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Calculation of chiral discrimination for the adsorption of L- and D-alanine molecules on crystalline cellulose
Chemical Physics 118 (1987) 233-240 North-Holland, Amsterdam
233
CALCULATION OF CHIRAL DISCRIMINATION FOR THE ADSORPTION OF L- AND D-ALANINE MOLECULES ON CRYSTALLINE CELLULOSE E. ALVIRA Departamento
and L. VEGA de Fisica Fundamental
y Experimental,
Uniuersidad de LA Laguna,
Tenerife, Spain
and C. GIRARDET Laboratoire Received
’
de Physique Moltkuiaire,
UA CNRS
772, UniuersitP de Besangon, 25030 Besanqon Cedex, France
14 May 1987
The differential adsorption of the two enantiomers of the alanine molecule on the crystalline native cellulose is calculated on the basis of a semi-empirical atom-atom description of the interactions between the molecule and the surface. In contrast with quartz surfaces for which the chirality has a structural nature, the chirality for the cellulose surface is intrinsic and local. The discriminatory ratio for the diastereoisomers is calculated to be close to 1% and it could be experimentally observed.
1. Introduction The L and D forms of amino acids are differently adsorbed on a chiral surface. The chiral discrimination for L- and D-alanine molecules adsorbed on a quartz surface has been recently analyzed [l-4] in terms of the difference in the interaction energy between two laevogyre (or two dextrogyre) partners and between one laevogyre and one dextrogyre partner. Experiments and calculations have shown that the diastereoisomers, L-alanine adsorbed on &quartz, were energetically more stable. Similar conclusions have been reached [5] for the preferential adsorption of other amino acids on a crystal of kaolinite. The energy discrimination is generally a small part (l-5%) of the total interaction energy, and originates, in the quartz crystal, from the helicoidal arrangement of the silicon and oxygen atoms forming the D, or D6 symmetry structures [2]. In contrast with the structural chirality of the
’ To whom correspondence
should
be addressed.
quartz crystal, an mtrmsic chirahty [4,6] can occur for solid media with specific basic elements. Cellulose exhibits such a specificity. Indeed the crystalline form of native cellulose (cellulose I) is built [7-91 from a set of parallel chains, each chain being formed by a succession of chiral glucose rings. The monomer, but not the spatial arrangement of the monomer, appears to be chiral. Moreover, cellulose can also occur in the amorphous phase for which the chiral monomers are built according to an helicoidal spatial distribution. Two chiral properties, the structural and the intrinsic, are then combined in this case and thus amorphous cellulose behaves as a superchiral medium. The aim of the present paper is a study of the chirality connected with the crystalline cellulose (intrinsic chirality); we leave for a forthcoming paper the analysis of the superchirality (intrinsic + structural chirality). The geometry of the two partners (alanine and cellulose) is presented in section 2. Section 3 is devoted to the discussion of the interaction potentials and the analysis of the numerical calculations
0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
234
E. Alvira et al. / Adsorption
of L- and D-alanine on crystalline cellulose
is done in section 4. Note here that fundamental models for the calculation of the long-range interactions between pairs of chiral molecules have been extensively proposed by Craig, Mellor and Mason [lo] (see also ref. [4]). However, the complexity of our physical system requires the use of simpler potential forms.
2. The model 2.1. Crystalline
cellulose
Five decades have been necessary to elucidate the structure of crystalline cellulose. Among the various models discussed in the literature, the structure presented by Meyer and Misch [7] on the basis of the analysis of X-ray diffraction diagrams, modified by Frey-Wyssling [8] and complemented very recently by conformational calculations of Pizzi and Eaton [9], seems to be the more convincing. Native cellulose (cellulose I) pertains to the base-centred monoclinic Bravais lattice with the following values of the conventional parameters: a=8.35A; c=7.9&
b=10.3A; ,0=84”.
The cellobioside structure is the monomer present throughout this cellulose I. The monomer is constituted by two glucose rings linked by an oxygen atom (fig. 1) and the structure of the crystallite appears to be made of infinite chains of monomers parallel to the axis b (the fiber axis). Five chains pertain to the crystalline cell, and are perpendicular to the plane (X, Z); the central chain located at the center of the rectangle (u X c) is antiparallel and displaced by 2.88 A with respect to the four others at the tops of the same rectangle. Hydrogen bonds between the chains allow the stability of the crystallite to be maximum. The spatial location of the linking oxygen atom between the glucose rings is determined by assuming that the projection of the bonds “oxygen-glucose rings” on a plane containing the rings is collinear to the chain axis (fig. 1). This model appears to be in reasonable agreement with X-ray
Fig. 1. The geometry of the monomer of the native cellulose, projected on the plane of the glucose rings. C labels a carbon atom and the smaller circles are oxygen atoms. The hydrogen atoms are not represented.
