Segregation into domains observed in liquid crystal phases: comparison of experimental and theoretical data

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Segregation into domains observed in liquid crystal phases: comparison ofexperimental and theoretical data

Heinz Amenitsch,a Cecilia Bombelli,bc Stefano Borocci,d Ruggero Caminiti,e Francesca Ceccacci,e

Simona Concilio,fg Camillo La Mesa,e Giovanna Mancini,*bc Stefano Piotto*gh and Michael Rappolta

Received 8th October 2010, Accepted 4th January 2011

DOI: 10.1039/c0sm01127d

The phase diagram of an amidic surfactant, sodium N-dodecanoylprolinate, was investigated by

experimental means such as optical microscopy, multinuclear NMR, and SAXS experiments, and by

dissipative particle dynamics and all-atoms molecular dynamics simulations. The organization in

domains based on the stereochemical information of the surfactant (E and Z), as well as being observed

previously under micellar aggregating conditions, was also observed in the liquid crystal phases. The

combination of the different experimental techniques and of the theoretical investigation allowed us to

clarify the nature of the domains and some of the involved interactions in their segregation and

organization.

Introduction

The segregation in domains of the components of biological

membranes controls many membrane specific functions, some

lipid domains being involved in signal transduction and intra-

cellular trafficking and being also intimately connected to

various diseases.1

In spite of their central role in cell life, the biological signifi-

cance of membrane domains has been considered only over the

last 15 years.2,3 Although the occurrence of specific molecular

species and the interactions responsible for the formation,

organization and functions of membrane domains have been

partly elucidated,2,3 some aspects of their role and nature are still

not fully understood.

aInstitute of Biophysics and Nanosystems Research, Austrian Academy ofSciences, Graz, AustriabCNR, Istituto di Metodologie Chimiche – Sezione Meccanismi di Reazioneand Dipartimento di Chimica, Universit�a degli Studi di Roma ‘‘LaSapienza’’, P.le Aldo Moro 5, 00185 Roma, Italy. E-mail: [email protected] di Eccellenza Materiali Innovativi Nanostrutturali per ApplicazioniCliniche, Fisiche e Biomediche, Universit�a di Perugia, Via Elce di Sotto,06123 Perugia, ItalydDipartimento di Scienze Ambientali, Universit�a della Tuscia, Largodell’Universit�a, 01100 Viterbo, ItalyeDipartimento di Chimica, Universit�a degli Studi di Roma ‘‘La Sapienza’’,P.le Aldo Moro 5, 00185 Roma, ItalyfDipartimento di Ingegneria Chimica e Alimentare, Universit�a di Salerno,Via Ponte don Melillo, 84084 Fisciano Salerno, ItalygNANOMATES (Research Centre for Nanomaterials andNanotechnology) Universit�a di Salerno, Via Ponte don Melillo, 84084Fisciano Salerno, Italy. E-mail: [email protected] di Scienze Farmaceutiche, Universit�a di Salerno, Via Pontedon Melillo, 84084 Fisciano Salerno, Italy

3392 | Soft Matter, 2011, 7, 3392–3403

Segregation of amphiphiles into domains has been observed

and investigated on a large variety of biomembrane models, such

as vesicle bilayers2–4 and also on Langmuir and crystal mono-

layers.5–11 Some of us observed the segregation into domains of E

and Z isomers (Scheme 1) of sodium N-dodecanoylprolinate,12 1,

under micellar aggregating conditions and suggested that segre-

gation takes place within the same aggregate rather than yielding

micelles containing a single isomeric population.13 On these

grounds, a similar behaviour is expected to occur in the corre-

sponding lyotropic phases. Domains made of the two different

isomers could occur and be responsible for changes in local

curvature, packing density and so forth.

Here we report an investigation aimed at clarifying the nature

of liquid crystal phases observed in the phase diagram of sodium

N-dodecanoylprolinate. Our goal was to verify if E and Z

isomers of such amidic surfactant also segregate into domains in

the liquid crystal phases as formely observed under micelle

aggregating conditions. This would shed some light on the

interactions that control the organization and segregation in

biological membranes. Liquid crystals have often been investi-

gated as biomembrane models, though a plasma membrane or an

intracellular organelle membrane cannot strictly be considered as

liquid crystals. Biomembranes do have, however, some features

Scheme 1 Equilibrium of the E and Z isomers of surfactant 1. The

relative amount of the isomers depends on the concentration.

This journal is ª The Royal Society of Chemistry 2011

Fig. 2 1H NMR spectra of samples of sodium N-dodecanoylprolinate

(a) 64%, (b) 73%, (c) 77%, in D2O.

Fig. 3 13C NMR spectra of samples of sodium N-dodecanoylprolinate

(a) 62%, (b) 70%, (c) 73%, (d) 77% in D2O.

of certain liquid crystal systems, such as the fluid state of lipid

components and the double layer and/or columnar arrangement.

The investigation was carried out by different physicochemical

techniques, namely polarized optical microscopy, X-ray

diffraction, 1H, 2H and 13C NMR. Further, simulations of the

aggregation of various blends of the 1E and 1Z isomers was

carried out using a coarse grain algorithm, i.e. the dissipative

particle dynamics (DPD), and all-atoms molecular dynamics.

Results and discussion

The experimental investigations were carried out on D2O/1

samples. The 1E and 1Z isomers are in equilibrium and their

relative amount depends on the concentration. It is known that

below the critical micelle concentration (cmc) their ratio is 1

whereas in the micelle concentration regime the equilibrium is

shifted in favour of the Z isomer, the Z/E ratio being 3.12

Optical microscopy

Optical microscopy investigations, carried out at 25 �C, allowed

observing anisotropic textures in the ranges 45–71% and 75–87%

in weight of surfactant, isotropic phases below 45% and in the

range 71–75%. Samples showing typical optically anisotropic

textures were classified according to the Rosevear classification.14

By raising the temperature up to 60 �C a transition to an

anisotropic phase at concentrations between 71 and 75% was

observed.

