pp as a function of solute weight fraction x, is given for the various pressures at which the experiments have been performed. This parametric expression is valid when the densities of the solutions at atmospheric pressure and their compression at pressure P can be considered to be linear functions of the solute weight fraction x,. The relation between Cipp and the partial specific Vz is discussed and it is shown that within the range of con- centrations considered and given the precision of the experiments under pressure, the two quantities are indistinguishable.

Introduction

In this article we report some results concerning the apparent specific volume V;PP

The general relationship between the specific volume of a solution and the partial of lysozyme chloride in pure water from atmospheric pressure up to 4000 bar.

specific volumes of its components is, at the pressure P:

V(P) = x, v, ( P ) + x, f , ( P ) ( 1 a)

x, +X, ’1 (1 b)

Here V is the specific volume of the solution, V , , V, and x , , x, stand for the partial specific volumes and weight fractions, respectively, of components 1 and 2. If, in Eq. (1 a) the partial specific volume of water GI is replaced by its specific volume V p , Eq. (1 a) may be alternatively written

V(P) = x, vp(P) + x, V;Pp(P) (1 c)

which defines the “apparent” specific volume V;PP of the solute. From Eqs. ( 1 a) and (1 c) it is readily found that

f p p = v, + (x1/x2)(f, - fp) (1 d)

114 J . Dayantis et al.

which relates V;PP to Vz; V;PP is the quantity most easily determined by experiment and it is the one considered in this work. However, as shown in the discussion, the differ- ence between V;PP and Vz in our experiments is less than the experimental accuracy, so that conclusions drawn for V;PP would also apply for V2.

Materials and Methods

The specific volumes of the lysozyme solutions under pressure have been measured using the trapped mercury method of Adams ') and Gibson') which has been perfected by Anderson3). As the latter author describes the method in full detail, we shall here recall only the principle: piezometers of pyrex glass, resembling ordinary pycnometers but provided with a long glass stopper through which passes a capillary, are filled with the solution to be studied and then immersed head down in a container partially filled with mercury. During compression, the mercury flows drop by drop inside the reversed piezometer; during decompression, the mercury which has flowed inside the piezometer is trapped and the determination of its weight permits the determination of the compression of the solution. Our piezometers had a capacity of about 35 ml, somewhat larger than that of the piezometers used by Anderson3). The container holding them inside the high pressure vessel could accommodate four of them at the same time. The pressure inside the high pressure vessel (a cylinder of 30 cm height and 7 cm in diameter) was generated by a two stages hydraulic press, the pressure transmitting liquid being silicone oil. The entire apparatus was enclosed in a room thermostated to within f 1 "C.

With our piezometers, the relative precision of the compression measurements is about 2 . at 1 000 bar. This leads to a relative precision for f;pp of the solutions studied of the order of 1 . 10- '. These precisions are in principle improved when the pressure is increased, due to a higher weight of trapped mercury.

The densities of the solutions at atmospheric pressure have been determined using a "Kratky Digital Densimeter DMA O Y 4 ) . This apparatus permits the determination of the fifth decimal of the density, which leads to a relative precision of the order of 1 . 10- in the determination of f;PP at atmospheric pressure. Therefore, the measurements under pressure were by one order of magnitude less precise than the measurements under atmospheric pressure.

The lysozyme used was a chloride of Sigma Chemical, St. Louis, USA. The concentrations (in grams of solute per gram of solution) have been determined by weighing and by correcting for the water content of the protein. This water content was determined by the Karl Fischer') test.

The compression K ( P ) of the solutions (i.e. the relative volume variation - A V / V ) was determined using the relationship 3,

Here V , V, and VHg are, respectively, the volumes at atmospheric pressure of the piezometer, the capillary and the trapped mercury; K H g and Kg are the compressions at the pressure of the experiment of the mercury and of the pyrex glass. They are given in tables computed by Anderson6). From the compression K ( P ) of the solution, f;PP(P) was determined using the relation

Here p and po are, respectively, the densities of the solutions and of water at atmospheric pressure. The compression Ko(P) of water has been taken from data by Bridgman'). All the experiments were performed at 20°C.