and neutron diffraction measurements and with the conformational calculations. Moreover, such a geometry permits a simple ordering of the chain structure. The hydrogen atoms, not represented on fig. 1, are located according to the conformational configuration calculated by Pizzi and Eaton [9]. This configuration leads to bond dista%C-H and O-H and orientations C-H and O-H in agreement with the formation of hydrogen bonds between consecutive chains (table 2 of ref. [9]). The surface plane of the cellulose crystal is taken to be the (101) plane, parallel to the chain orientation, which is a breaking plane. This plane contains the axes X and Y and the crystal thus fills the half-space Z < 0. The origin Z = 0 is chosen, arbitrarily, to correspond to the outer atoms of the chains parallel to the surface, i.e. the H atoms of the parallel chain, as shown on fig. 2. Note finally that the geometry of the crystalline cellulose does not yield the chirality. The chirality is an intrinsic property of the monomer due to the presence of the C-O-H bond in the glucose ring (cf. figs. 1 and 2).
E. Aluira et al. / Adsorption
235
of L- and D-alanine on crystalline cellulose
solutions,
in order to eliminate
ing adsorption surface.
of water
the possible
molecules
In such pH conditions,
spoil-
on the chiral
the molecule
hence
appears as a zwitterion CaH,C*H(NH:)CO;. The nucleus of the tetrasubstituted carbon atom C” is the center of mass of the molecule, the position absolute
of which is referred with respect to the frame as (X, Y, 2). The molecular axis z,
is collinear is located tional
to the C”-CO; bond and the atom Cp inside the plane (x, z). The conven-
Euler
angles
(4,
6, x)
define
the orienta-
tion of the molecular frame (x, y, Z) with respect to the absolute frame (X, Y, Z). The location of all the atoms of the molecule ref. [2]. The enantiomeric obtained
after reflection
is given in table 1 of
form of the L-alanine of the molecule
the plane (x, Z) (interchange the NH:
group).
molecules
(b)
is
through
of the H atom
and
Note that the L- and D-alanine
are respectively
dextrogyre
and laevo-
gym 3. The interaction potential The conformational study of the cellulose crystal has been developed [9] by considering three types of interactions between sion + repulsion contribution
atoms. The disperis generally rep-
resented
or a Buckingham-
Corner
by a Lennard-Jones potential.
between
Stockmayer form.
contribution
couples of atoms, which do not belong to
the same glucose Fig. 2. (a) 2D primitive cell for the cellulose surface (plane 101) including the carbon C, oxygen (0) and hydrogen (0) atoms. Note the displacement along Y of the second (parallel) chain with respect to the first (antiparallel) chain). (b) Same figure showing the four glucose rings in the 3D space. The carbon and oxygen atoms of the rings are not located in the same planes. The figure plane has been rotated around the axis X by an angle equal to 55 o
The hydrogen-bond
The
electrostatic
residue,
potential
can be represented
by a
or a Lippincott-Schroeder
remaining
contribution
contribution
between
describes partial
the
charges
of atoms, as calculated by the MO LCAO method; the magnitude of this latter interaction has been found to represent a small fraction of the total cohesion energy of the crystal. The calculations of the interaction energy between the zwitterion and the cellulose crystal are performed with the following potential model:
2.2. The alanine molecule The molecular structure of the alanine molecule C,H,NO, has been accurately determined from neutron diffraction experiments [ll]. In fact, discrimination measurements are generally performed
for
alanine
hydrochloride
in anhydrous
cl
k=l
where V;$ characterizes a Lennard-Jones atomatom potential between the i th atom of the cellulose and the jth atom of the alanine. The Len-
236
E. Alum
et al. / Adsorption
of L- and D-nlanme on crystalline cellulose
The chiral discrimination for the interaction I’ is characterized by the discriminatory ratio p which defines the energy difference between the L-alanine and the D-alanine interacting with the cellulose crystal, divided by the half-sum of the two interactions:
Table 1 Interaction parameters Lennard-Jones
i, i
c-o H-O o-o H-O c-c C-H H-H C-N N-H
C$J
c;:
(eV A6)
(eV K2)
21.71 24.88 33.59 8.61 15.85 6.06 2.13 17.65 6.88
19.828 26.115 22.488 3.627 17.017 3.318 0.545 22.386 4.534
x
10’
-
Dk (eV) 1 2
- 3.0 -3.3
+ VD(XD>
bk
(‘k 6.66 6.66
2.01 1.94
y,,
X [:lwL
hydrogen bonds
k
G(XLh
The indices L mation of the indexed by L configurations
z,,
1c/D> 4l9
YL> z,> YD,
z,>
4,>
#L,
XD> I OL, XL)
&I,
XII>
II -'.(3)
and D are connected to the conforalanine molecule and the variables or D correspond to the equilibrium for the molecules L and D.