Multinuclear NMR investigation

A multinuclear NMR investigation was performed on several

samples in the range 25–60 �C. The results obtained allowed

drawing a phase diagram later confirmed and implemented by

SAXS experiments. Relevant 1H, 2H and 13C spectra are reported

in Fig. 1–4.2H NMR spectra give information on the state of water

molecules interacting with the surface of aggregates. The NMR

spectrum of heavy water, in fact, is ruled by the interaction of the

deuteron quadrupole moment with the electric field gradient at

the nucleus.15 In anisotropic phases the quadrupole interactions

split the main resonance in two signals. Their separation depends

on the orientation of deuterium-containing molecule with respect

to the applied magnetic field. Hetereogeneity of orientation

within the sample yields simultaneous various spectra that are

Fig. 1 2H NMR spectra of samples of sodium N-dodecanoylprolinate

(a) 40%, (b) 73% in D2O.

Fig. 4 2H NMR spectra of samples of sodium N-dodecanoylprolinate

(a) 60%, (b) 64%, (c) 68%, (d) 70%, (e) 76%, (f) 77% in D2O.

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Fig. 5 Tentative phase map of sodium N-dodecanoylprolinate in water

as function of surfactant concentration and temperature traced on the

basis of NMR, optical microscopy and SAXS experiments. In the pure

phase region the L1, H1, V1 (Ia3d) and La phases are identified. A small

phase region (dashed red circle) could not be identified unambiguously.

superimposed in a standard Pake pattern.16 On the other hand, in

an isotropic phase, the interactions of the quadrupole moment

with the electric field gradient are averaged to zero as the result of

rapid and isotropic molecular motions, or of an isotropic

distribution of the directions of the electric field gradient;

accordingly the 2H NMR spectrum shows a singlet.2H NMR spectra reported in Fig. 1 are diagnostic of isotropic

phases, in particular, a micellar (Fig. 1a) and two cubic phases

(Fig. 1b) at 40.0% and at 73.0% wt%, respectively. The occur-

rence of micellar phase at 40% concentration (Fig. 1a) was

confirmed by 1H and 13C NMR spectra (data not shown) in

agreement with previous studies.13 The two superimposed

singlets17 in Fig. 1b are tentatively ascribed to different liquid

crystal cubic phases, as suggested by other evidences; among

them, the sample location in the phase map,18 their glassy

hardness, the 1H and 13C resolved spectra (Fig. 2b and Fig. 3c,

respectively), both typical of isotropic environments.19,20 The

occurrence of two coexisting phases is evidenced also by splitting

of signals in the 13C spectrum, reported in Fig. 3c. In fact, the

conformation of amide bond is not transmitted along the

hydrophobic chain and splitting of resonances due to chain

carbons, as those relative to terminal methyl (at �17 ppm), is

diagnostic of two magnetically different domains.12 Spectra

relative to samples in the 45–68 wt% concentration range show

deuterium quadrupole doublets with large parallel components

in the 62–67 wt% concentration range (Fig. 4b) and strictly

related effects below 60 wt% (Fig. 4a).

The most interesting feature of the 2H spectra in the 60–67 wt%

concentration samples is the presence of two anisotropic phases.

According to the position of samples in the phase diagram the

phase can be hexagonal. Splitting of signals is evident in Fig. 4b

whereas the spectrum reported in Fig. 4a shows only line

broadening of parallel and orthogonal components at high fields.

In 13C NMR spectra, splitting of signal due to terminal methyl is

also diagnostic of the presence of two phases. 1H spectra of

samples in the range 45–68 wt% lack any fine structure due to line

width broadening (an example is reported in Fig. 2a).

Samples in the 68–70 wt% concentration range yield 2H spectra

that show the coexistence of different phases (Fig. 4c and 4d)

confirmed by the splitting of signals in 13C NMR spectra as

observed in the spectrum reported in Fig. 3b.2H NMR spectra of samples in the 75–87 wt% range show

deuterium quadrupole doublets characterized by intense

orthogonal components, as shown in Fig. 4e and 4f. The sample

location in the phase diagram suggests the occurrence of lamellar

phases.

Fig. 6 Selected diffraction patterns of the sample at 52% surfactant

concentration (a) and of the sample at 72% surfactant concentration at 25�C (b), and 35 �C (c). The Ia3d phase, with a lattice spacing of 8.1 nm,

formed as a single phase above 35 �C (c), and in coexistence with other

phases below 35 �C. At 52% surfactant concentration the H1 phase was

detected over a wide temperature range, its lattice spacing ranging

between a ¼ 4.1 and 4.2 nm (a).

Small angle X-ray experiments

Small angle X-ray scattering experiments performed with

synchrotron radiation were carried out from 1.8 to 92.0 wt%

surfactant in a temperature range from room temperature to

60 �C. In Fig. 5 the phase diagram based on SAXS, NMR and

optical microscopy experiments is reported. On increasing

surfactant concentration the following phase sequence was

observed: up to 45–50% a micellar solution, L1, was detected. As

we reported earlier,13 micelles have a diameter of about 4.4 nm,

and a hydrophobic core radius of �1.4 nm. In the 50–65 wt%

concentration regime a normal hexagonal phase, H1, was found.

3394 | Soft Matter, 2011, 7, 3392–3403

As shown in Fig. 6a the lattice spacing is 4.1 nm, in agreement

with the overall micellar cross-sectional size. In the 65–80 wt%

concentration regime (depending on temperature) a cubic phase

belonging to the space group Ia3d appeared (Fig. 6c), with

a lattice spacing of 8.1 nm. Above 72–80 wt% a lamellar fluid

phase, La, was found. Its diffraction pattern exhibits a very

strong first order reflection with d-spacing in the range

2.8–3.1 nm (referring to 72% and 90% surfactant, respectively).

This journal is ª The Royal Society of Chemistry 2011

In short, the phase sequence L1 / H1 / V1 (Ia3d)/ La was

observed.

While in most concentration and temperature regimes the

phase assignment is univocal, in a region at �68–73 wt% of

surfactant and between 22 and 33 �C (Fig. 5) the coexistence of

different phases (and the slow kinetics of phase transformation)

did not allow us to identify all phases unambiguously. In fact, the

samples giving 2H NMR spectra with presence of two isotropic

phases (in Fig. 1b) yielded SAXS spectra with many Bragg

reflections (Fig. 6b). Two of them were ascribed to a Ia3d phase

as shown in the comparison with Fig. 6c, and another reflection

could be ascribed to the H1 phase, not observed in the 2H NMR

spectrum. All other reflections could not be ascribed.

Fig. 7 Ternary phase diagram mapped out on the basis of DPD simu-

lations. The relative abundances of water and 1Z and 1E isomers are

reported. The four main morphologies are color mapped in the diagram.

