Pascale Royer
email: pascale.royer@umontpellier.fr

Low scale separation induces modification of apparent solute transport regime in porous media

First order asymptotic homogenization allows to determine the effective behaviour of a porous medium by starting from the pore scale description, when there is a large separation between the pore scale and the macroscopic scale. When the scale ratio is â ȂIJsmall but not too small,â Ȃİ additional terms need to be taken into account, which can be obtained by exploiting higher order equations in the asymptotic homogenization procedure. The aim of the present study is to derive second order models to describe solute transport in a macroscopically homogeneous porous medium at low scale separation. The three following macroscopic transport regimes are successively considered: pure diffusion with fluid at rest, predominant diffusion with fluid in motion and advection-diffusion. The results show that while the transport regime remains of diffusive type when the fluid is at rest, low scale separation induces modification of apparent transport regime when fluid is in motion. Indeed, predominant diffusion and advection-diffusion lead to the apparent regimes of advection-diffusion and of dispersion, respectively.

I. Introduction

Most studies in the theory of flow and transport in porous media are based on the exploitation of the continuum theory, which requires that the condition of separation of scales be fulfilled. First order asymptotic homogenization can be used to derive such continuum models. When the scale ratio is "small but not too small", the additional terms which are required to account for micro-structural scale effects can be obtained by considering higher order correctors in the asymptotic homogenization procedure. The present paper is aimed at analysing the influence of low scale separation on solute transport in macroscopically homogeneous rigid porous media. The objective is to derive second order homogenized models for the three following macroscopic transport * regimes: pure diffusion with the fluid at rest, predominant diffusion with the fluid in motion and advection-diffusion. The results show that low scale separation induces modification of apparent transport regime when fluid is in motion. The paper is organised as follows. Section II presents a brief description of the homogenization methodology. Second order homogenization of pure diffusion is detailed in Section III, and second order homogenization of convection-diffusion in the regimes of predominant diffusion and of advection diffusion is the purpose of Section IV. Finally, Section V presents a summary of the main theoretical results contained in this work and highlights conclusive remarks.

II. Homogenization method i. Medium under consideration

We consider a periodic porous medium, of macroscopic characteristic size L, and made of a solid matrix and of a fluid-saturated pore space. We further denote the periodic cell by Ω, its characteristic length by l, and we formulate the condition of separation of scales by ε = l/L 1. Within the periodic cell, we denote by Ω p the fluid-saturated pore domain, by Ω s the solid matrix, and by Γ their common interface, as depicted in Fig. 1. Using the two characteristic lengths, l and L, and the physical space variable, X, we define two dimensionless space variables: y = X/l, x = X/L, and y and x describe variations on the microscopic and the macroscopic scales, respectively. Invoking the differentiation rule of multiple variables, the gradient operator with respect to X is written as

∇ X = 1 l ∇ y + 1 L ∇ x . (1)
ii. Nondimensionalisation of pore scale description

The methodology firstly consists in writing the dimensionless pore scale description, which is the set of dimensionless equations that describe the phenomena being considered within the periodic unit cell. Each quantity in a dimensionless equation is the ratio of its physical counterpart to its characteristic value (indexed by c). This writing gives rise to dimensionless numbers, which are defined by means of characteristic values. These dimensionless parameters are then estimated with respect to powers of the small parameter ε. A parameter P is said to be of order ε p , P = O(ε p ), when

ε p+1 P ε p-1 . (2)
The dimensionless writing of the equations requires the choice of a characteristic length for the dimensionless writing of space derivatives. We arbitrarily choose L as the reference characteristic length. The dimensionless gradient operator is thus L ∇ X , which by Eq. ( 1) is given by ∇

= L ∇ X = ε -1 ∇ y + ∇ x . (3)
iii. Homogenisation procedure

The homogenization method being used is an asymptotic approach. It is therefore based upon the fundamental assumption that the unknown fields can be written in the form of asymptotic expansions in powers of ε

ψ = ψ 0 ( y, x) + εψ 1 ( y, x) + ε 2 ψ 2 ( y, x) + ... (4)
in which functions ψ i are Ω-periodic in variable y. The method consists in incorporating the asymptotic expansions in the dimensionless local description, while replacing the dimensionless numbers by their orders of magnitude in power of ε and taking into account the expression of the dimensionless gradient operator Eq. ( 3). This leads to approximated governing equations and boundary conditions at the successive orders, which together with the condition of periodicity define well posed boundary value problems within the periodic unit cell, from which functions ψ i can be determined. Existence of solutions requires that volume averaged equations be satisfied. These latter actually describe the macroscopic behaviour at successive orders.

III. Second order homogenization of pure diffusion

Considering the fluid-saturated medium depicted in Fig. 1, let us assume that the fluid phase which contains a low concentration of solute, is at rest, so that the solute is only transported by diffusion.

i. Pore scale dimensionless description

The transport of solute by diffusion in the pore domain is described by conservation of mass within Ω p and the no-flux boundary condition over Γ. When cast in dimensionless form, these equations read

(b) (a) Ω s Γ Ω p
   N ∂c ∂t -∇ • (D 0 ∇c) = 0 within Ω p , (5) (D ∇c) • n = 0 over Γ, (6)
where c denotes the solute concentration (mass of solute per unit volume of fluid), t is time, D 0 denotes the coefficient of molecular diffusion and n represents the unit vector giving the normal to Γ exterior to Ω p . Parameter N is a dimensionless number, which is defined by

N = L 2 D 0 c t c = t diff t c , t diff = L 2 D 0 c , ( 7
)
where t c is the characteristic time of observation and t diff is the characteristic time of diffusion. We take t c = t diff , i.e.

N = O(ε 0 ), (8)
which fixes the time of observation so as to get a transient regime on the macroscopic scale.

ii. Second order homogenization

We consider Eq.( 5) with estimate Eq. ( 8), and boundary condition Eq. ( 6), and we look for solutions in the form of Eq. ( 4) for c. Incorporating the asymptotic expansion of c and the expression of the dimensionless gradient operator Eq. (3) into Eqs.( 5)-( 6), and then identifying terms of same power of ε, leads to boundary value problems in terms of functions c i at the successive orders.

Boundary value problem for c 0 Considering Eq. ( 5) at O(ε -2 ) and Eq. ( 6) at O(ε -1 ), we get the first order boundary value problem

             ∂ ∂y i D 0 ∂c 0 ∂y i = 0 within Ω p , (9)
D 0 ∂c 0 ∂y i n i = 0 over Γ, (10)
c 0 : periodic in y, (11)
from which it is clear that the concentration c 0 is constant over the period

c 0 = c 0 ( x, t). ( 12
)
Boundary value problem for c 1

At the second order, we obtain the following boundary value problem for c 1 :

             ∂ ∂y i D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i ) = 0 within Ω p , ( 13
) D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i ) n i = 0 over Γ, ( 14
)
c 0 : periodic in y. ( 15
)
By virtue of linearity, the solution reads

c 1 = χ j ( y) ∂c 0 ∂x j + c1 ( x, t), (16)
where c1 ( x, t) is an arbitrary function. Note that, to render the solution unique, we impose that χ is average to zero < χ >= 0 (e.g. [START_REF] Bensoussan | Asymptotic Analysis for Periodic Structures[END_REF], [START_REF] Sanchez-Palencia | Non-Homogeneous Media and Vibration Theory[END_REF]), where the volume mean over Ω p is defined by

< • >= 1 | Ω | Ω p • dΩ. ( 17
)
Note further that, since we are considering a macroscopically homogeneous medium, χ doesn't depend on variable x: χ = χ( y).

First order macroscopic description

Let consider the boundary value problem Eqs.