1.04 0.97
4. Numerical results and discussion nard-Jones coefficients CgJ and C,li are given for the various pairs in table 1. V,!i labels hydrogen bond interactions which can occur between the NH; group of alanine and the 0 atoms of the cellulose surface (N-H.. .O bond; k = 1) or/and between the hydroxyl group OH of cellulose and the CO; group of alanine (O-H. ..O bond; k = 2). The use of the Lippincott-Schroeder model [12] for k = 1 and 2 yields: (R-a,)’ R-b
,
for
R>b,,
for
R
k
= 0,
The parameters D,, (Ye, ak and b, are given in table 1 and R labels the distance between the atoms N and 0 (k = 1) and the two atoms 0 (k = 2) intervening in the bond. Moreover the strong directionality of the hydrogen bond potential is accounted for by requiring that the angles (N-H,H...O) for k=l and (0-H,H...O) for k = 2 do not exceed 20 o [13]. Beyond this value, the hydrogen bond does not exist in this model. The electrostatic and the induction interactions have been disregarded here because their inclusion in the calculations would lead to an enhanced (time consuming) complexity.
In the surface plane, the primitive cell is a rectangle with dimensions equal to 10.88 A along the axis X and 10.30 A along Y. This cell contains two glucose rings of a parallel chain and two glucose rings of an adjacent antiparallel chain (cf. fig. 2a). The alanine center of mass C” is moved in a plane parallel to the surface of the cellulose in the edges of the two-dimensional cell, in such a way that the shortest distance between the possible locations of this center of mass is 0.42 A along X and 0.39 A along Y. Thus 26 X 26 points in this area are explored. For each point, the three angles of the molecules ($, 0, X) are moved from the triplet value (0, 0, 0) to (27, 7, 271) with an interval of 71/6, and the distance Z between C” and the cellulose surface is varied with an interval of 0.2 A. A dichotomic numerical method is then applied around the different points and for the various orientations of the molecule. This allows us to calculate the orientations of the molecules with an error less than q/90. One of the difficulties encountered in the calculation is connected with the considerable number of atoms which must, in principle, be considered in the potential sum procedure. In fact, tests performed on the potential magnitude show that the second inner shell of glucose chains contributes to
231
E. Alvira et al. / Adrorprion of L- and D-nlanine on crysralline cehlose
the total interaction by around 1%. Thus the interactions between the alanine molecule and the cellulose crystal can be limited to the chains closer to the surface. Similar tests for the convergence of the atom-atom potential inside the plane (X, Y) lead to take into account of all the atoms located in a disk of radius 15 A around the running point. Fig. 3 exhibits the equipotential surfaces V as a function of the position (X, Y) of the alanine center of mass. These surfaces are drawn for the minimized orientational configurations of the molecule and the minimized adsorption distances 2. Figs. 3a and 3b show the interaction of Lalanine and D-alanine with cellulose, respectively. The surface is very corrugated with extrema of energy between -0.2 and -0.9 eV. The positions above the glucose rings are more stable than above
the interchain spacing where in-crystal hydrogen bonds are present. Several minima are observed; indeed, the fact that the size of the alanine molecule is much smaller than the surface cell area, leads to local equilibrium configurations. The absolute minima correspond to energies equal to - 0.95 eV for the L-alanine and - 0.89 eV for the D-alanine, with a discriminatory ratio p = 0.06. Note that the hydrogen bond potential Vu is not chiral, in opposition with the Lennard-Jones contribution. However, the strong interactions generated by hydrogen bonding tend to impose the configuration of the alanine molecule above the cellulose surface, or at least, that part of the molecule which enters in the hydrogen bond formation. So, Vu acts to reveal the chirality of the Lennard-Jones potential although Vu is achiral.
v
L.
ml”(e”
-0.205
2
-0.284
5
-0.363
4
-0.442
8
-0.520
5
-0.599 -0.678
Fig. 3. Equipotential
P URAUN -._._.
13 9
-0.756
12
-0.e35
2
-0.914
1
surface for the L-alanine (a) and the D-alanine (b) adsorbed on the cellulose surface. Energy in eV unit. The rectangle represents the primitive cell of fig. (2a).
E. Alvim et al. /Adsorption
238
of L-
and D-alanine on crystalline cellulose
(b) -0.205 -0.277 -0.349 -0.421 -0.493 -0.565 -0.638 -0.710 -0.782 -0.854
Fig. 3b
The fact that the alanine molecule and the cellulose surface are bonded through hydrogen bridges is another cause of the occurrence of local minima. To illustrate the importance of VH, we calculate the value of the hydrogen bond interaction N-H.. .O between the NH: group of alanine and an oxygen atom of the cellulose surface, at the energy minimum for the L- and D-alanine. These values of VH are - 1.360 eV for the L-alanine and - 1.122 eV for the D-alanine at the position defined by the arrow in fig. 2a. Note still that the other chemical bond considered O-H.. .O, remains in general weaker. Fig. 4 represents the equipotential surfaces for the energy difference A defined as: A(X,
Y)=
V,(X> - V,(X,
Y, Z,,
$J,_, @,, XL)
Y, Z,,
$0,
&I, XII).