The boundaries are not sharp due to the intrinsic uncertainty of DPD

simulations. The white arrow indicates the well known progression

micellar/hexagonal/cubic/lamellar phases for systems containing

equal amounts of 1Z and 1E isomers.

Theoretical calculation

The ternary system 1E-1Z-water was investigated by the dissi-

pative particle dynamics approach, to clarify experimental X-ray

and NMR observations on multi-phase areas which could be due

to domains with different amphiphile compositions.

The dynamics of lipid phase transitions is very slow on an

experimental time-scale, typical values being of the order of

seconds. Long time scales are typical of colloidal and liquid

crystals systems, and are much larger compared to motions

occurring on molecular scales. Because of the above reasons and

of the involvement of a large number of molecules, an atomic

description of mesoscale systems by classical molecular dynamics

simulations would require very long computational times. This is

why a hybrid simulation method was used to mimic the meso-

scale, as described in the Methods section. Actually, in the

context of liquid crystals systems, an atomistic simulation by

classical molecular dynamics is used only in cases where meso-

scale morphologies are known and ‘‘sub-mesoscale’’ molecular

structures, embedded in the mesoscale scaffold, have to be

elucidated.

The system 1Z-1E-water system was investigated by 32 coarse

grain simulations covering water contents from 16% to 72%. In

the real systems the 1E and 1Z isomers are in equilibrium, though

we do not know their relative amount above micellar aggregating

conditions. For this reason and because composition does not

change during the simulation, calculations were carried out at

different percentages of the isomers. Phase assignment was done

through the identification of the elements of symmetry of the

aggregates. This was done by visual inspection in the self-evident

cases and by a Fourier analysis of the electron density in the most

complex cases.

To represent the succession of phases in the 1Z-1E-water

system, we reported the results of simulated compositions (black

circles) in a ternary phase diagram (Fig. 7).

By decreasing water content, i.e. moving along the white

arrow, the common sequence micellar, hexagonal, cubic,

lamellar phase, is observed. However, due to the intrinsic limits

of any coarse grain simulation, the phase borders are not sharp.

To avoid artifacts making troublesome the correct structural

assignment, simulation boxes 2–3 times larger than the unit cell

of the aggregate, were used. As a consequence a very slow

convergence and, in some cases, the presence of competing

domains were observed. A smooth color mapping distinguishes

regions where the position of the boundary is not sure. The

This journal is ª The Royal Society of Chemistry 2011

simulation results are reported in Table 1 and 2. In particular,

Table 1 reports the results of the simulations relative to balanced

1Z/1E systems, whereas Table 2 reports those relative to unbal-

anced systems.

It was observed that in systems composed by equimolar 1E

and 1Z mixtures (along the diagonal in Fig. 7) phase transitions

occurred at surfactant concentration lower than in unbalanced

systems. Qualitatively, mixtures containing a larger amount of

1E isomer showed a slightly wider region of existence of hexag-

onal and cubic phases. In our opinion, this is not a simulation

artifact. In the following, we describe the main features observed

in the DPD simulations.

The simulations of systems characterized by a high content of

water 50-0-50, 0-50-50, 17-17-66, and 14-14-72 (1Z-1E-water)

yielded micelles floating in water. The formation of micelles was

very fast and occurred in less than 100 ns. 1E and 1Z isomers

showed the tendency to segregate in fluid domains. The domains

lifetime was hundreds of nanoseconds, and at the molecular level

the domain boundary interface was rather diffuse. In Fig. 8 the

presence of domains in the micellar 14-14-72 system is shown by

means of color mapping the density of 1Z head groups at the

water–micelle interface.

At concentrations of surfactants between 40% and 64%, the

formation of elongated rods organized in hexagonal phases,

characterized by a lattice constant, a ¼ 4.1–4.3 nm, and

a hydrocarbon core diameter dc ¼ 2.7–2.8 nm, was observed.

The unbalanced system (0-55-45, 64-0-3, 13-51-36 and

10-48-42) showed a hexagonal phase morphology at lower water

content with respect to balanced ones (22-22-56 and 20-20-60,

1Z-1E-water). In mixed systems, 1E and 1Z segregated in

domains after circa 200 ns, though the domain boundaries were

not well defined.

In Fig. 9 we report the hexagonal phase structure obtained by

the simulation relative to the 13-51-36 mixture. Although the

rods are deformed, the hexagonal pattern can be easily recog-

nized by slicing water density. This is not surprising because it is

well known that the phase transition from hexagonal to cubic

Soft Matter, 2011, 7, 3392–3403 | 3395

Table 1 Results of DPD simulations relative to to mixtures containing equal amounts of 1Z and 1E isomers. The spacing, where appropriate, isindicated by three values: dc, dw and dt, which indicate the thickness of the membrane core, the thickness of the water-polar portion, and the totalthickness respectively. For cubic and hexagonal phases, the cell parameters are listed. All distances are measured in nm with an error of 0.2 nm

Surfactant (%)Composition1Z-1E-water (%) Phase Spacing dc – dw – dt Observationsa

84 42-42-16 Lamellar 1.2 1.3 2.5 Aggregation occurs within 100 ns. After400 ns 1E and 1Z molecules aresegregated in pure domains.

76 38-38-24 Lamellar 1.2 1.3 2.5 Aggregation occurs in �200 ns. After 400ns 1E and 1Z molecules are segregatedin pure domains.

72 36-36-28 Lamellar 1.3 1.3 2.6 Aggregation occurs in �500 ns. After 700ns 1E and 1Z molecules are segregatedin pure domains. Defects on lamellaeare in the form of water filled pores. Theregions with high negative curvatureshow a mixed composition in ratio 1 : 1

66 33-33-34 Lamellar 1.4 1.4 2.8 Aggregation occurs in 1 ms. The lamellaeare rotten by several pores.

62 31-31-38 Lamellar 1.4 1.4 2.8 Aggregation occurs in 800 ns. The lamellaeare rotten by several pores. Simulationrun of 1 ms

58 29-29-42 Sponge phase not applicable Sponge phase. The convergence isextremely low (>1 ms). Within 1.2 ms thegenus remains highly variable.

54 27-27-46 Sponge phase a � 9.4 Formation of a bicontinuous sponge phasewithin circa 0.5 ms. The systems hasa cubic periodicity with latticeparameter of circa 9.4 nm. The meancurvature is close to zero overall thesurface. Simulation run of 1.2 ms.