(5)-( 6) at the third order:

                   ∂c 0 ∂t - ∂ ∂y i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) - ∂ ∂x i D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i ) = 0 within Ω p , ( 18
)
D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) n i = 0 over Γ. (19)
The homogenization procedure consists now in integrating Eq. ( 18) over Ω p . This leads to the so called compatibility condition, which is a necessary and sufficient condition for the existence of solutions, and further represents the first order macroscopic description. Integrating equation Eq. ( 18) and invoking Gauss' theorem, while taking boundary condition Eq. ( 19) into account, together with the condition of periodicity, yields

φ ∂c 0 ∂t - ∂ ∂x i < D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i > = 0. (20)
Now, using Eq. ( 16), we can write:

∂c 1 ∂y i + ∂c 0 ∂x i = γ 0 ij ∂c 0 ∂x j , γ 0 ij = ∂χ j ∂y i + I ij . ( 21
)
Eq. ( 20) can thus be rewritten as follows

φ ∂c 0 ∂t - ∂ ∂x i (D ij ∂c 0 ∂x j ) = 0, ( 22
)
where

D ij = 1 | Ω | Ω p D 0 γ 0 ij dΩ (23)
is the tensor of effective diffusion. Eq. ( 22) may be expressed as

      φ ∂ < c > ∂t - ∂ ∂x i (D ij ∂ < c > ∂x j ) = O(εφ ∂ < c > ∂t ). (24)
In the above writing < c > represents the first order average concentration, where the first order average of any field ψ is defined by

< ψ >=< ψ 0 > +O(ε < ψ >). ( 25
)
The above equation represents the first order macroscopic description for pure diffusion.

Boundary value problem for c 2

The third order boundary value problem Eqs. ( 18)-( 19) can be transformed so as to obtain the following well-posed problem for c 2

                           ∂ ∂y i D 0 ( ∂c 2 ∂y i + χ j ∂ 2 c 0 ∂x i ∂x j + ∂ c1 ∂x i ) = ( 1 φ D ij -D 0 γ 0 ij ) ∂ 2 c 0 ∂x i ∂x j within Ω p ,( 26
)
D 0 ( ∂c 2 ∂y i + χ j ∂ 2 c 0 ∂x i ∂x j + ∂ c1 ∂x i ) n i = 0 over Γ, (27)
whose solution reads

c 2 = η jk ( y) ∂ 2 c 0 ∂x j ∂x k + χ j ( y) ∂ c1 ∂x j + c2 ( x, t), (28)
where c2 ( x, t) is an arbitrary function and where < η jk >= 0.

Derivation of the second order corrector

The fourth order of Eqs. ( 5)-( 6) yields:

                   ∂c 1 ∂t - ∂ ∂y i D 0 ( ∂c 3 ∂y i + ∂c 2 ∂x i ) - ∂ ∂x i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) = 0 within Ω p , ( 29
) D 0 ( ∂c 3 ∂y i + ∂c 2 ∂x i ) n i = 0 over Γ. ( 30
)
The second order corrector of the macroscopic description is obtained by integrating Eq. ( 29) over Ω p . This leads to

φ ∂ c1 ∂t - ∂ ∂x i (E ijk ∂ 2 c 0 ∂x j ∂x k + D ij ∂ c1 ∂x j ) = 0, ( 31
)
where

E ijk =< D 0 ( ∂η jk ∂y i + χ i I jk ) > . ( 32
)
The third order tensor E ijk is symmetric with respect to its last two indices and antisymmetric with respect to its first two indices, and, as a result of this anti-symmetry property, the second order gradient term of Eq. ( 31) vanishes (Cf. A). Thus, the second order corrector finally reads:

φ ∂ c1 ∂t - ∂ ∂x i (D ij ∂ c1 ∂x j ) = 0. ( 33
)

Second order macroscopic description

Let add Eq. ( 22) to Eq. ( 33) multiplied by ε. We get

         φ ∂ < c > ∂t - ∂ ∂x i D ij ∂ < c > ∂x j = O(ε 2 φ ∂ < c > ∂t ). (34)
In the above writing, < c > represents the second order mean concentration, where, the second order mean of any fied ψ is defined by

< ψ >=< ψ 0 > +ε < ψ 1 > +O(ε 2 < ψ >).
(35) Therefore, the second order macroscopic description of pure diffusion is identical to the first order model, but with a precision O(ε 2 ).

IV. Second order homogenization of convection diffusion i. Pore scale dimensionless description

When the fluid is in motion, the solute is transported by diffusion and convection. Then, the dimensionless transport equations on the pore scale read

       N ∂c ∂t -∇ • (D 0 ∇c -Pe c v) = 0 in Ω p , ( 36
) v = 0 over Γ, (37)
(D 0 ∇c) • n = 0 over Γ, (38)
where Pe = v c L/D c denotes the Péclet number. Considering the slow flow of a Newtonian incompressible fluid, its motion is described by Stokes equations

F µ∆ v -∇p = 0 within Ω p , ( 39
) ∇ • v = 0 within Ω p , (40)
where [START_REF] Auriault | Filtration law in porous media with poor separation of scales[END_REF]). Homogenization of the above equations leads to the following macroscopic transport regime accordingly to the order of magnitude of Pe [START_REF] Auriault | Taylor dispersion in porous media: Analysis by multiple scale expansions[END_REF]:

F = µ c v c /Lp c = O(ε 2 ) (e.g.
     diffusion when Pe ≤ O(ε) advection-diffusion when Pe = O(ε 0 ) advection-dispersion when Pe = O(ε -1 )
Whilst the first two models are first order models, the dispersive model requires to account for the second order corrector. Our purpose here is to derive the second order models for Pe = O(ε) and Pe = O(ε 0 ).

ii. Second order homogenization of fluid flow

Homogenization of the fluid flow equations has been performed up to the third order in [START_REF] Auriault | Filtration law in porous media with poor separation of scales[END_REF]. For a macroscopically homogeneous medium, the results at the first two orders can be summarised as follows

                   ∂ ∂x i (< v n i >) = 0, (n = 1, 2) (41) < v 0 i >= - K ij µ ∂ < p 0 > ∂x j < v 1 i >= - N ijk µ ∂ 2 < p 0 > ∂x j ∂x k - K ij µ ∂ < p 1 > ∂x j
iii. Second order homogenization of convection diffusion at Pe = O(ε)

First order macroscopic description

We consider Pe = O(ε) and N = O(ε 0 ) in Eq. ( 36). At the first two orders, we get the same boundary value problems as those obtained in Section III, and which lead to Eq. ( 12) and Eq. ( 16), for c 0 and c 1 , respectively. At the third order, Eq. ( 36) yields

         ∂c 0 ∂t - ∂ ∂y i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) -c 0 v 0 - ∂ ∂x i D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i ) = 0. ( 42
)
Considering Eq. ( 40) at the first order

∇ y • v 0 = 0, ( 43
)
and Eq. ( 12), Eq. ( 42) reduces to Eq. ( 18). Therefore, its integration leads to Eq. ( 22) and the first order macroscopic description is the model of diffusion given by Eq. ( 24). Furthermore, c 2 is given by Eq. ( 28).

Second order macroscopic description

Eq. ( 36) at the fourth order gives

         ∂c 1 ∂t - ∂ ∂y i D 0 ( ∂c 3 ∂y i + ∂c 2 ∂x i ) -c 0 v 1 -c 1 v 0 - ∂ ∂x i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) -c 0 v 0 = 0, ( 44
)
and its integration over the period yields

φ ∂ c1 ∂t - ∂ ∂x i (D ij ∂ c1 ∂x j )+ < v 0 i > ∂c 0 ∂x i = 0. ( 45
)
By adding Eq. ( 22) to Eq. ( 45) multiplied by ε, we get

         φ ∂ < c > ∂t - ∂ ∂x i D ij ∂ < c > ∂x j +ε < v i > ∂ < c > ∂x i = O(ε 2 φ ∂ < c > ∂t ), ( 46
)
where < c > is the second order average concentration, while < v i > is the first order fluid average velocity and verifies

       < v i >= - K ij µ ∂ < p > ∂x j + O(ε < v i >), (47) ∂ < v i > ∂x i = O(ε ∂ < v i > ∂x i
).