(4)
The interaction potentials V, and VD have been minimized with respect to the orientation (Ic/, 8, X) of the alanine molecule and to the distance Z between the center of mass of the molecule and the surface; but X and Y are free to vary inside the primitive cell area. A can be positive or negative according to the values of X and Y. The values of A range between -0.18 and +0.30 eV and the extrema are calculated in the neighborhood of the hydroxyl groups which are located at the outer surface of the cellulose. A similar behavior, not presented here, could be observed for p( X, Y) which varies between - 0.29 and + 0.54 inside the primitive cell area. The negative (respectively positive) sign for A or p corresponds to the preferential adsorption of L-alanine (respectively D-ala&e) on the cellulose surface. Figs. 3 and 4 show that the regions of the primitive cell of
E. Alvira et al. / Adsorption of L- and D-alanine on crystalhw
239
cellulose
CONTOUR
A
pro
cev
D DRRWI;
L -0.146
3
-0.097
7
-0.049
31
-0.000
29
0.049
27
0.091
12
0.146
6
8
0.194
4
9
0.243
1
0.292
I
10
Fig. 4. Equipotential surface for the energy difference A between Energy in eV unit. Full and broken curves correspond
cellulose for which A < 0 seem to be more important, indicating a trend for a better adsorption of the L species. But such a remark is only qualitative, at this stage, since it does not account of the absolute value of the potential energy (cf. discussion below). The available experimental data are relative to the preferential adsorption of alanine on structurally chiral crystals (quartz surface). Chromatographic studies of a racemic solution of alanine adsorbed on native cellulose are presently developed in order to verify the validity of the predictive results given here. However, a direct comparison with forthcoming experimental data will not be straightforward. Indeed, it has been shown, in this work, that the chirality is essentially local, given the great difference between the size of the adsorbed molecule and the size of the
and “D-alanine-cellulose”. the partners “L-alanine-cellulose” to positive and negative values of A, respectively.
primitive chiral cell of the cellulose surface. Hence, the alanine adsorption can take place on several sites of the primitive cell, with different adsorption energies and configurations. The discriminatory ratio, as defined by eq. (3) is clearly unadapted to account for this phenomenon. More suitable definitions of the discriminatory ratio, for a comparison with experiments, could be given by the relations: P1=
$
CP(X,,
yp),
(5)
%P
or p2=
IV,)-Wo)l ?I(V,‘.+(VnJI’ L I \ L, \ “I I
(6)
In eq. (5) the sum extends over the various config-
E. Aluira et al. / Adsorption of L- and D-alanine on crystalline cellulose
240
urations (X, Y) which have been explored, i.e. 1 < (cu, p) < 25 and N is the normalizing term (N = 25’). pi appears as a direct algebraic average, In contrast, ,$ defined by eq. (6) accounts for the thermal distribution of the values of the interaction potentials since the average ( ) is nothing but the Boltzmann average of p( X, Y):
Acknowledgement A partial support on computational from the Gobierno Autonomo de greatly acknowledged.
procedure Canarias is
References 111C. Girardet and L. Vega, Surface Sci. 157 (1985) 447. 121L. Vega, J. Breton, C. Girardet and L. Galatry, J. Chem.
When eqs. (5) and (6) are applied to the alanine molecule adsorbed on the native cellulose at T = 300 K, we find & = 1%
(T
independent),
p* = 10%. In both cases, the discriminatory ratio is not negligible and could thus be observed in experiments. To summarize, the chiral discrimination discussed in this letter has a different nature of that already studied with a quartz crystal. The differences are connected to the intrinsic and local nature of the chirality. The use of amorphous cellulose will lead to an additional effect, the superimposition of the intrinsic and structural chirality.
Phys. 84 (1986) 5171. [31 A. Julg, A. Favier and Y. Ozias, Surface Sci. 165 (1986) L53. [41 C. Girardet and C. Girard, J. Chim. Phys. 84 (1987) 637. [51 A. Julg, Cont. Rend. Acad. Sci. (Paris) 303 (1986) 1773. J. Mol. Struct. 144 [61 L. Vega, J. Breton and C. Girardet, (1986) 371. [71 K.H. Meyer and L. Misch, Helv. Chim. Acta 20 (1937) 232. K. Miihlethaler and R. Muggli, Holz. PI A. Frey-Wyssling, Roh- Werkst. 24 (1966) 443. Sci. Chem. A 21 [91 A. Pizi and N. Eaton, J. Macromol. (1984) 1443; A 22 (1986) 105, 139, and references therein. PO1 D.P. Craig and D.P. Mellor, Topics Current Chem. 63 (1976) 1, and references therein; S.F. Mason, in: Molecular optical activity and the chiral discrimination (Cambridge Univ. Press, Cambridge, 1982). J. Am. [Ill MS. Lehmann, T.F. Koetzle and W.C. Hamilton, Chem. Sot. 94 (1972) 2647. and R. Schroeder, J. Chem. Phys. 23 [=I E.R. Lippincott (1955) 1099. P31 D. Halzi, Chimia 26 (1972) 7.