50 25-25-50 Cubic a ¼ 8.7 Formation of bicontinuous cubic phasewith space group Ia3d within circa 0.5ms. The genus of the reduced unit cell isequal to 3. Simulation run of 1.2 ms.

44 22-22-56 Hexagonal a ¼ 4.2 dc ¼ 2.7 After circa 200 ns the formation ofelongated rods in hexagonal packing isobserved. Simulation run of 600 ns

40 20-20-60 Hexagonal a ¼ 4.1 dc ¼ 2.8 After circa 200 ns the formation ofelongated rods in hexagonal packing isobserved. Simulation run of 600 ns

34 17-17-66 Micellar Isotropic phase. Simulation run of 600 ns28 14-14-72 Micellar Isotropic phase. Simulation run of 600 ns

a The times reported in the table were derived from t ¼ trrcO(m/kBT) where m is the molar mass of the beads, T the temperature, kB the Boltzmannconstant, rc is the radius of the bead and tr is the time in DPD arbitrary units. Since the potentials with DPD are not given by a physical model(unlike molecular dynamics), the relation of natural DPD length and time scales to physical units is not straightforward and the times reportedshould be read simply as a relative indication.31

phases takes place with a continuous distortion of the surfactant

rods into helices which can come in contact and fuse together.21

The systems 48-16-36 and 29-29-42 self-assembled into rods

within 600–800 ns, however these were observed to fuse together

and split apart in the remaining time of simulation. The genus for

the water–surfactant interface was highly variable and an univ-

ocal phase assignment was not always possible (the genus is

a topological invariant; for a closed surface the genus equals to

the number of handles added to a sphere to form the surface).

In five simulations, at concentration of surfactants between

67% and 50% (the systems with composition 1Z-1E-water 27-27-

46, 25-25-50, 11-56-33, 56-11-33, 0-67-33), we observed cubic

phases. The aggregation process occurred in hundreds of nano-

seconds.

Within this range of concentrations, the amount of amphiphile

was not itself sufficient to predict a bicontinuous morphology,

since the same overall amount of 1 could induce the formation of

hexagonal and lamellar phases (see Tables 1 and 2). It is of note

3396 | Soft Matter, 2011, 7, 3392–3403

that systems featuring a balanced composition of 1E and 1Z

showed cubic phases in a wider range of concentration (�50–58%

of surfactant) whereas unbalanced systems showed cubic phases

in a narrow range of concentration (�64–67%). In the balanced

systems (namely 27-27-46, 25-25-50) we observed the formation

of bicontinuous cubic phases at lower amphiphile content.

The same symmetries were observed in unbalanced systems at

surfactant concentration of 67% (11-56-33, 56-11-33, 0-67-33),

with many trivial dislocations.22

For the balanced 25-25-50 system, as well as for the unbal-

anced 56-11-33 and 0-67-33 systems, the morphology was iden-

tified as double gyroid. This cubic morphology consists of a pair

of 3-D continuous and interwoven networks with space group

Ia3d, as shown in Fig. 10 where the Ia3d cubic phase relative to

the 0-67-33 mixture is reported. The lattice constant for the

gyroid phases was a ¼ 8.6–8.7 nm.

The systems 27-27-46 and 11-56-33 appeared severely dis-

torted. Therefore, we performed a Fourier analysis of the

This journal is ª The Royal Society of Chemistry 2011

Table 2 Results of DPD simulations relative to mixtures containing unequal amounts of 1Z and 1E isomers. The spacing, where appropriate, isindicated by three values: dc, dw and dt, which indicate the thickness of the membrane core, the thickness of the water-polar portion, and the totalthickness respectively. For cubic and hexagonal phases, the cell parameters are listed. All distances are measured in nm with an error of 0.2 nm

Surfactant(%)

Composition1Z-1E-water (%) Phase Spacing dc – dw – dt Observationsa

78 0-78-22 Lamellar 1.2 1.2 2.4 Aggregation occurs in 100 ns.78 78-0-22 Lamellar 1.2 1.3 2.5 Aggregation occurs in 100 ns.77 77-0-23 Lamellar 1.2 1.3 2.5 Aggregation occurs in 200 ns.77 62-15-23 Lamellar 1.2 1.3 2.5 Aggregation occurs in �300 ns. After 500 ns 1E and

1Z molecules are segregated in pure domains.77 58-19-23 Lamellar 1.2 1.3 2.5 Aggregation occurs in �300 ns. After 500 ns 1E and

1Z molecules are segregated in pure domains.74 74-0-26 Lamellar 1.2 1.3 2.5 Aggregation occurs in 200 ns.74 59-15-26 Lamellar 1.2 1.3 2.5 Aggregation occurs in �400 ns. After 600 ns 1E and

1Z molecules are segregated in pure domains.74 55-19-26 Lamellar 1.2 1.3 2.5 Aggregation occurs in � 500 ns. After 1.2ms 1E and

1Z isomers segregate in pure domains. From 700ns and 1.2ms several defects in the form of waterfilled pores are present. The regions with highnegative curvature show a mixed composition of1E-1Z in a 1 : 1 ratio.

70 11-59-30 Lamellar 1.2 1.3 2.5 Aggregation occurs in � 500 ns. On the surfaces 1Eand 1Z isomers segregate in pure domains. After 1ms several dislocations are still presents. Theregions with high negative curvature show a mixedcomposition 1E-1Z in a 1 : 1 ratio.

67 67-0-33 Lamellar 1.3 1.4 2.7 Aggregation occurs in�800 ns. Several defects on thewater-surfactant interface are present.

67 11-56-33 Sponge phase a�9.4 Formation of a bicontinuous sponge phase withincirca 0.5 ms. The systems has a cubic periodicitywith lattice parameter of circa 9.4 nm. The meancurvature is close to zero overall the surface.Simulation run of 2 ms.

67 56-11-33 Cubic a ¼ 8.6 Formation of bicontinuous cubic phase with spacegroup Ia3d within circa 0.5 ms. The genus of thereduced unit cell is equal to 3. Simulation run of2 ms.

67 0-67-33 Cubic a ¼ 8.7 Surfactants aggregates into a bicontinuous phaseafter 0.2 ms. The genus of the water/surfactantinterface of the reduced unit cell equal to 3 and thecorresponding space group Ia3d with numeroustrivial dislocations.Within circa 0.8 ms of thesimulation there are no indication of evolution intolamellar phase. Simulation run of 2 ms.