The second order model is therefore the model of advection diffusion, with a precision O(ε 2 ) and in which the velocity is the first order velocity and verifies Darcy's law.

iv. Second order homogenization of convection diffusion at Pe = O(ε 0 )

First order macroscopic description

We now consider Eq. ( 36) with Pe = O(ε 0 ) and N = O(ε 0 ). The first order boundary value problem is identical to Eqs. ( 9)-( 10), and by Eq. ( 43), Eqs. ( 36)-( 38) at the second order reduce to Eqs. ( 13)-( 14). Consequently, c 0 and c 1 verify Eq. ( 12) and Eq. ( 16), respectively. At the third order, Eq. ( 36) reads

         ∂c 0 ∂t - ∂ ∂y i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) -c 0 v 1 i -c 1 v 0 i - ∂ ∂x i D 0 ( ∂c 1 ∂y i + ∂c 0 ∂x i ) -c 0 v 0 i = 0, (49)
and the associated boundary conditions are Eq. ( 19) and:

v 0 i = v 1 i = 0 over Γ.
Let us now integrate Eq. ( 49), so as to obtain the first order homogenized description. Applying the divergence theorem and then using the boundary conditions and the periodicity, we end up with

φ ∂c 0 ∂t - ∂ ∂x i (D ij ∂c 0 ∂x j )+ < v 0 i > ∂c 0 ∂x i = 0. (50)
Therefore, the first order macroscopic description is the model of advection-diffusion and reads

         φ ∂ < c > ∂t - ∂ ∂x i D ij ∂ < c > ∂x j + < v i > ∂ < c > ∂x i = O(εφ ∂ < c > ∂t ), (51)
in which < c > is the first order mean concentration.

Second order macroscopic description

The third order equation Eq. ( 49), can be transformed to obtain a formulation for determining c 2 (Cf. Appendix B):

                     ∂ ∂y i D 0 ( ∂c 2 ∂y i + χ j ∂ 2 c 0 ∂x i ∂x j + ∂ c1 ∂x i ) = ( 1 φ D ij -D 0 γ 0 ij ) ∂ 2 c 0 ∂x i ∂x j (52) +(v 0 i γ 0 ij - 1 φ < v 0 j >) ∂c 0 ∂x j .
The above equation with the associated boundary condition, given by Eq. ( 27), constitute a well-posed boundary value problem for c 2 , whose solution reads

         c 2 = η jk ( y) ∂ 2 c 0 ∂x j ∂x k + π j ( y) ∂c 0 ∂x j +χ j ( y) ∂ c1 ∂x j + c2 ( x, t), (53)
where c2 ( x, t) is an arbitrary function and where < η jk >= 0, < π j >= 0. Note that by definition, vector π depends on the fluid velocity. At the fourth order, equation Eq. ( 36) yields

                 ∂c 1 ∂t - ∂ ∂y i D 0 ( ∂c 3 ∂y i + ∂c 2 ∂x i ) + ∂ ∂y i c 0 v 2 i -c 1 v 1 i -c 2 v 0 i (54) - ∂ ∂x i D 0 ( ∂c 2 ∂y i + ∂c 1 ∂x i ) -c 0 v 1 i -c 1 v 0 i = 0,
and the associated boundary conditions are Eq. (30) and:

v 0 i = v 1 i = v 2 i = 0 over Γ.
The secondorder corrector of the macroscopic description is obtained by integrating Eq. ( 54) over Ω p . This leads to

         φ ∂ c1 ∂t - ∂ ∂x i (D ij ∂c 0 ∂x j + D ij ∂ c1 ∂x j ) + < v 1 i > ∂c 0 ∂x i + < v 0 i > ∂ c1 ∂x i = 0, ( 55
)
where

D ij =< D 0 ∂π j ∂y i -v 0 i χ j > . ( 56
)
From its definition Eq. ( 56), we see that the second order tensor D ij contains a convective term: it is therefore a dispersion tensor. Let us add Eq. ( 22), to Eq. ( 55) multiplied by ε. We get:

         φ ∂ < c > ∂t - ∂ ∂x i (D ij + εD ij ) ∂ < c > ∂x j + < v i > ∂ < c > ∂x i = O(ε 2 φ ∂ < c > ∂t ).( 57
)
In the above equation, < v i > is the second order fluid velocity, given by

             < v i >= - N ijk µ ∂ 2 < p > ∂X j ∂ k - K ij µ ∂ < p > ∂X j +O(ε 2 < v i >), ( 58
) ∂ < v i > ∂X i = O(ε 2 ∂ < v i > ∂X i
).

Therefore, the second order macroscopic transport description is a model of advectiondispersion, in which the fluid velocity verifies a second order law Eq.( 58).

V. Conclusion

In the present paper, second order asymptotic homogenization is performed for three regimes of solute transport in macroscopically homogeneous porous media. When the fluid is at rest, the second order model remains of diffusive type. This shows that low scale separation has no impact on the apparent transport regime, and furthermore highlights the robustness of the model of effective diffusion, when the fluid is at rest. When the fluid is in motion and at Pe = O(ε), we get the model of effective diffusion at the first order, and the model of advection-diffusion at the second order. This result can be generalised to lower orders of the Péclet number: at Pe = O(ε p ) with p ≥ 1, the apparent advective-diffusion regime occurs at order p + 1 and the model of effective diffusion applies at orders lower or equal to p. When the fluid is in motion and at Pe = O(ε), the transport regime is advective-diffusive and low scale separation induces an apparent regime of dispersion. Therefore, predominant diffusion and advection-diffusion in a porous medium at low scale separation lead to apparent regimes of advection-diffusion and dispersion, respectively. We may therefore conclude that scale separation is a crucial issue whenever the fluid is in motion, since low scale separation then induces modification of the apparent transport regime, while it remains of diffusive type at the second order when the fluid is at rest.

The left hand side of the above equation is actually the definition of E jlm . Using Eq. ( 62) for determining the expression of E jlm , we get: E jlm = E jlm . Since the medium is macroscopically homogeneous, E ijk does not depend on the macroscopic variable x. Consequently, the anti-symmetry with respect the first two indices implies that

∂ ∂x i (E ijk ∂ 2 c 0 ∂x j ∂x k ) = 0. (63)
B. Boundary value problem for c 2 when Pe = O(ε)

Firstly, using Eq. ( 43), and the second order of Eq. ( 40)

∂v 1 i ∂y i + ∂v 0 i ∂x i = 0, (64)
while bearing Eq. ( 12) in mind, we obtain

         ∂ ∂y i (c 0 v 1 i ) = -c 0 ∂v 0 i ∂x i , ( 65
)
∂ ∂y i (c 1 v 0 i ) = v 0 i ∂c 1 ∂y i . ( 66
)
Next, we use Eq. ( 50) and Eq. ( 16) to derive the expressions of ∂c 0 /∂t and of ∂c 1 /∂x i , respectively. Finally, substituting the thus derived expressions into Eqs. (49), while using Eq. ( 21), we obtain Eq. ( 52).

Figure 1 :

 1 Figure 1: Porous medium : (a) Macroscopic sample ; (b) Periodic unit cell.

  A. Anti-symmetry of tensor E ijk with respect to its first two indices Let α be a test function satisfying the condition of having zero mean. The variational formulation associated with χ j is By taking α = η lm in Eq. (60) and α = χ j in Eq.