233
CALCULATION OF CHIRAL DISCRIMINATION FOR THE ADSORPTION OF L- AND D-ALANINE MOLECULES ON CRYSTALLINE CELLULOSE E. ALVIRA Departamento
and L. VEGA de Fisica Fundamental
y Experimental,
Uniuersidad de LA Laguna,
Tenerife, Spain
and C. GIRARDET Laboratoire Received
’
de Physique Moltkuiaire,
UA CNRS
772, UniuersitP de Besangon, 25030 Besanqon Cedex, France
14 May 1987
The differential adsorption of the two enantiomers of the alanine molecule on the crystalline native cellulose is calculated on the basis of a semi-empirical atom-atom description of the interactions between the molecule and the surface. In contrast with quartz surfaces for which the chirality has a structural nature, the chirality for the cellulose surface is intrinsic and local. The discriminatory ratio for the diastereoisomers is calculated to be close to 1% and it could be experimentally observed.
1. Introduction The L and D forms of amino acids are differently adsorbed on a chiral surface. The chiral discrimination for L- and D-alanine molecules adsorbed on a quartz surface has been recently analyzed [l-4] in terms of the difference in the interaction energy between two laevogyre (or two dextrogyre) partners and between one laevogyre and one dextrogyre partner. Experiments and calculations have shown that the diastereoisomers, L-alanine adsorbed on &quartz, were energetically more stable. Similar conclusions have been reached [5] for the preferential adsorption of other amino acids on a crystal of kaolinite. The energy discrimination is generally a small part (l-5%) of the total interaction energy, and originates, in the quartz crystal, from the helicoidal arrangement of the silicon and oxygen atoms forming the D, or D6 symmetry structures [2]. In contrast with the structural chirality of the
’ To whom correspondence
should
be addressed.
quartz crystal, an mtrmsic chirahty [4,6] can occur for solid media with specific basic elements. Cellulose exhibits such a specificity. Indeed the crystalline form of native cellulose (cellulose I) is built [7-91 from a set of parallel chains, each chain being formed by a succession of chiral glucose rings. The monomer, but not the spatial arrangement of the monomer, appears to be chiral. Moreover, cellulose can also occur in the amorphous phase for which the chiral monomers are built according to an helicoidal spatial distribution. Two chiral properties, the structural and the intrinsic, are then combined in this case and thus amorphous cellulose behaves as a superchiral medium. The aim of the present paper is a study of the chirality connected with the crystalline cellulose (intrinsic chirality); we leave for a forthcoming paper the analysis of the superchirality (intrinsic + structural chirality). The geometry of the two partners (alanine and cellulose) is presented in section 2. Section 3 is devoted to the discussion of the interaction potentials and the analysis of the numerical calculations
0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
234
E. Alvira et al. / Adsorption
of L- and D-alanine on crystalline cellulose
is done in section 4. Note here that fundamental models for the calculation of the long-range interactions between pairs of chiral molecules have been extensively proposed by Craig, Mellor and Mason [lo] (see also ref. [4]). However, the complexity of our physical system requires the use of simpler potential forms.
2. The model 2.1. Crystalline
cellulose
Five decades have been necessary to elucidate the structure of crystalline cellulose. Among the various models discussed in the literature, the structure presented by Meyer and Misch [7] on the basis of the analysis of X-ray diffraction diagrams, modified by Frey-Wyssling [8] and complemented very recently by conformational calculations of Pizzi and Eaton [9], seems to be the more convincing. Native cellulose (cellulose I) pertains to the base-centred monoclinic Bravais lattice with the following values of the conventional parameters: a=8.35A; c=7.9&
b=10.3A; ,0=84”.
The cellobioside structure is the monomer present throughout this cellulose I. The monomer is constituted by two glucose rings linked by an oxygen atom (fig. 1) and the structure of the crystallite appears to be made of infinite chains of monomers parallel to the axis b (the fiber axis). Five chains pertain to the crystalline cell, and are perpendicular to the plane (X, Z); the central chain located at the center of the rectangle (u X c) is antiparallel and displaced by 2.88 A with respect to the four others at the tops of the same rectangle. Hydrogen bonds between the chains allow the stability of the crystallite to be maximum. The spatial location of the linking oxygen atom between the glucose rings is determined by assuming that the projection of the bonds “oxygen-glucose rings” on a plane containing the rings is collinear to the chain axis (fig. 1). This model appears to be in reasonable agreement with X-ray
Fig. 1. The geometry of the monomer of the native cellulose, projected on the plane of the glucose rings. C labels a carbon atom and the smaller circles are oxygen atoms. The hydrogen atoms are not represented.