The Partial Specific Volume of Lysozyme Chloride in Water under Pressure 115

Results

The densities at atmospheric pressure are summarized in Tab. 1. It is seen from Tab. 1 that i i ;PP presents a minimum somewhere between 1070 and

2% in lysozyme chloride content. It has been checked that the pH of the solutions

Tab. 1 . with different contents of lysozyme chloride at 20°C

Densities p and apparent specific volume f;pp of aqueous lysozyme chloride solutions

Lysozyme chloride (L.C.) P content in water (in g L.C./kg solution)

g/cm3

f;PP

cm3/g

0,ooOo 4,8065 7,2154

10,002 10,677 18,660 29,O 13 33,968

Fig. 1. Compression K versus lysozyme chloride content in grams of solute per 100 grams of solution of aqueous lysozyme chloride solutions at 1 OOO, 2000, 2 750 and 4 OOO bar as indicated

0,998206 1,000148 1,001145 1,002268 1,002536 1,005606 1,009943 1,011880

- 0,6276 0,6262 0,6235 0,6240 0,6225 0,6261 0,6329

I o-o-o

1000 bar

0’89 2 000

0*841 1,15 2 750

1 I I I

1 2 3 g Lysozyme chloride/100g solution

116 J. Dayantis et al.

remain very nearly constant throughout the concentration range investigated (the pH varies from 4,57 to 4,52 when x, is varied from 0,005 to 0,04). Consequently, the minimum observed cannot be ascribed to a variation of pH with solute concentration. On the other hand, our results for C2PP at atmospheric pressure are not readily com- parable to previous result^*^^), since the lysozyme we used was a chloride, which was not the case in the previous investigations. If we consider only the four first decimals of the density at atmospheric pressure, the density versus concentration plot of the solutions yields a straight line. This remark will be used in what follows.

In Fig. 1 we have plotted the compression K as a function of lysozyme chloride content at the various pressures studied. It is seen that the compression is a linear function of the lysozyme concentration in the range covered by the experiments. As already indicated, the precision of the compression measurements is about 2 . at 1 OOO bar, so that, when using Eq. (3), consideration of more than four decimals of the density is not warranted. At this precision the density versus lysozyme chloride content plot is a straight line so that we can write

K = K o - ax, (4 a)

P = P O + bx2 (4 b)

where a and b are experimentally determined positive constants. Here x, is expressed as grams solute per gram solution. Introducing Eqs. (4a) and (4b) into Eq. (3) one obtains

A + Bx, p;PP =

Po + b x ,

where

We can take po = 0,99821 g/cm3 and b = 0,4052 g/cm3. The constants A and B, determined using values of a from the slopes of the straight lines in Fig. 1 are given in Tab. 2.

From the constants in Tab. 2 it is easy to calculate CiPP for any concentration at a given pressure, provided that one remains in the domain of validity of Eqs. (4a) and (4b). It is found that the variation with concentration at a given pressure is linear, and bears on the third decimal only of CiPP. If only two decimals are considered, as warranted by the precision of the experiments, C$PP is constant with concentration at a given pressure. To the same precision, C;PP at atmospheric pressure would be constant, the variation observed being apparent only if the full set of decimals is considered. On the other hand, at a given concentration, CiPP goes through a maximum before decreasing with increasing pressure. This behaviour is due to the fact that in the compression versus lysozyme chloride content plot (Fig. I ) , the slope

The Partial Specific Volume of Lysozyme Chloride in Water under Pressure 117

Tab. 2. Numerical values for KO, a, A and B from Eqs. (5a) and (5 b) for aqueous lysozyme chloride solutions at 20°C and different pressures P, where x2 is expressed in grams solute per gram solution

P / b a

KO U

A B

1000 2000 2 750 4000

0,03958 0,06937 0,08776 0,11371 0,02569 0,06032 0,07520 0,05982 0,5963 0,6132 0,6172 0,5864 0,3900 0,3777 0,3703 0,3597

of the straight lines increases in absolute value before decreasing when the pressure is increased.