		Ω p	D 0	∂α ∂y i	∂χ j ∂y i	dΩ = -	Ω p	D 0	∂α ∂y j	dΩ, (60)
	and the variational formulation associated with
	n jk reads
			    		Ω p		∂α ∂y i	D 0 (	∂n lm ∂y i	+ χ m δ il ) dΩ =
			   		Ω p		αD 0 (	∂χ m ∂y l	+ δ lm ) dΩ.	(61)
	(61), we deduce
	    	Ω p	D 0 (	∂η lm ∂y j	+ χ j I lm ) dΩ =	Ω p	D 0 χ m	∂χ j ∂y l
	   	-	Ω p	D 0 χ j	∂χ m ∂y l	dΩ.


D.-W Lee

PRODUCTION AND APPLICATION OF METAL-BASED NANOPARTICLES

A number of metal-based nanopowders such kinds as Fe, Co, Fe/Co alloy, Fe/C, Fe/organic shell were successfully produced by aerosol synthesis method. The mechanism of nanoparticles formation and the influence of experimental parameters on shape, size distribution, structure, chemical and phase composition of oxide-, carbon-, or organic-coated nanoparticles were evaluated.

The sizes of particles can be varied from 6-100 nm with narrow size distribution. The several application fields of synthesized nanoparticles have been studied.

INTRODUCTION

In recent years, much attention has been paid to the synthesis and study of nanoparticles because of wide range of potential applications [START_REF] Hu | Preparation of Ultrafine Powder: the Frontier of Chemical Engineering (review) // Materials Chemistry and Physics[END_REF]. Particularly, magnetic nanoparticles can have the special characteristic of exhibiting single-domain magnetism and can be used in magnetic tapes, ferrofluid, magnetic refrigerants, etc, because of their ultra fine size dimensioned with magnetic domain size [START_REF] Hadjipanayis | Science and Technology of Nanostructured Magnetic Materials[END_REF]. Oxide coated iron nanoparticles are non-toxic materials and due to enhanced magnetic properties can be more effective as compare with magnetite nanoparticles for biomedical application [START_REF] Zhang | Surface modification of superparamagnetic magnetite nanoparticles and their intracellular uptake[END_REF][START_REF] Bomatґ -Miguel | Fe-based nanoparticulate metallic alloys as contrast agents for magnetic resonance imaging[END_REF].

A wide range of techniques to fabricate nanoparticles has been developed rapidly over the past decades [START_REF]Fine Particles-Synthesis, Characterization and Mechanism of Growth[END_REF][START_REF]Ultra-Fine Particles: Exploratory[END_REF][START_REF] Veintemillas-Verdaguer | Continuous production of g-Fe2O3 ultrafne powders by laser pyrolysis[END_REF]. Among them, chemical synthesis of nanoparticles is a rapidly growing field because of its versatile applicability to almost all materials and high rate of production capability with little agglomeration. Since the properties of these nanoparticles are basically determined by their mean size, size distribution, external shape, internal structure, and chemical composition, the characteristics of powders must be controlled during the production of the nanoparticles [START_REF]Fine Particles-Synthesis, Characterization and Mechanism of Growth[END_REF].

Production of metal-based nanoparticles had been developed by gas phase synthesis through the pyrolysis of organometallic precursors. We adjust this method as the method for industrial synthesis of commercially available nanopowder of mean size of 6-100 nm. This method runs without vacuum and gives a relative high productivity of laboratory equipment. This paper will devote to synthesis of the different kinds magnetic Fe-based nanoparticles with the shells of different chemical composition, such as the oxide, carbide or organic matters. It is a brief review of our works on magnetic particles production and application. The effect of processing parameters on microstructure, size distribution, chemical and phase composition, and morphology of nanoparticles were investigated.

EXPERIMENTAL

Nanoparticles production

We had produced nanoparticles by improved chemical vapor condensation method (CVC), which was adjusted for mass production of nanoparticles. The general scheme of CVC process is shown in Fig. 1. To produce nanoparticles, a carrier gas of high purity argon or helium is fed through a heated bubbling unit containing the metalloorganic precursor at the vaporization temperature. The flow of carrier gas entraining precursor vapor passed through the heated tubular reactor to the work chamber.

The precursor decomposed in that reactor and condensed in the clusters or particles. In order to produce nanoparticles based on different metals or chemical compounds the suitable precursors should be used. For example, we used iron Fe(CO) 5 , cobalt Co 2 (CO) 7 , or tungsten W(CO) 6 carbonyls for synthesis of Fe, Co and W-based nanoparticles, respectively.

The system includes independent vaporization units, connecting directly with the entrance of high-temperature reactor with two or more reaction zones. Zone temperatures were in the range of 230-1100°C, and were optimized for each experiment. Using accelerating gas as well as carrier gas was applied for changing precursor residential time in reaction zone and it concentration in gas phase. All particles were deposited on the surface in the work chamber, from which powders can be scrapped and collected. After exposure on air, usually metallic nanoparticles, specially iron, show spontaneous combustion. Hence, it is necessary to form nanoparticles with core-shell structure [START_REF] Choi | Preparation of iron nanoparticles by chemical vapor condensation[END_REF]. Shell cover metallic core and save it from oxygen atmosphere. Generally, oxide coated nanoparticles can be produced by passivation of asproduced nanoparticles in the mixing gas of Ar contained a trace O 2 flowed for 10h with pressure of 1kg/cm 2 . That has slowly oxidized nanoparticles surface and than particles can be used on atmosphere air.

However, other kind of shells also can be created, such as carbide, noble metals, polymer, etc., by using the same experimental setup. The presence of two reaction zones allowed providing successive decomposition of precursors vapor in the same gas flow. If different chemical compound are used as the precursors for core and shell, usually temperature regime of it decomposition is also different. Therefore, in the gas phase, the formation of solid clusters of one component starts at first zone of reactor, than it follows to the next zone of higher temperature for decomposition another precursor. By that way as-formed clusters or nanoparticles can be covered by different substances.

Synthesis of nanoparticles-polymer composites

The polyimide based thin film magnetic composites were synthesized and investigated. At the first step the nanoparticles were ultrasonically dispersed in solvent, where all necessary for synthesis components were also added. Then the formed solution of forpolimer (polyamidacid (PAA)) with dispersed nanoparticles had been spilt on flat glass substrates. After drying the dense elastic films with the thickness of about 40 µm were obtained.

Finally those films were heat-treated in vacuum by three steps regime: 100 о С/1h, 200 о С/1h and 250 о С/1h.

Characterization methods

The synthesized powders were characterized for crystal structure, phase composition, volume fraction of phases, particle size, and chemical impurities by using X-ray diffraction (XRD) method, That is common, that the coercivity of ferromagnetic materials increases with the decrease of particle size until it is maximized to the size of single magnetic domain. The maximum coercivity obtained so far is about 1 kOe, measured from the iron nanopowder with the average particle size of 20-25 nm.

Iron-cobalt nanoparticles with improved magnetic properties

To produce alloyed Fe-Co metallic nanoparticles the evaporation of precursors was organized in independent vaporization units and precursors vapor concentration in carrier gas was controlled.

Joint decomposition of iron and cobalt precursors was done at the same pyrolytic temperature in reactor. Oxide shells were formed by the said passivation process. Particles have approximately spherical shape with mean size in range of 13-60 nm. TEM images (Fig. 3) shows non agglomerated particles with core-shell structure and the typical morphology of passivated Fe-based nanoparticles [START_REF] Choi | Preparation of iron nanoparticles by chemical vapor condensation[END_REF][START_REF] Kim | Aerosol Synthesis and Growth Mechanism of Magnetic Iron Nanoparticles[END_REF]. XRD analysis shows single phase BCC solid solution.