64 48-16-36 Sponge phase not applicable The rods of hexagonal phases are very distorted and,in some cases, fused together. After 1.2 ms themorphologies is intermediate between cubic andhexagonal phases.

64 64-0-36 Hexagonal a ¼ 4.1 dc ¼ 2.8 After circa 100 ns, the formation of elongated rods inhexagonal packing is observed. Simulation run of600 ns.

64 13-51-36 Hexagonal a ¼ 4.3 dc ¼ 2.7 After circa 100 ns, the formation of elongated rods inhexagonal packing is observed. Simulation run of600 ns.

59 10-48-42 Hexagonal a ¼ 4.2 dc ¼ 2.8 The organization in elongated rods takes place in�100 ns. Between 200 ns and 600 ns localsegregation of 1E and 1Z isomers is observed at theaggregate/water interface. Simulation run of600 ns.

55 0-55-45 Hexagonal a ¼ 4.2 dc ¼ 2.8 After circa 200 ns the formation of elongated rods inhexagonal packing is observed. Simulation run of600 ns.

50 50-0-50 Micellar Isotropic phase. Simulation run of 600 ns.50 0-50-50 Micellar Isotropic phase. Simulation run of 600 ns.

a The times reported in the table were derived from t ¼ trrcO(m/kBT) where m is the molar mass of the beads, T the temperature, kB the Boltzmannconstant, rc is the radius of the bead and tr is the time in DPD arbitrary units. Since the potentials with DPD are not given by a physical model(unlike molecular dynamics), the relation of natural DPD length and time scales to physical units is not straightforward and the times reportedshould be read simply as a relative indication.31

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Fig. 8 Elongated micelles observed in the DPD simulation of the 14-14-

72 1Z-1E-water system. The interface water-surfactant is color mapped

with the probability to find 1Z isomers (red – high probability, blue – low

probability).

Fig. 10 The Ia3d symmetry (double gyroid) yielded by the DPD simu-

lation of the 0-67-33 1Z-1E-water system, after 0.8 ms. The TAIL and

TERM beads are plotted in light and dark grey, respectively. The 1E

headgroups are in red; water beads are in blue. Visual inspection is

allowed by the shown interface.

electron densities of the last 10 frames of each simulation23 to

unambiguously assign the correct symmetry; the Fourier

patterns were then reoriented and averaged to highlight the

symmetry elements. Unfortunately only few peaks were detected

and the space group could not be unambiguously assigned. The

sponge like molecular organization of the system is shown on the

top of Fig. 11, whereas on the bottom we plotted the isosurface

that separates the water from the hydrophobic core to highlight

the symmetry and the labyrinth topology. The sponge like phase

appeared to have cubic periodicity with lattice constants

a ¼ 9.4 nm. The surface curvature analysis showed mean

curvature close to zero overall the interface. This is an indication

that the system reach an energy minimum related to a periodic

minimal surface.23

Fig. 9 The hexagonal phase observed in the DPD simulation of the 13-

51-36 1E-1Z-water system is very distorted, however, the hexagonal

pattern is clearly detectable when the sample is sliced and the water

density is shown in red, and with the help of a superimposed hexagonal

pattern. On the top left corner a portion of the DPD dynamics is shown.

The TAIL and TERM beads are plotted in light and dark grey, respec-

tively. The 1E and 1Z headgroups are in red and yellow, respectively;

water beads are in blue.

3398 | Soft Matter, 2011, 7, 3392–3403

In general, we observed that a balanced composition 1Z-1E

permitted the formation of a bicontinuous system at higher

concentration of water with respect to unbalanced systems

(�46–50% versus �33%). This is probably due to the formation

of pairs 1Z-1E that favor the hyperbolic interfaces and, conse-

quently, permit the accommodation of a higher number of water

molecules, as will be discussed in the Molecular dynamics

section.

In some of the simulations relative to concentrations of

surfactants above 62% we observed the formation of lamellar

phases (15 simulations as listed in Table 1 and 2). In the

concentration range 62–74% the lamellae showed several defects,

in the form of pores filled with water. It is worth noticing that in

the range of concentrations (62–67%), we observed lamellar

phases only in the simulations relative to balanced systems,

namely 31-31-38 and 33-33-34 (1Z-1E-water), whereas above

Fig. 11 DPD simulation of the 11-56-33 1Z-1E-water system exhibits

a sponge morphology. The TAIL and TERM beads are plotted in light

and dark grey, respectively. The 1E and 1Z headgroups are in red and

yellow, respectively; water beads are in blue. Visual inspection is allowed

by the interface shown on the bottom.

This journal is ª The Royal Society of Chemistry 2011

Fig. 12 Typical lamellar phase yielded by the DPD simulation of the

62-15-23 1Z-1E-water system. The TAIL and TERM beads are plotted in

light and dark grey, respectively. The 1E and 1Z headgroups are in red

and yellow, respectively; water beads are in blue. On the right the iso-

surfaces that separate the solvent from the bilayers are shown.

Fig. 13 Defective lamellar phase yielded by the DPD simulation of the

55-19-26 1Z-1E-water system. The density of 1E headgroups is color

mapped in red at the water–membrane interface. It is remarkable that the

1E beads, that are less abundant, segregate in the regions characterized by

high curvature.

Table 3 Mixing energies (kcal mol�1), c values and DPD repulsiveparameters

Bead i Bead j c Emix aij

Z Z 0.000 0.000 25.00Z E 7.823 4.632 52.38Z WATER -0.850 -0.503 22.03Z TERM 4.932 2.921 42.26Z TAIL 5.392 3.193 43.87E E 0.000 0.000 25.00E WATER -1.202 -0.712 20.79E TERM 5.107 3.024 42.88E TAIL 5.581 3.305 44.53WATER WATER 0.000 0.000 25.00WATER TERM 13.058 7.732 70.70WATER TAIL 14.606 8.648 76.12TAIL TERM 0.000 0.000 25.00TAIL TAIL 0.963 0.570 28.37

67% we observed a lamellar phase in all simulations, regardless of

their composition. Therefore the range 62–67% appeared critical

to define phase transition boundaries, since different composi-

tions yielded different phases. Reduction of the water content

from 38% to 16% was accompanied also by a reduction of the

self-assembly time which fell from �800 ns–1 ms, observed in the

31-31-38, 33-33-34 and 67-0-33 systems, to 100 ns, observed in

the systems with a content of water lower than 23%.