Discussion

The physically relevant quantity to be studied is the partial specific volume V2 = (i3V/i3m2),,, T , p , where m1 and m2 are the weights of solvent and solute in the solution. If the apparent specific volume V;PP has been considered instead, it is because this quantity is more easily experimentally determined. The relation between V2 and V;PP is given by Eq. (1 d). If V , = Vf, (i.e. if the partial specific volume of the solvent is independent of the solute concentration), then V2 = ViPP. Furthermore, since, following the Gibbs-Duhem relation, m,dV, + nz2dV2 = 0, in this case V2 is also independent of solute concentration. It suffices therefore, in order to determine the concentration range where the near equality V2 = i j ;PP applies, to determine the experimental domain where, within experimental precision, V2 may be considered to be a constant quantity. We have seen previously that considering only two decimals, V;PP is constant through the concentration range studied, so that we expect that the near equality V2 = V;PP applies for our experiments. That this is true may more precisely be shown as follows:

Let rn2 grams of solute be dissolved in m, grams of solvent, let K be the compres- sion and V the volume of the solution. Then,

V(m,, m2, K ) = (m, + m2) V(x2, K ) = (m, + m2) f2(x2, 0) (1 - K ) = (m, + mz) (1 - K ) / P ( X ~ , 0)

Using Eqs. (4a) and (4b) and developing to the second order one finds:

Po Po

where we have neglected third order terms. From V2 = (i3V/i3m2),,,T,p taking into account that (8x2/i3m2),, = ( l /m2)x2(1 - x2) it follows that

118 J. Dayantis et al.

At 4000 bar, a = O,M, KO = 0,11 and as b = 0,405, one finds

1 - [0,59 + 0,28 X, - 0,14 x;] Po

f2

For x, = 0,03, the highest concentration used, C, = (l/p0)(0,59 + 0,0084), so that the contribution of the first order term in x, amounts to about 1,4070 of the constant term. From this we may conclude that the value 0,03 for the concentration is about the limiting value where the near equality Cz = @’P applies, taking into account the precision of our experiments. We therefore conclude that insofar as the experimental results are relevant, the maximum observed for CtPP when increasing the pressure at constant concentration should also be true for Vz. This maximum may be interpreted in terms of changes of hydration with pressure lo). We hope to examine this point in more detail in a forthcoming article.

One of the authors (J.D.) thanks Dr. R e d Charmusson, Maitre-Assistant B 1’Universitt de Provence, for his help in preparing the above described experiments.

’) L. H. Adams, J. Am. Chem. SOC. 53, 3769 (1931) 2, R. E. Gibson, J. Am. Chem. SOC. 59, 1521 (1937) 3, G. R. Anderson, Arkiv Kemi 20, 513 (1963) 4, 0. Kratky, H. Leopold, H. Stassinger, Z. Angew. Phys. 27, 273 (1969) ’) J. Mitchell and D. M. Smith, “Aquametry. Application of the Karl Fischer reagent to

quantitative analyses involving water”, Interscience, New York 1948 6, Tables computed by G. R. Anderson and available at the Institute of Physical Chemistry of

the University of Uppsala, Sweden ’) P. W. Bridgman, Proc. Am. Acad. Arts Sci. 48, 309 (1913) *) I . Pilz, G. Czerwenka, Makromol. Chem. 170, 185 (1973) 9, F. J . Millero, G. K. Ward, P. Chetirkin, J. Biol. Chem. 251, 4001 (1976)

lo) S. D. Hapann, “Physico-Chemical Effects of Pressure”, Butterworths, London 1957