Carbon-coated Fe-based nanoparticles

To produce Fe and Fe-C nanoparticles, a high purity carbon monoxide (CO) was used as a source of carbon and as a carrier gas. It is known that carbon appears through the reaction of CO disproportionation reaction: 2CO g =C s +CO 2 g , ∆H=169 kJ/mol. To run that reaction metallic catalytic surface is necessary. In order to study the preferable conditions for that reaction, the kinetic investigations using 15 nm sized iron particles were carried out.

The appreciable reaction rates are in the temperature interval from 470 to 820 °C with a maximum rate at 625°C [START_REF] Vasilieva | Synthesis of nanoparticles by the gas phase decomposition of iron pentacarbonyl in the carbon monoxide atmosphere[END_REF] Fig. 4. Saturation magnetization of iron-cobalt alloyed nanoparticles versus cobalt content.

This reaction occurs also even at lower temperatures (down to 325°C) and temperatures up to 1000°C however at very low rates.

In order to investigate the effect of experimental parameters on particle size, phase composition and structure, several particle samples were synthesized at various pyrolytic temperatures from 400 0 C to 1100 0 C. The increasing of gas flow rate decreases particle size and leads to the changes in particle phase composition as shown in the Fig. 5. Particles have core-shell structure. XPS and TEM study of shells shows that the shell structure depends on reactor temperature. At the lowest temperatures (400 and 500°C) the shell was soot and at the higher temperatures it was graphite. At the temperatures higher than 1100°C the fullerene -like structure of shells and single walled carbon nanotubes can be formed [START_REF] Nasibulin | Studies on Mechanism of Single-Walled Carbon Nanotube Formation[END_REF].

Organic coated magnetic nanoparticles

In case of synthesis of surface-modified iron nanoparticles, the organic medium with chemical composition of R fо -S-S-S-R fо , where S is sulphur and R fо is radical of Produced particles shows the better damping in organic mediums, specially in compatible with shell medium, hereby stable of suspension in time was significantly improved. Such magnetic fluids can be applicable for machinery as well as for medical diagnostic and treatment.

CF 3 OCF 2 CF 2 CF 2 OCF 2 CF 2 ,

Polymer-based composites

CONCLUSION

The possibility to produce multicomponent, alloyed nanoparticles and nanoparticles of chemical compounds by gas phase synthesis method was shown. Iron-based magnetic nanoparticles, such as oxide-coated iron, Fe 3 C, Fe-Co alloyed, organic and carboncoated iron nanoparticles of 6-75nm were successfully produced.

Size distribution, phase and chemical composition of nanoparticles and shells can be precisely controlled by experimental parameters.

It is possible to produce superparamagnetic nanoparticles and nanoparticles with H c of ~ 1.2 kOe, and high magnetization (up to 245 emu/g), which would be applicable "in-vivo" for magnetic resonance imaging as contrast-increasing materials, for drug delivery, and for experiments on magnetic hyperthermia, as same as for magnetic recording media, permanent magnets and magnetic plastics.

Fig. 1 .

 1 Fig.1. Scheme of equipment for method of aerosol synthesis of nanoparticles.

  photoelectron spectroscopy. The carbon content of the iron nanoparticles and Fe/Co ratio in the alloyed nanoparticles were determined by chemical elemental analysis. Magnetization of nanoparticles and polyimide composite samples was measured by

Fig. 2 .

 2 Fig. 2. Coercive force (H c ) and maximal magnetization (M s ) with particle size

Fig. 3 .

 3 Fig.3. TEM microphotographs of iron-cobalt alloyed nanoparticles.

Fig. 4

 4 Fig. 4 shows the Co content dependence of the saturation magnetization of the Fe-Co particles. Although a variation in M s can be induced by a change in the average particle size. With increasing Co content the saturation magnetization increases and reaches its maximum at near 40 wt% Co, and then decreases and coercive force continuously increases and have maximal measured value of 1250 Oe.

Fig. 5 .

 5 Fig.5. Phase composition and particle size versus gas flow rate at different decomposition temperatures (T D ).

  had been specially synthesized and applied for nanoparticles covering. It has evaporation temperature of 100°C and decomposition temperature higher that 250°C. The decomposition run through the sulphur links. After decomposition it has opened sulphur link strongly connected through the sulphur with perfluorineoxide radical. Organic-coated nanoparticles were produced by decomposition of iron carbonyl with iron nanoparticles formation at 230°C and it subsequent reaction with R fо -S-vapor, which had connected with iron through the Fe-S link and covered as-formed iron nanoparticles by R f0 radicals.

Fig. 6 .

 6 Fig.6. TEM microphotographs of organic coated iron nanoparticles.

  Flexible polyimide-based films were synthesized at the nanoparticles content was changed from 1 to 20 wt.%. With increasing particles weight up to 30 wt.% we couldn't get uniform distribution of particles in matrix and flexible samples wasn't achieved. Samples were optically transparent at the particles content up to 10 wt.%. With increasing particles content the composite film have about the same tensile strength of 105±2 MPa. It is important to notice that Young modulus increase from 2,4 to 3,0 GPa with increasing particles content from 0 to 20wt.%, respectively. Micrograph of ached nanoparticles filled polyimide is shown in the Fig.7.

Fig. 7 .

 7 Fig. 7. Structure of nanoparticles-polymer composite.


Mustapha Hamdi
email: mustapha.hamdi@ensi-bourges.fr

Antoine Ferreira
email: antoine.ferreira@ensi-bourges.fr

DNA NANOROBOTICS

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

There has been a great interest and many reports in the use of DNA specifically to actuate and assemble microand nano-sized systems. In nano-electronics, DNA could be used as molecular switchs for molecular memories or electronic circuitry to assemble future nano-electronics transistors [START_REF] Hoummady | Micromachines for nanoscale science and technology[END_REF], [START_REF] Diez | Stretching and Transporting DNA Molecules using Motor Proteins[END_REF]. In nanorobotics (Fig. 1), structural elements could be carbon nanotubes while the passive/active joints are formed by appropriately designed DNA elements [START_REF] Dwyer | Design tools for a DNA-guided self-assembling carbon nanotube technology[END_REF]. In such nanodevices, nature assembles nano-scene components using molecular recognition [START_REF] Montegano | Constructing nanomechanical devices powered by biomolecular motors[END_REF]. In the case of DNA, hydrogen bonding provides the specificity behind the matching of complementay pairs of single-stranded (ss) DNA to hybridize into a double strand (ds) of helical DNA. While these tasks have been performed by nature efficiently and perfectly, roboticians and engineers should use prototyping tools for a CAD design process of future bionanorobotic systems. To achieve these long-term goals, prototyping tools based on molecular dynamic (MD) simulators should be developed in order to understand the molecular mechanics of proteins and develop dynamic and kinematic models to study their performances and control aspects. The ability to visualize the atom-to-atom interaction in real-time and see the results in a fully immersive 3-D environment is an additional feature of such simulations [START_REF] Hamdi | Molecular Mechanics Study on Bionanorobotic Components using Force Feedback[END_REF]. Virtual Reality (VR) technology is applied here, which not only provides immersive visualization but also gives an added functionality of CAD-based design, simulation, navigation and interactive manipulation of molecular graphical objects. Using simulated biological nanoenviroments in virtual environments, the operator can design and characterize through physical simulation the behavior of molecular robots. Adding haptic interaction, the operator can explore and prevent the problems of bionanorobots in their native environment.