and neutron diffraction measurements and with the conformational calculations. Moreover, such a geometry permits a simple ordering of the chain structure. The hydrogen atoms, not represented on fig. 1, are located according to the conformational configuration calculated by Pizzi and Eaton [9]. This configuration leads to bond dista%C-H and O-H and orientations C-H and O-H in agreement with the formation of hydrogen bonds between consecutive chains (table 2 of ref. [9]). The surface plane of the cellulose crystal is taken to be the (101) plane, parallel to the chain orientation, which is a breaking plane. This plane contains the axes X and Y and the crystal thus fills the half-space Z < 0. The origin Z = 0 is chosen, arbitrarily, to correspond to the outer atoms of the chains parallel to the surface, i.e. the H atoms of the parallel chain, as shown on fig. 2. Note finally that the geometry of the crystalline cellulose does not yield the chirality. The chirality is an intrinsic property of the monomer due to the presence of the C-O-H bond in the glucose ring (cf. figs. 1 and 2).
E. Aluira et al. / Adsorption
235
of L- and D-alanine on crystalline cellulose
solutions,
in order to eliminate
ing adsorption surface.
of water
the possible
molecules
In such pH conditions,
spoil-
on the chiral
the molecule
hence
appears as a zwitterion CaH,C*H(NH:)CO;. The nucleus of the tetrasubstituted carbon atom C” is the center of mass of the molecule, the position absolute
of which is referred with respect to the frame as (X, Y, 2). The molecular axis z,
is collinear is located tional
to the C”-CO; bond and the atom Cp inside the plane (x, z). The conven-
Euler
angles
(4,
6, x)
define
the orienta-
tion of the molecular frame (x, y, Z) with respect to the absolute frame (X, Y, Z). The location of all the atoms of the molecule ref. [2]. The enantiomeric obtained
after reflection
is given in table 1 of
form of the L-alanine of the molecule
the plane (x, Z) (interchange the NH:
group).
molecules
(b)
is
through
of the H atom
and
Note that the L- and D-alanine
are respectively
dextrogyre
and laevo-
gym 3. The interaction potential The conformational study of the cellulose crystal has been developed [9] by considering three types of interactions between sion + repulsion contribution
atoms. The disperis generally rep-
resented
or a Buckingham-
Corner
by a Lennard-Jones potential.
between
Stockmayer form.
contribution
couples of atoms, which do not belong to
the same glucose Fig. 2. (a) 2D primitive cell for the cellulose surface (plane 101) including the carbon C, oxygen (0) and hydrogen (0) atoms. Note the displacement along Y of the second (parallel) chain with respect to the first (antiparallel) chain). (b) Same figure showing the four glucose rings in the 3D space. The carbon and oxygen atoms of the rings are not located in the same planes. The figure plane has been rotated around the axis X by an angle equal to 55 o
The hydrogen-bond
The
electrostatic
residue,
potential
can be represented
by a
or a Lippincott-Schroeder
remaining
contribution
contribution
between
describes partial
the
charges
of atoms, as calculated by the MO LCAO method; the magnitude of this latter interaction has been found to represent a small fraction of the total cohesion energy of the crystal. The calculations of the interaction energy between the zwitterion and the cellulose crystal are performed with the following potential model:
2.2. The alanine molecule The molecular structure of the alanine molecule C,H,NO, has been accurately determined from neutron diffraction experiments [ll]. In fact, discrimination measurements are generally performed
for
alanine
hydrochloride
in anhydrous
cl
k=l
where V;$ characterizes a Lennard-Jones atomatom potential between the i th atom of the cellulose and the jth atom of the alanine. The Len-
236
E. Alum
et al. / Adsorption
of L- and D-nlanme on crystalline cellulose
The chiral discrimination for the interaction I’ is characterized by the discriminatory ratio p which defines the energy difference between the L-alanine and the D-alanine interacting with the cellulose crystal, divided by the half-sum of the two interactions:
Table 1 Interaction parameters Lennard-Jones
i, i
c-o H-O o-o H-O c-c C-H H-H C-N N-H
C$J
c;:
(eV A6)
(eV K2)
21.71 24.88 33.59 8.61 15.85 6.06 2.13 17.65 6.88
19.828 26.115 22.488 3.627 17.017 3.318 0.545 22.386 4.534
x
10’
-
Dk (eV) 1 2
- 3.0 -3.3
+ VD(XD>
bk
(‘k 6.66 6.66
2.01 1.94
y,,
X [:lwL
hydrogen bonds
k
G(XLh
The indices L mation of the indexed by L configurations
z,,
1c/D> 4l9
YL> z,> YD,
z,>
4,>
#L,
XD> I OL, XL)
&I,
XII>
II -'.(3)
and D are connected to the conforalanine molecule and the variables or D correspond to the equilibrium for the molecules L and D.