At the simulated temperature of 25 �C, the bilayer appeared

highly interdigitated, as suggested by the small values of the

spacing of the hydrophobic part (1.2–1.4 nm, Table 1). In fact,

fully elongated 1E and 1Z have a length of �1.66 nm (the small

difference between 1E and 1Z length is not significant). We

observed the same values of spacing, for both the hydrophobic

and the hydrophilic parts, over all the lamellar regime. In ternary

systems, we observed the spontaneous organization in domains

of pure 1E and pure 1Z. This lateral segregation occurred over

times longer than required for self-assembly.

In Fig. 12 we report, as an example, the results of the simu-

lation relative to the 62-15-23 (1Z-1E-water) mixture that shows

a lamellar phase.

In the simulations that yielded defective lamellar phases, we

observed the formation of channels filled with water, as shown in

Fig. 13 where we report the results of the simulation relative to

the 55-19-26 1Z-1E-water mixture. In this simulation the defects,

in the form of pores (channels) filled with water, appeared in the

range of time between 700 ns and 1.2 ms. Further, we observed

the segregation of the 1Z isomer (the isomer in excess) on the

zero curvature surface and the formation of mixed 1Z-1E

domains in a 1 : 1 ratio in the high curvature regions. This is

shown in Fig. 13 where we color-mapped the isosurface sepa-

rating the water region from the hydrophobic region by the 1E

isomer density.

The spontaneous lateral segregation in pure 1E and 1Z domains

is due to DPD repulsive parameters that are higher between 1E

and 1Z isomers compared to those between 1E and 1E, and 1Z

and 1Z (see Experimental and Table 3). Actually, in the lamellar

phases the domains of the pure isomers are stable and we observed

patchworks of pure 1E and 1Z domains in the planar regions of

This journal is ª The Royal Society of Chemistry 2011

the lamellae (those devoid of defects). However, it appeared that

the curvature might play a crucial role in the control of the

composition of the domains. In fact, in correspondence of pores

and/or of hyperbolic water–surfactant interfaces (i.e. negative

Gaussian curvature of the interface) we observed mixtures of

1Z/1E in a 1 : 1 ratio. Therefore a correlation seems evident

between curvature and domain composition. Molecular dynamics

simulations are consistent with this scenario, since for the 36-36-

28 (1Z-1E-water) system (lamellar phase) we have observed the

formation of 1Z-1E dimers with the correct geometry to promote

hyperbolic interfaces, as discussed in the next section.

Molecular dynamics

The DPD investigation was extremely useful for investigating the

overall behavior of 1Z-1E-water systems, but some points

remained unexplained and required further investigation at the

atomic level. In particular, in most lamellar phases we observed

the spontaneous segregation in pure 1E and 1Z domains that was

justified by the DPD repulsive parameters that are higher for the

1Z-1E interaction compared to 1E-1E and 1Z-1Z interactions.

On the other hand, we observed the presence of 1Z-1E mixed

domains (in a �1 : 1 ratio) in the high curvature regions of the

Soft Matter, 2011, 7, 3392–3403 | 3399

Fig. 14 Snapshots of 1Z-1Z, 1E-1Z, and 1E-1E pairs in a molecular

dynamics simulation of the 36-36-28 1Z-1E-water system. Molecular

graphics created with YASARA (www.yasara.org) and PovRay

(www.povray.org).

defects of the lamellar phases formed at higher content of water.

Further, as evident in the phase diagram reported in Fig. 7,

systems with a balanced composition of 1E and 1Z isomers

yielded cubic phases in a wider range of concentrations

compared to unbalanced systems. These evidences suggested to

us that the hypothesis that mixed domains in a�1 : 1 ratio might

stabilize negatively curved interfaces. Therefore we investigated

the possible correlation between the formation of mixed domains

and curvature of the surface by means of a molecular dynamics

simulation of the 36-36-28 1Z-1E-water system.

We found that for dimers 1Z-1E the N–N distance is signifi-

cantly lower (5.0 �A) compared to 1E-1E and 1Z-1Z distances

(5.9 �A and 5.4 �A respectively), as shown in Fig. 14.

The closing of the head groups in the 1Z-1E pairs is accom-

panied by a slight elongation of the chains, and, if the balance of

these two effects were in favor of the first one (closing of head

groups), it could result in an increase of the tendency of mixed

1Z-1E domains to segregate in the hyperbolic regions. This

would explain why balanced systems evolved into cubic phases at

higher content of water and why they assembled in these topo-

logical arrangements in a wider range of concentration.

After coarse grain and atomistic simulations, it is possible to

draw some general considerations.

In a number of simulations, we observed the spontaneous

formation of surfactant domains of defined composition. In all

ternary systems with lamellar morphology, we observed the

formation of pure 1E and 1Z domains in a patchwork mode in

the interface regions of zero curvature. This was an obvious

consequence of the different values in the repulsive aij

parameters.

More interesting, we have observed the presence of mixed

1E-1Z domains in curved systems, preferentially where the

interface is bent with a negative Gaussian curvature. The pres-

ence of lateral segregation of surfactants can also justify the

sponge morphology observed in the systems 27-27-46 and

11-56-33. The transition from lamellar to cubic phase is ener-

getically costly due to the change in topology, and the conse-

quent change in genus.24 From the Gauss–Bonnet theorem, the

cost depends on the Gaussian bending parameters kG: the lower

the parameter, the lower is the energy necessary for the transi-

tion. For unbalanced systems kG is smaller than for balanced

system and the transition from lamellar to cubic phase and from

cubic phase to hexagonal phase result less hindered. Molecular

dynamics simulations for balanced systems show the formation

3400 | Soft Matter, 2011, 7, 3392–3403

of stable dimers that favor the formation of highly curved

surfaces. Systems with small kG can reasonably favor the

uprising of morphologies with 0 Gaussian curvature such as

hexagonal phases.24 It is unclear if the presence of a transient raft

on the surface induces its bending, or if the formation of the

curved interface is capable to attract the proper isomer.

Conclusions

At this point, after having discussed the results of the experi-

mental and theoretical results, we can make some comparison

and draw some conclusions. The coarse grain and atomistic

simulation helped us to clarify many of the results obtained by

NMR and SAXS experiments, though it must be pointed out

that the time scale of simulation are much shorter than time scale

involved in NMR measurements. Further, X-ray analysis

provides information about the long range order of surfactant

systems in equilibrium condition and is averaged over millimetre

sized samples, whereas molecular simulation can only be applied

to samples of limited size. Consequently, defects, thermal fluc-

tuation and kinetic traps might render troublesome the correct

identification of symmetries and topologies.