Several types of software for displaying 3D models of bio-molecules have been developed. Most of these programs provide haptic manipulation and 3D visualization in combination with molecular dynamics simulation such as Visual Molecular Dynamics (VMD) [START_REF] Humphrey | VMD:Visual Molecular Dynamics[END_REF], that can be connected to Molecular Dynamics Simulation program (NAMD) [START_REF] Nelson | NAMD-A Parallel Object-Oriented Molecular Dynamics Program[END_REF] via Interactive Molecular Dynamics Simulation (IMD) [START_REF] Stone | A System for Interactive Molecular Dynamics Simulation[END_REF] and Virtual-Reality Peripheral Network (VRPN) [START_REF] Taylor | VRPN: A Device-Indenpendent, Network-Transparent VR Peripheral System[END_REF] (the reader can refer to [START_REF] Sharma | Virtual Reality and Haptics in Nano-and Bionanotechnology[END_REF] for a good introduction to the domain). Based on VR technology and MD simulators, our long-term goal is to prototype virtually bionanorobotic systems and optimize mechanically their design considering the native microenvironment. In this work,

Graphite sheet

Linear DNA-based actuator dsDNA dsDNA we consider real-time force-feedback technology for improving the methodology of mechanical molecular studies of DNA molecules acting as passive and/or active joints in bionanorobotic systems, as illustrated in Fig. 1. Understanding the molecular mechanics behavior of such DNA molecules is an important challenge for interfacing DNA to structural (CNTs, graphite) or biological (biological nanotube, proteins) elements.

The paper is organized as follows. First, section II presents the developed virtual CAD simulator Then, different design concepts of DNA-based devices are proposed: section III deals with DNA-based springs and section IV introduces a novel DNA-based nanogripper.

CAD SYSTEM BIO-NANOROBOTIC PROTOTYPING

The application of advanced virtual reality techniques in bio-nanotechnology allowed to study, simulate, visualize and interact with molecular biology, genomics, proteomics, structural and computational biology. As far we know, only basic molecular elements have been studied until now. As a perspective of these developments, VR-based technology could be used for the molecular robot design. Several types of software for displaying 3D models of bio-molecules have been developed supporting VR devices such as stereo glasses, 3D trackers, and force-feedback (haptic) devices. Realtime exploration is what attracts researchers to develop man-machine interfaces for nanoscale manipulation that use haptic display technologies. The developed simulation system presented in Fig. 2 permits manipulation of bionanorobotic components during molecular dynamic (MD) simulations with real-time force feedback and 3D graphical display. It consists of three primary components: a haptic device controlled by a computer that generates the force environment, a MD simulation for determining the effects of force application, and a visualization program for display of the results. Communication is achieved through IMD protocol between the visualization program Visual Molecular Dynamics (VMD) and the molecular dynamics program (NAMD) running on multiple machines. A force-feedback PHANToM device measures a user's hand position and exerts a precisely controlled force on the hand in order to apply different mechanical constraints, force and energy fields on the virtual model in order to prototype bionanorobotic components. The application of the mechanical constraints are applied by a virtual AFM microlever and can be manipulated with a mouse or a haptic interface with force-feedback. The principal idea of this application is to let the user drive le molecule in the space of precomputed conformations and transitions: • The user steers virtually he molecule protein with a cursor, which is a small spherical ball that is position controlled by the stylus. The system allows application of stretching, shearing and bending mechanical constraints on the protein.

• The user distinguish possible conformational paths and feels the energy barriers associated with particular paths.

DESIGN OF CONTROLLABLE DNA PASSIVE SPRINGS

Mechanical Characteristics of dsDNA

Chemically, DNA is a long polymer made up of a linear series of subunits known as nucleotides. Structurally, DNA is usually found as a double helix, with two strands wrapped around one another. However, DNA can adopt other configurations and can also exist in single-stranded forms. Double-stranded DNA (ds-DNA) has sparked the renewed interest in the force versus extension of polymers for biomolecular springs. The DNA is solvated in water with 30 Na + ions added to neutralize the charge. The water-DNA system was gradually heated over 7ps to 300K, and then equilibrated with a thermal bath at 300K for another 7ps. The dynamics of the DNA as shown in Fig. 5 were performed with the double-stranded terminations stretched and the other end fixed. This elastic behavior is thus purely entropic. For very low tension f ≤1pN, the restoring force is provided by "entropic elasticity". In the absence of any force applied to its ends, the DNA's RMS end-to-end distance (chain length, L) is small compared to its contour length defined as the maximum end-to-end distance (maximum length, L 0 ) and the chain enjoys a large degree of conformational disorder.

Stretching DNA reduces its entropy and increases the free energy. The corresponding force f increases linearly as a Hooke's law with the extension L:

0 0 , 3 L L L L A T k f DNA B << ≅ (1)
The length A DNA is known as the "thermal persistence length" of DNA and is of the order 50nm. For higher forces (f ≥10pN), the end-to-end distance L is close to L 0 and the elastic restoring force is due to distortion of the internal structure of DNA. In this regime, the force extension curve can be approximated by two models that are often used to describe the entropic elasticity of DNA.

In the freely jointed chain (FJC) model, the molecule is made up of rigid, orientationally independent Kuhn segments whose length, b, is a measure of chain stiffness.

The resulting entropic elastic behavior can be summarized in the force-extension relation :

b f T k T k b f L z B B tot - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = coth (2)
defining the well-known Langevin function. Expanding Eq.( 2) gives the effective spring constant for the FJC as

b T k k B FJC / 3 =
. The terms L tot represent the total length of the protein and f the stretching force. The alignment of segments by tension is described by Boltzmann distribution. In the inextensible worm-like chain model (WLC) model [START_REF] Park | Free energy calculation from steered molecular dynamics simulations using Jarzynski's equality[END_REF], the molecule is treated as a flexible rod of length L that curves smoothly as a result of thermal fluctuation. The WLC model of entropic elasticity predicts the relationship between the relative extension of a polymer (z/L) and the entropic restoring force (f) through

( )[ ] 4 / 1 ) ) / 1 ( 4 / 1 ( / / 2 - - + = L z L z A T k f B (3)
where k B is the Boltzmann constant, T is absolute temperature, A is the persistence length, z is the end-toend length, and L is the length. Results, shown in Fig. 5a, indicate that, even though the FJC model can describe the behavior of ds-DNA in the limit of low and intermediate forces, it fails at high forces. The WLC model, on the other hand, provides an excellent description of molecular elasticity at intermediate and high forces. Both models behave as a Hooke's law for low stretching forces. In the case of an anti-parallel stretching (Fig. 5b), the forceextension curve is quite similar for the Parts I and II when the ds-DNA is unfolding. When it is totally stretched, lateral mechanical unzipping of the hairpins occurs sequentially leading to an increase of the stretching force (Part III) until to reach its point of rupture (Part IV). As it is shown, the strand unzipping occurred abruptly at 500pN and displayed a reproductible "saw-tooth" force variation pattern with an amplitude of +/-10pN along the DNA.

Passive DNA-SWNT Elastic Joint

Considering the interesting stretching characteristics of ds-DNA of (Fig. 5a), we designed a passive DNA-based elastic joint (see Fig. 6a) composed of two single walled carbon nanotubes (SWNT) as structural components. The covalent linkage between DNA-SWNT are realized at the terminations through atoms of carbon (Fig. 6b). As shown in Fig. 7, the passive dsDNA-based joint is fully reversible in the domain of linear elasticity of the DNA molecule (Part I and II). The spring constant is estimated to be as K DNA = 780 N/m with a thermal bath at 300K and constant acidic pH=5. Fig. 8b shows the change of the protein stiffness with respect to the pH value. For a neutral acidic pH value (pH=11), the DNA protein is in a partially α-helical stranded coiled coil. The value of pH=5.5 corresponds to the neutral state. An increase occurs at lower pH between 5.5 and 10 leading to a stiffness variation ranging from 670 N/m to 780 N/m. For this configuration, it is necessary to protonate the amino acid side chain of the protein by adding proton inside the native environment. Finally, the increase or decrease of the electron density (namely, the electric charge Q in Coulombs) has been investigated. The concept of using electrons as a medium for such purposes is not unreasonable because electron density will readjust along the molecular backbone in response to an inflow/outflow of electronic charge. Moreover, using electrons as a mechanism for changing the shape and rigidity of molecular systems has precedence [START_REF] March | Advanced Organic Chemistry. Reactions, Mechanism and Structure[END_REF]. Fig. 8c shows the change of spring stiffness according to the electron charge of the protein.