1.04 0.97
4. Numerical results and discussion nard-Jones coefficients CgJ and C,li are given for the various pairs in table 1. V,!i labels hydrogen bond interactions which can occur between the NH; group of alanine and the 0 atoms of the cellulose surface (N-H.. .O bond; k = 1) or/and between the hydroxyl group OH of cellulose and the CO; group of alanine (O-H. ..O bond; k = 2). The use of the Lippincott-Schroeder model [12] for k = 1 and 2 yields: (R-a,)’ R-b
,
for
R>b,,
for
R
k
= 0,
The parameters D,, (Ye, ak and b, are given in table 1 and R labels the distance between the atoms N and 0 (k = 1) and the two atoms 0 (k = 2) intervening in the bond. Moreover the strong directionality of the hydrogen bond potential is accounted for by requiring that the angles (N-H,H...O) for k=l and (0-H,H...O) for k = 2 do not exceed 20 o [13]. Beyond this value, the hydrogen bond does not exist in this model. The electrostatic and the induction interactions have been disregarded here because their inclusion in the calculations would lead to an enhanced (time consuming) complexity.
In the surface plane, the primitive cell is a rectangle with dimensions equal to 10.88 A along the axis X and 10.30 A along Y. This cell contains two glucose rings of a parallel chain and two glucose rings of an adjacent antiparallel chain (cf. fig. 2a). The alanine center of mass C” is moved in a plane parallel to the surface of the cellulose in the edges of the two-dimensional cell, in such a way that the shortest distance between the possible locations of this center of mass is 0.42 A along X and 0.39 A along Y. Thus 26 X 26 points in this area are explored. For each point, the three angles of the molecules ($, 0, X) are moved from the triplet value (0, 0, 0) to (27, 7, 271) with an interval of 71/6, and the distance Z between C” and the cellulose surface is varied with an interval of 0.2 A. A dichotomic numerical method is then applied around the different points and for the various orientations of the molecule. This allows us to calculate the orientations of the molecules with an error less than q/90. One of the difficulties encountered in the calculation is connected with the considerable number of atoms which must, in principle, be considered in the potential sum procedure. In fact, tests performed on the potential magnitude show that the second inner shell of glucose chains contributes to
231
E. Alvira et al. / Adrorprion of L- and D-nlanine on crysralline cehlose
the total interaction by around 1%. Thus the interactions between the alanine molecule and the cellulose crystal can be limited to the chains closer to the surface. Similar tests for the convergence of the atom-atom potential inside the plane (X, Y) lead to take into account of all the atoms located in a disk of radius 15 A around the running point. Fig. 3 exhibits the equipotential surfaces V as a function of the position (X, Y) of the alanine center of mass. These surfaces are drawn for the minimized orientational configurations of the molecule and the minimized adsorption distances 2. Figs. 3a and 3b show the interaction of Lalanine and D-alanine with cellulose, respectively. The surface is very corrugated with extrema of energy between -0.2 and -0.9 eV. The positions above the glucose rings are more stable than above
the interchain spacing where in-crystal hydrogen bonds are present. Several minima are observed; indeed, the fact that the size of the alanine molecule is much smaller than the surface cell area, leads to local equilibrium configurations. The absolute minima correspond to energies equal to - 0.95 eV for the L-alanine and - 0.89 eV for the D-alanine, with a discriminatory ratio p = 0.06. Note that the hydrogen bond potential Vu is not chiral, in opposition with the Lennard-Jones contribution. However, the strong interactions generated by hydrogen bonding tend to impose the configuration of the alanine molecule above the cellulose surface, or at least, that part of the molecule which enters in the hydrogen bond formation. So, Vu acts to reveal the chirality of the Lennard-Jones potential although Vu is achiral.
v
L.
ml”(e”
-0.205
2
-0.284
5
-0.363
4
-0.442
8
-0.520
5
-0.599 -0.678
Fig. 3. Equipotential
P URAUN -._._.
13 9
-0.756
12
-0.e35
2
-0.914
1
surface for the L-alanine (a) and the D-alanine (b) adsorbed on the cellulose surface. Energy in eV unit. The rectangle represents the primitive cell of fig. (2a).
E. Alvim et al. /Adsorption
238
of L-
and D-alanine on crystalline cellulose
(b) -0.205 -0.277 -0.349 -0.421 -0.493 -0.565 -0.638 -0.710 -0.782 -0.854
Fig. 3b
The fact that the alanine molecule and the cellulose surface are bonded through hydrogen bridges is another cause of the occurrence of local minima. To illustrate the importance of VH, we calculate the value of the hydrogen bond interaction N-H.. .O between the NH: group of alanine and an oxygen atom of the cellulose surface, at the energy minimum for the L- and D-alanine. These values of VH are - 1.360 eV for the L-alanine and - 1.122 eV for the D-alanine at the position defined by the arrow in fig. 2a. Note still that the other chemical bond considered O-H.. .O, remains in general weaker. Fig. 4 represents the equipotential surfaces for the energy difference A defined as: A(X,
Y)=
V,(X> - V,(X,
Y, Z,,
$J,_, @,, XL)
Y, Z,,
$0,
&I, XII).