In the real systems we observed phase transition at the

concentration of 45% of surfactant (from micellar to hexagonal

phases), at 71% (from hexagonal to cubic phases) and at 75%

(from cubic to lamellar phases). In the simulated systems we

observed phase transitions at concentrations lower than the

actual ones with differences between balanced and unbalanced

systems, however the phase diagram relative to the unbalanced

systems is certainly more similar to the actual one obtained by

optical microscopy, SAXS and NMR experiments. This obser-

vation suggests that in the real systems the equilibrium of 1E and

1Z isomers is shifted toward one isomer, probably the Z isomer

as observed previously in micellar aggregates.12

In the actual system we observed the organization in a hexag-

onal symmetry between 45% and 68% of surfactant concentra-

tion, however, on the one hand SAXS experiments gave

evidences of a single phase (characterized by a ¼ 4.1–4.2 nm), on

the other 2H NMR spectra showed two phases. The coarse grain

simulations yielded hexagonal phases (characterized by a ¼4.1–4.3 nm) in the concentration range 40–64% and in some cases

put in evidence the segregation in pure 1E and 1Z domains. The

presence of such domains could give reason of different electric

field gradients experimented by the deuterated water and of

signal broadening or splitting observed in the NMR spectra

reported in Fig. 4a and 4b.

At 68–70% of surfactant concentration, in the real system we

are at the boundary between hexagonal and cubic phase; in the

simulations of unbalanced systems this boundary was found at

64% and corresponded to a sponge phase (not discussed above,

see Table 2) where rods of the hexagonal phase are very distorted

and eventually fuse together. Such an organization would imply

the occurrence of many different local electric field gradients that

interacting with the deuteron quadrupole moments of oriented

deuterated water molecules could yield the spectra given by the

actual systems (Fig. 4c and 4d).

In the range of surfactant concentration, 71–75% the experi-

mental results gave evidence of the occurrence of cubic phases. In

particular the 2H NMR experiments gave evidence of two coexisting

This journal is ª The Royal Society of Chemistry 2011

cubic phases (Fig. 2b). One of them, according to the indexing of

SAXS spectra and to the concentration regime was reasonably

assigned as Ia3d (Fig. 6). In the coarse grain simulations we

observed the formation of two cubic phases (a sponge like and

Ia3d), though never in the same mixture. Yet, the experimental and

theoretical results are not in contrast, because the formation of

gradients of concentrations to yield different local concentrations of

isomers and water can give a reason for the formation of different

cubic phases in the same sample. Because of the different local

concentrations, the occurrence of topological arrangements that do

not correspond strictly to the overall concentration regime could

also be possible. Results of simulations suggest that the two cubic

phases observed by NMR and SAXS do not correspond to segre-

gation of 1E and 1Z in pure domains.

Above 75% surfactant concentration, optical microscopy,

SAXS and NMR experiments gave evidence of the formation of

lamellar phases; in particular SAXS experiments showed a strong

Bragg-peak with d-spacing ranging from 2.8 to 3.1 nm. The

simulations yielded a lamellar phase with a d-spacing ranging

between 2.4 and 2.8 (depending on the concentration regime). In

the coarse grain simulations we observed the formation of pure

1Z and 1E domains in the regions of lamellae devoid of defects,

however it was not possible to detect different d-spacings relative

to the domains. On the other hand, a small difference was found

in the values of d-spacing of water in the simulations relative to

two pure isomeric systems with the same content of water,

namely 0-78-22 and 78-0-22 systems (Table 2), thus suggesting

that the different stereochemistry of 1E and 1Z could be

responsible for a different penetration of water in the isomeric

domains, and therefore of the different d-spacing of intercalated

water. The different d-spacings found in the real system, at

different concentrations of surfactant, could therefore be

explained by a minor interdigitation of the hydrophobic chains

and/or by a shift of the of 1E-1Z equilibrium toward the isomer,

1Z, that allows a minor water penetration.

An additional observation that supports the consistency of the

comparison between experimental and theoretical results

involves the segregation in pure isomeric domains observed in

the simulations relative to micellar aggregates, in agreement with

experimental observations reported previously.12,13

In the theoretical calculation the formation of domains was

therefore observed all over the phase diagram. In particular, as

the consequence of the DPD repulsive parameters we observed

segregation in pure 1Z and 1E domains in micelles, in the

hexagonal phases, and in the lamellar phases devoid of defects.

Interestingly, in the hyperbolic surfaces we observed the forma-

tion of mixed 1E-1Z domains in a well defined 1 : 1 ratio.

Though it was not possible to identify the second cubic phase

observed by NMR experiments and in some of the simulations,

we believe that crossing of experimental and theoretical means

allowed us to shed some light on the molecular interactions that

might control the segregation in domains.

Experimental section

Materials and methods

Sodium N-dodecanoylprolinate, 1, has been prepared and puri-

fied as previously described.12

This journal is ª The Royal Society of Chemistry 2011

Sample preparation. Samples of 1 were prepared by mixing

weighted amounts of surfactant and D2O (44.0–90.0% w/w) in

3 mm diameter glass tubes that were immediately sealed.

Percentages were calculated with respect to light water. Sealed

tubes were heated to 50 �C and centrifuged several times.

Samples were checked several times by 2H NMR and were finally

investigated after ten months from preparation, when no more

phase change was observed in the 2H NMR spectra.

Optical microscopy

Preliminary visual observation of the samples was performed between

crossed Polaroid lens in a home-made polarisation tube, illuminated

from the rear side. The optical textures of the samples were examined

with a Ceti optical microscope, working in white and polarized light.

The microscope is equipped with a hot stage, Linkam, operating

between 10 and 100 �C with an accuracy of�0.5 �C. To get accurate

results, the samples were slightly heated, kindly pressed between the

glass plate and the cover slip, to make the sample thickness uniform,

and allowed to equilibrate at 25 �C for some minutes. More details on

the experimental procedures are reported elsewhere.25

Multinuclear NMR

1H NMR, 2H NMR and 13C NMR spectra were recorded on

a Bruker AC 300 P spectrometer operating at 300.13, 46.1 and

75.5 MHz respectively, equipped with a sample tube thermo-

stated apparatus.

The spectra were performed on 1 samples by inserting the sealed

3 mm diameter glass tube directly in the NMR 5 mm tube. The more

concentratedsamples requestedtheadditionofasmallamountofD2O

in the NMR tube for locking in the case of 1H and 13C NMR spectra.