From these results we derive that the force stiffness bracket a range from 680 N/m to 780 N/m for the ds-DNA protein. Experimentally one can add or remove electrons with a potentiostat, or by appending suitably placed electron-donating or withdrawing groups. Singlestranded DNA (ss-DNA) and double-stranded DNA (ds-DNA) proteins have interesting characteristics due to their elastic behavior and structural conformation [START_REF] Bustamante | Single-molecule of DNA mechanics[END_REF]. As example, DNA can provide three independent reversible degrees of freedom: stretching, shearing and twisting. They can be used to construct molecular building blocks by virtue of their conformation pathways. Branched DNA molecules with sticky ends are promising for selfassembling macromolecular periodic structures [START_REF] He | DNA-modified carbon nanotubes for selfassembling and biosensing applications[END_REF].

CONTROLLABLE DNA-BASED NANOGRIPPER

In this part, we study the molecular properties of DNA proteins to change their 3D conformation depending on the temperature level of the native medium. Thus, a new biomolecular gripper type called dsDNA-SWNT nanogripper is designed (Fig. 9). It is composed of a dsDNA protein with two SWNT as nano endeffectors. The structure is like an hairpin composed of two coils, having each C-terminal connected to a SWNT and undergoing a conformational change induced by temperature variation (increase or decrease) in mildly acidic conditions (i.e., pH around 5. As example, Fig. 10 shows the front view trajectory of both free terminations of dsDNA when considering temperature augmentation from 300K to 400K. The finger's motion are composed of a linear finger opening (y-z plane) connected to carbon nanotubes as nano end-effectors. In order to assess the interaction forces when handling a nanoobject, we simulated a contact force by using two nonlinear spring K 1 and K 2 at each end-effector. Fig. 11 shows the evolution of the gripping force during the opening of the nanotweezers.

The contact force is estimated by F i =K i ∆x i,j with (i,j)=(1,2) for each nanofinger. It should be noticed that when the nanofingers are in closed contact with the nanoobject, the forces provided by the ds-DNA are quite linear with the opening displacement ∆x. For large opening displacements, the forces are dissimilar due the small parasitic rotation of the fingers. Fig. 12 shows the motion reversibility of the nanofingers during a temperature cycle time (heating and cooling) from 300K to 400K. Although the overall unfolding pathway is independent of temperature cycling, differences are observed from trajectory-to-trajectory during the cooling

CONCLUSION

This paper presents a computational molecular mechanics study carried out by an interactive CAD simulator interface. The preliminary mechanical force results given in this study corroborates the force results when stretching double-helical DNA molecules for controllable passive elastic joints such as shock absorbers. We demonstrated also that DNA material is well suited to the development of active joints for the control of nanorobotic tasks such as nanotweezers.

Fig. 1 :

 1 Fig.1: Basic DNA-based molecular components. Passive joints (a) 1 d.o.f. and (b) multidegree of freedom elastic spring. Their elastic behavior can be used as a passive control element or as the restitution force that will bring the mobile component back to its original position. Active joints (c) single degree of freedom parallel platform. The platform is actuated by double stranded DNA-type linear nanoactuator.

Fig. 2 .

 2 Fig.2. Basic concept of virtual environment and haptics technology for bionanorobot simulation.

Fig. 5 :

 5 Fig.5: Double-stranded DNA mechanical simulations: (a) force-extension curve when applying a stretching force. The data are fit to a WLC model solved numerically assuming A=43nm. The FJC curve assumes b=2P=106nm. (b) force-extension curve when applying an anti-parallel stretching and (c) force-extension curve when applying an anti-parallel shearing.

Fig. 4 :

 4 Fig.4: Structure of water-DNA system ionized with 3O Na + ions.

  anti-parallel shearing of ds-DNA (Fig.5c), a mechanical longitudinal unzipping of the 12 hairpin DNA occurs sequentially (Part I) after a phase of extension of ds-DNA structure (Part II) before the rupture point (Part III).

Fig. 6 :

 6 Fig.6: (a) Passive joint composed of a dsDNA protein attached at both ends by carbon nanotubes (CNT). The water molecules are not shown. (b) schematic illustration of chemical scheme for SWNT-DNA linkage.

Fig. 7 :

 7 Fig.7: Reversibility of the DNA-based elastic joint during a stretchingrelaxation phase.

Fig. 8 :

 8 Fig.8: Evolution of the spring stiffness of ds-DNA during stretching for changing medium properties: (a) temperature, (b) level of acidic pH and (c) level of electron charge Q.

  5). With the change of temperature, the N-terminals pop out of the inner side and the peptide acquires a straightened position. Two known states are established, i.e., the native state and the fugeonic state of the 12-hairpin peptide of DNA. The representative "open" structure can be generated by forcing the structure away from the native conformation to open state (conformation) with constrained hightemperature molecular dynamics (molecular dynamic program NAMD with the CHARMM22 force field). Both the forward (closed-to-open) and the reverse (open-toclose) transformations are carried out for two end-point structures of 7Å. The dsDNA is able to perform repeatable motion controlled by variation of temperature.

Fig. 9 :

 9 Fig.9: dsDNA-SWNT nanogripper. In the native state the nanogripper is closed (T=300K) and in the conformational state (T=400K) the nanogripper is open.

  reversibility error is less than 8% in the worst case.

Fig. 10 :

 10 Fig.10: Motion of the nanofingers during elevation of the temperature from native state (nanogripper closed) to conformational state (nanogripper open). Influence of the ds-DNA configuration with single walled carbon nanotubes.

Fig. 11 :

 11 Fig.11: Simulation of gripping forces when handling a nanoobject.

Fig. 12 :

 12 Fig.12: Reversibility of the nanotweezers when increasing and decreasing the temperature from T=300K to 400K.


V Cortes

Carralero

J M Pingarrón

P Yáñez-Sedeño

A González-Cortés

V Carralero

NANOSTRUCTURED IMMUNOSENSORS. APPLICATION TO THE DETECTION OF PROGESTERONE

Nanostructured Immunosensors. Application to the detection of Progesterone

INTRODUCTION

The use of nanoparticles for the construction of biosensing devices is nowadays one of the most exciting trends in modern bioanalytical chemistry. Of course, one of the most important goals in the preparation of reliable biosensors is to achieve immobilization of biological recognition elements without significant losses of their activity. In particular, the use of gold nanoparticles allows the adsorption of biological molecules retaining their biological activity [START_REF] Zhao | Direct electron transfer at horseradish peroxidase -colloidal gold modified electrodes[END_REF]. Considering specifically electrochemical biosensors, modification of electrodes with gold nanoparticles provides a microenvironment similar to that of proteins in native systems, with gold nanocrystals acting as conductiving tunnels and facilitating electron transfer [START_REF] Luo | Application of nanoparticles in electrochemical sensors and biosensors[END_REF].

In this communication, a novel electrochemical immunosensor for the determination of progesterone is proposed. The approach combines the properties of gold nanoparticles with the use of a graphite -Teflon composite electrode matrix, into which gold nanoparticles are incorporated by simple physical inclusion. Moreover, the experimental approach implied the direct attachment of the antibody anti-progesterone to the electrode surface.