(4)
The interaction potentials V, and VD have been minimized with respect to the orientation (Ic/, 8, X) of the alanine molecule and to the distance Z between the center of mass of the molecule and the surface; but X and Y are free to vary inside the primitive cell area. A can be positive or negative according to the values of X and Y. The values of A range between -0.18 and +0.30 eV and the extrema are calculated in the neighborhood of the hydroxyl groups which are located at the outer surface of the cellulose. A similar behavior, not presented here, could be observed for p( X, Y) which varies between - 0.29 and + 0.54 inside the primitive cell area. The negative (respectively positive) sign for A or p corresponds to the preferential adsorption of L-alanine (respectively D-ala&e) on the cellulose surface. Figs. 3 and 4 show that the regions of the primitive cell of
E. Alvira et al. / Adsorption of L- and D-alanine on crystalhw
239
cellulose
CONTOUR
A
pro
cev
D DRRWI;
L -0.146
3
-0.097
7
-0.049
31
-0.000
29
0.049
27
0.091
12
0.146
6
8
0.194
4
9
0.243
1
0.292
I
10
Fig. 4. Equipotential surface for the energy difference A between Energy in eV unit. Full and broken curves correspond
cellulose for which A < 0 seem to be more important, indicating a trend for a better adsorption of the L species. But such a remark is only qualitative, at this stage, since it does not account of the absolute value of the potential energy (cf. discussion below). The available experimental data are relative to the preferential adsorption of alanine on structurally chiral crystals (quartz surface). Chromatographic studies of a racemic solution of alanine adsorbed on native cellulose are presently developed in order to verify the validity of the predictive results given here. However, a direct comparison with forthcoming experimental data will not be straightforward. Indeed, it has been shown, in this work, that the chirality is essentially local, given the great difference between the size of the adsorbed molecule and the size of the
and “D-alanine-cellulose”. the partners “L-alanine-cellulose” to positive and negative values of A, respectively.
primitive chiral cell of the cellulose surface. Hence, the alanine adsorption can take place on several sites of the primitive cell, with different adsorption energies and configurations. The discriminatory ratio, as defined by eq. (3) is clearly unadapted to account for this phenomenon. More suitable definitions of the discriminatory ratio, for a comparison with experiments, could be given by the relations: P1=
$
CP(X,,
yp),
(5)
%P
or p2=
IV,)-Wo)l ?I(V,‘.+(VnJI’ L I \ L, \ “I I
(6)
In eq. (5) the sum extends over the various config-
E. Aluira et al. / Adsorption of L- and D-alanine on crystalline cellulose
240
urations (X, Y) which have been explored, i.e. 1 < (cu, p) < 25 and N is the normalizing term (N = 25’). pi appears as a direct algebraic average, In contrast, ,$ defined by eq. (6) accounts for the thermal distribution of the values of the interaction potentials since the average ( ) is nothing but the Boltzmann average of p( X, Y):
Acknowledgement A partial support on computational from the Gobierno Autonomo de greatly acknowledged.
procedure Canarias is
References 111C. Girardet and L. Vega, Surface Sci. 157 (1985) 447. 121L. Vega, J. Breton, C. Girardet and L. Galatry, J. Chem.
When eqs. (5) and (6) are applied to the alanine molecule adsorbed on the native cellulose at T = 300 K, we find & = 1%
(T
independent),
p* = 10%. In both cases, the discriminatory ratio is not negligible and could thus be observed in experiments. To summarize, the chiral discrimination discussed in this letter has a different nature of that already studied with a quartz crystal. The differences are connected to the intrinsic and local nature of the chirality. The use of amorphous cellulose will lead to an additional effect, the superimposition of the intrinsic and structural chirality.
Phys. 84 (1986) 5171. [31 A. Julg, A. Favier and Y. Ozias, Surface Sci. 165 (1986) L53. [41 C. Girardet and C. Girard, J. Chim. Phys. 84 (1987) 637. [51 A. Julg, Cont. Rend. Acad. Sci. (Paris) 303 (1986) 1773. J. Mol. Struct. 144 [61 L. Vega, J. Breton and C. Girardet, (1986) 371. [71 K.H. Meyer and L. Misch, Helv. Chim. Acta 20 (1937) 232. K. Miihlethaler and R. Muggli, Holz. PI A. Frey-Wyssling, Roh- Werkst. 24 (1966) 443. Sci. Chem. A 21 [91 A. Pizi and N. Eaton, J. Macromol. (1984) 1443; A 22 (1986) 105, 139, and references therein. PO1 D.P. Craig and D.P. Mellor, Topics Current Chem. 63 (1976) 1, and references therein; S.F. Mason, in: Molecular optical activity and the chiral discrimination (Cambridge Univ. Press, Cambridge, 1982). J. Am. [Ill MS. Lehmann, T.F. Koetzle and W.C. Hamilton, Chem. Sot. 94 (1972) 2647. and R. Schroeder, J. Chem. Phys. 23 [=I E.R. Lippincott (1955) 1099. P31 D. Halzi, Chimia 26 (1972) 7.