Small-angle X-ray diffraction

Diffraction patterns were recorded on the Austrian SAXS

beamline at the synchrotron ELETTRA of Trieste.26,27 X-Ray

small- and wide-angle powder diffraction patterns were recorded

simultaneously using two one-dimensional position sensitive

detectors28 to monitor the corresponding s-ranges (s ¼ 2 sin q/l,

where 2q is the scattering angle and l the wavelength of the

X-rays) of interest from about 1/70 nm�1 to 1/1 nm�1 and from

1/0.3 nm�1 to 1/0.9 nm�1, respectively. The angular calibration of

the detectors was determined by using the SAXS-diffraction

patterns of dry rat tail tendon collagen (d-spacing ¼ 65.0 nm)

and silver-behenate (CH3(CH2)20COOAg, d-spacing ¼5.84 nm),29 and the WAXS-diffraction patterns of p-bromo-

benzoic acid as ref. 30. For each X-ray measurement about 40 mL

of sample were transferred into a 1 mm-thick quartz capillary,

which, held in a steel cuvette, provides good thermal contact to

the Peltier heating unit (Anton Paar, Graz, Austria). All scat-

tering patterns were normalized by incident flux and background

was subtracted. The transmission coefficients of the samples and

pure water were measured with a photodiode.

DPD parameterization

The coarse graining of the 1E and 1Z isomers was accomplished

following the original protocol of Groot and Warren.31

Soft Matter, 2011, 7, 3392–3403 | 3401

Fig. 15 Coarse grain representation of N-dodecanoylprolinate in 5

interacting beads of three types: headgroup (1E or 1Z), TAIL, and

TERM. The size of bead is approximately 3 �A in diameter.

The bead volume was set equal to 0.017 nm3, i.e. the volume of

a -CH2-CH2-CH2- portion, (TAIL), that is approximately half

the volume of the prolinate headgroup. The molecule of

N-dodecanoylprolinate was described as composed by 5 beads as

reported in Fig. 15.

In particular, two beads were used for the hydrophilic head

and other three for the hydrophobic tail. Because the prolinate

headgroup occurs in 1Z and 1E form, the corresponding beads

were indicated as Z and E. The tail beads were set in two forms,

the TAIL and the terminal bead, TERM. Therefore the two

isomers have the topologies Z-Z-TAIL-TAIL-TERM and

E-E-TAIL-TAIL-TERM, respectively.

The bead WATER corresponds to a cluster of water molecules

with roughly the same volume of 0.017 nm3.

The bead mass, m, was used as the unit of mass and the

thermal energy, kBT, as the unit of energy. All properties were

expressed in reduced units derived from m and kBT. The calcu-

lation of mixing energies and Flory–Huggins parameter c values

are reported in Table 3.

In the present work, to calculate the mixing energies, we used

the CVFF forcefield,32 that resulted the most adherent to

experimental observations.33 Groot and Warren31 performed

a series of DPD calculations on binary mixtures in which they

found a linear relationship between c and repulsion parameters.

This relationship can be used to obtain input parameters for

a pair of species with a known c value. The relationship between

the Flory–Huggins parameter and the repulsion parameter is:

aij ¼ 25 + 3.50 c (1)

Comparison of the DPD free energy with the Flory–Huggins

equivalent suggests that the two theories correspond, if the c

parameter is proportional to the repulsion parameters, as spec-

ified by eqn (1).

Because most of the parameterization of surfactants were

made in aqueous solutions, we calculated the free energy of

mixing among all the species listed in the Table 3 and water

clusters. The values of c were rescaled to completely adhere to

the original Groot–Warren interaction values. The DPD repul-

sion parameters among the five bead types were calculated

according to eqn (1) and listed in Table 3. For all DPD simula-

tions we have used a time step of 25 ps. The results of the

simulations, in terms of spacing and symmetry, when appro-

priate, are listed in Table 1 and 2. All measurements relative to

3402 | Soft Matter, 2011, 7, 3392–3403

the last 10 frames of dynamics were averaged in space. The time

length varied from 1 to 3 ms and the error in measuring the

spacing is 0.1 nm.

Molecular dynamics

The molecular dynamics calculations were carried out with the

Yasara program34 running on double core Intel processors under

Windows XP program. The simulation box was of 7.07 nm,

5.37 nm, 5.33 nm respectively for the a, b, and c axis under periodic

boundary conditions. The box contained 85 copies of 1E,

85 copies of 1Z in a minimized membrane with random distri-

bution of the two components. The membrane was neutralized

imposing a pH of 8.5, which corresponds to the experimental

value. We calculated the pKa of surfactants,35 and we add 3615

water molecules to reach a solvent density of 0.997 g mL�1.

The simulation of the 1/water system was carried out under the

NPT ensemble at 298 K and 1 atm by coupling the system with

a Berendsen thermostat36 and by controlling the pressure in the

in the manometer pressure control mode.36

The Yasara2 force field were used for 1E and 1Z isomers, and

new force fields parameters were generated using the Autosmiles

method.37 Briefly, the geometry of monomers were optimized by

semi-empirical AM1 method using the COSMO solvation

model.38

Partial atomic charges were calculated using the same level of

theory by the Mulliken point charge approach,39 and were then

improved by applying the ‘AM1 Bond Charge Correction’.

Electrostatic interactions were calculated with a cutoff of

7.86 �A, and the long-range electrostatic interactions were

handled by the particle mesh Ewald (PME)40 algorithm using

a sixth-order B-spline interpolation and a grid spacing of 0.1 nm.

The leap-frog algorithm was used in all simulations with a 1.25 fs

time step for intramolecular forces and 2.5 fs time step for

intermolecular forces. After an equilibration period of 2 ns, we

simulated the system (production period) for 10 ns. The analysis

of the simulation was carried out in the last 5 ns, in particular,

distances among all neighbor nitrogens were divided in 3 groups:

1E-1E, 1E-1Z, and 1Z-1Z and the N–N mean distances were

further averaged in time with steps of 500 ps. The elongation

distances of the alkyl chains of 1E and 1Z were calculated

averaging the distance Ca-Cterminal among all molecules.

Acknowledgements

We thank Dr Giulio Caracciolo for helpful discussion on the

X-ray diffraction data. We acknowledge the financial support

from Dipartimento di Progettazione Molecolare of CNR.

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