EXPERIMENTAL

Fabrication of the gold nanoparticle-graphite-Teflon composite electrode

A colloidal gold suspension, with gold nanoparticles diameter of 16+2 nm, was prepared as described previously [START_REF] Mena | A comparison of different strategies for the construction of amperometric enzyme biosensors using gold nanoparticle-modified electrodes[END_REF]. Then, 150 mg of graphite powder (Ultra Carbon, Bay City, MI, USA), and 900 μl of the colloidal gold suspension were thoroughly mixed for 2h. Water was evaporated under air current, and then 450 mg of Teflon powder (Aldrich) were added and thoroughly mixed by hand. The mixture was pressed into pellets at 10,000 Kg cm -2 for 10 min. The resulting pellets were 1.3 cm diameter and around 0.4 cm thick. From each of these pellets, five or six 3.0 mm diameter cylindrical portions were bored, each portion constituting a different composite electrode. Each electrode was press-fitted into a Teflon holder, and the electrical contact was made through a stainless steel screw.

Fabrication of the immunosensor

5 μl of a 0.5 μg ml -1 monoclonal antiprogesterone (anti-Prog) (Sigma) solution was deposited on the gold nanoparticles-modified graphite-Teflon electrode surface and allowed to dry at air under room temperature. Then, the bioelectrode was immersed for 5 min into a 2 % (w/w) BSA solution prepared in 0.

Electrochemical detection of progesterone

The progesterone detection was accomplished by depositing 8 μl of the appropriate 5:3 (v/v) alkaline phosphatase-labelled progesterone (Prog-AP, Ridgeway Science Ltd, Alvington, Gloucestershire, UK): progesterone (Prog, Aldrich) solution, on the immunosensor surface. After drying at room temperature, the immunosensor with the immuno-conjugate layer was placed into the electrochemical cell containing 1 mM MgCl 2 and 0.1 M diethanolamine-HCl buffer solution of pH 10.0. Next, 500 μl of 0.1 M 1-naphtyl phosphate (Fluka) were added, and the corresponding oxidation current from 1-naphtol was amperometrically measured at +0.3 V vs. Ag/AgCl.

RESULTS AND DISCUSSION

The immunosensor functioning is depicted in Scheme 1, where it can be observed as it is based on competitive assay between Prog and Prog-AP. Monitoring of the affinity reaction was carried out by the electrochemical oxidation of 1-naphtol as the product of the alkaline phosphatase enzyme reaction with 1-naphtylphosphate used as the enzyme substrate. Using a detection potential of +0.3 V vs. Ag/AgCl, the steady-state current measured for 10 -4 M 1-naphtol was 43% higher at the gold nanoparticles-modified electrode that at the unmodified graphite-Teflon electrode.

Different experimental variables involved both on the immunosensor preparation and the immunosensing conditions were optimized. The selected parameters are summarized in Table 1. Under these experimental conditions, as expected, the steady -state current decreased as the concentation of progesterone increased, and this decrease is related to the antigen concentration. Furthermore, the analyte responses were fast, the steady-state current being reached in 30 -40s from the addition of the enzyme substrate. A linear range (r = 0.991) for progesterone was found over the 0 -30 ng ml -1 concentration range, which is useful to analyze progesterone in milk, with a slope value of -1.2 nA ng -1 ml. It should be pointed out that this slope value is approximately 8-fold higher than that reported for screenprinted carbon electrode progesterone biosensors coated with IgG [START_REF] Xu | Quantitative analysis of the response of an electrochemical biosensor for progesterone in milk[END_REF]. The limit of detection according to the ∆S/N = 3 criterion was 0.84 ng ml -1 .

A RSD value of 3.5 % was obtained for 10 successive amperometric responses from a 20 ng ml -1 progesterone solution, indicating a good repeatability of the electroanalytical measurements with the same immunosensor. Furthermore, responses obtained with three different immunosensors yielded a RSD value of 8.2 %, showing an acceptable reproducibility in the biosensor construction.

The developed immunosensor was applied to the determination of progesterone in spiked milk samples at a 3.5 ng ml -1 progesterone concentration level. The methodology employed was extremely simple since it involved only dilution of spiked milk with the diethanolamine -HCl buffer solution of pH 10. A 3-μl aliquot of this solution were mixed with 5 μl of Prog-AP solution and then deposited on the electrode surface.

A calibration curve for progesterone following this procedure was needed to be constructed as a consequence of the remarkable matrix effect observed. Using this calibration curve, the analysis of seven milk samples yielded a mean progesterone concentration value of 3.5 + 0.2 ng ml -1 (mean recovery of 101 + 6%), which demonstrated fairly well the usefulness of the immunosensor for this type of analysis.

Detection at a graphite -Teflon -gold nanoparticles-Tyrosinase electrode

An alternative detection method of the antigen-antibody reaction based on the use of a composite graphite-Tefloncolloidal gold -Tyrosinase bioelectrode has been also evaluated. This biosensor exhibits suitable amperometric responses at -0.10 V for different phenolic compounds [START_REF] Carralero | Development of a high analytical performance -tyrosinase biosensor based on a composite graphite-Teflon electrode modified with gold nanoparticles[END_REF]. The presence of colloidal gold into the composite matrix was demonstrated to enhance kinetics of both the enzyme reaction involving Tyrosinase, and the electrochemical reduction of the corresponding o-quinones at the electrode surface. Therefore, these advantages were profited to monitor the anti-Prog-Prog affinity reaction.

The antibody was also directly attached onto the electrode surface and the immunosensor is also based on competitive assay between Prog and Prog-AP, but, in this case the AP-substrate was phenylphosphate in order to generate phenol, which is subsequently reduced at -0.1 V at the Tyrosinase-colloidal gold composite electrode. A scheme of the biosensor functioning is depicted in Scheme 2. Apart from the fact of measuring at a potential such as -0.1 V, the enhancement of the reaction kinetics due to the presence of colloidal gold allows the achievement of a high sensitivity for the detection of phenol. This produces a further improvement in the sensitivity for the progesterone detection. So, a linear calibration curve for progesterone (r=0.995) was constructed in the 0 -50 ng ml -1 concentration range, with a slope value of -82.3 nA ng -1 ml. As can be observed, the sensitivity achieved now is almost one hundred-fold higher than that provided with the former detection approach, and consequently, almost one thousand higher than that reported with screenprinted progesterone biosensors coated with IgG. The limit of detection, calculated for a signal-to-noise ratio equal to 3, was 0.34 ng ml -1 . Moreover, 10 successive measurements for a 10 ng ml -1 progesterone concentration yielded a RSD value of 4 %. Amperometric responses obtained with six different immunosensors at the same progesterone concentration level gave a RSD value of 2.3 %, which demonstrated the excellent reproducibility achieved in the construction of the nanostructured biosensors.

Figure 1 .

 1 Scheme 1

  Scheme 2

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		Authors
	Title.
			1 M diethanolamine-
		HCl buffer of pH 7.2, and washed carefully with a DEA
		buffer solution of pH 10.0.
	©TIMA Editions/ENS 2006	-page-	ISBN:

©TIMA Editions/ENS 2006

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Table 1 .

 1 Experimental variables selected for the construction of a progesterone biosensor based on gold nanoparticles -graphite-Teflon electrodes Authors Title. Cut at approx. 70 characters if it is too long....

	Teflon percentage	70 %
	Colloidal gold	900 μl
	Amount of antibody	0.5 μg ml -1
	1-naphtylphosphate
	concentration	5 mM
	pH	10.0
	Prog-AP/Prog ratio	5:3
	Prog-AP/Prog volume	8 μl

©TIMA Editions/ENS 2006-page-ISBN:

Authors

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CONCLUSIONS

The sinergic combination of the advantages provided by nanostructured biosensors with gold nanoparticles and the use of a composite bioelectrode matrix, into which the nanoparticles are incorporated by physical inclusion, permits the development of robust immunosensors in which the antibody is directly attached to the electrode surface. The detection approaches allowed by this immunosensor design, imply a significant improvement of the analytical characteristics for the determination of progesterone with respect to previous immunosensor designs, and permits their application for the analysis of real samples.

Authors

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