Modeling particle scattering structure factor for branched bio-inspired polymers in solution: A small angle X-ray scattering study

Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 2536–2541

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Modeling particle scattering structure factor for branched bio-inspired polymers in solution: A small angle X-ray scattering study Lucio Bonaccorsi a, Pietro Calandra b, Edoardo Proverbio a, Domenico Lombardo b,n a b

Dipartimento di Chimica Industriale e Ingegneria dei Materiali, Universita di Messina, Salita Sperone, 31-98166 S. Agata (Messina), Italy CNR–IPCF, Istituto per i Processi Chimico Fisici-(Sez. Messina) Viale F. Stagno D’Alcontres, 37. I-98158 Messina, Italy

a r t i c l e in f o

abstract

Article history: Received 6 February 2012 Received in revised form 6 June 2012 Accepted 15 June 2012 Available online 21 June 2012

We present a study which illustrates the modeling of the Particle Scattering Structure Factor of an hyperbranched biopolymer in water solution using the Small Angle X-ray Scattering (SAXS) data. The studied sample was a sodium carboxilate terminated poly(amidoamine) dendrimer (generation 2.5) dispersed in water medium. The experimental inter-dendrimer structure factor S(q) has been analyzed in the framework of liquid integral equation theory for charged systems in solution. From that, we derive an effective interparticle interaction composed of a screened Coulombic plus hard-sphere repulsion potential, which allows the estimation of the dendrimer effective charge Zeff. The present analysis strongly supports the finding that structures and interaction of dendrimer are strongly influenced by charge effects. As a result, this quantity can be considered as a crucial parameter for the modulation of the degree of structural organization in solution, suitable for a number of potential applications. We conclude our form factor analysis with the investigation of the long-range assembly conditions during the growth of the intermediate nanoaggregates generated by the inclusion of aluminosilicate components of zeolite 13X on the surface of dendrimers. & 2012 Elsevier Ltd. All rights reserved.

Keywords: X-rays Scattering Structure factor analysis Spectral lineshape modeling

1. Introduction The interaction of electromagnetic radiation with particles represents a fundamental way to approach a variety of spectroscopic techniques [1–6]. When a material is irradiated the scattering intensity patterns are caused by the interference of secondary waves that are emitted from various structures (electrons for X-rays and light, or nuclei for neutrons). The relevant response function of these materials varies strongly with several parameters, such as their size, shape and environmental conditions, thus requiring significant characterization efforts in order

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0022-4073/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2012.06.015

to gain a deeper insight into the physics governing their structural and dynamic behavior [7–13]. Among the electromagnetic scattering techniques, particularly interesting are those exploring the spectral range of the X-rays. When the energy and angle of the inelastically scattered X-rays are monitored, scattering techniques can be used to probe the electronic band structure of materials. On the other hand elastic scattering of monochromatic X-rays probes structural properties of materials in the nanometer to micrometer range by measuring scattering intensity at a given scattering angle. More specifically the Small angle X-ray scattering (SAXS) represents a powerful technique for nanoparticle description in a very broad resolution range (from nanometer to micrometer) which provides unique information on the nanostructure and kinetics at the boundaries of many disciplines in the field of science

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2. Experimental Scattering objects, represented by a polyamidoamine (PAMAM) dendrimers of generation g ¼2.5 (Mw ¼ 6265 g/mol), were purchased from Sigma Aldrich and consists of a tetrafunctional ethylenediamine core [4 NCH2CH2No] and [–CH2CH2(C¼ O)NHCH2CH2No] spacers and is terminated at the final generation with 32 sodium carboxilate terminal groups (COO–Na) in average. The dendrimers were dispersed in deionised water at the temperature of T¼25 1C, while the obtained solutions were filtered with Teflon filters (filter diameter was D¼0.02 mm). The solutions were also checked by dynamic light scattering prior to SAXS measurements to remove the presence of possible aggregates in the system. The Small Angle X-ray Scattering (SAXS) patterns have been recorded by a laboratory instrumentation consisting of a Philips PW X-ray generator (providing Cu K, Ni-filtered ˚ with a KratkyX-ray radiation of wavelength 1.5418 A) type small-angle camera in the ‘‘finite slit height geometry’’ equipped with step scanning motor and scintillator counter as detector. The range of scattering vector covered is 0.07 nm  1 oqo6 nm  1. All measurements were carried out at the temperature of T¼ 25 1C. The scattering data were normalized with respect to transmission and were corrected by the empty cell and solvent contribution. The Scanning Electron Mycroscopy (SEM) experiments were performed using a scanning electron microscope JEOL 5600 LV operated at 10 kV in low-vacuum condition. Samples of the reactant solution were left drying overnight at room temperature and then gathered on specimen stubs and submitted to the analysis.

3. Results and discussion In Fig. 1 the SAXS intensity profile is reported for the sample at the concentration of C ¼10 wt%. The main macroscopic effect in water solution of the presence of chargeable carboxylate (COO  Na þ ) terminal groups of the investigated nanoparticles is the observation of a sharp structure factor peak in the small angle X-ray scattering spectra. This circumstance is a consequence a long range ordering effect throughout the system caused by the electrostatic repulsive interaction that can be ascribed to a partial ionization of the dendrimers terminal groups. Assuming the dendrimer solution as a monodisperse nanoparticles system, the SAXS scattering intensity I(q) can be expressed as a product of the form factor P(q), which contains information on the shape and dimension of the scattering particles and the structure factor S(q) describing the interparticle interaction [15]. IðqÞ ¼ NðDrÞ2 PðqÞSðqÞ

ð1Þ

where N is the number density of the particles, and Dr ¼(r  r0) is the so-called ‘‘contrast’’ (i.e., the difference between the scattering length density of the particle r and that of the solvent r0). In the dilute region the interparticle interaction can be neglected (i.e., S(q)E1), so that the analysis of scattering intensity I(q) can furnish direct information on morphological features of the scattering particles [15,16]. In this case assuming the dedrimer as uniform sphere of radius R, the corresponding form factor can be written as P(q)¼[3J1(qR)/(qR)]2 (where J1(x)¼[sin(x) x cos(x)]/x2 is the first-order spherical Bessel function) [15]. The analysis for the scattering form factor for the sample at the concentration of C¼ 0.5 wt% is reported in Fig. 2 and ˚ We also assumed Gausfurnish a value of R¼17.470.8 A. sian size distribution during data fitting in order to take into proper account possible polydispersity in the dendrimer size. Moreover a dendrimer radius of gyration Rg ¼13.8 A˚ has been obtained from the slope of the representation ln I(q) vs. q2 in the so called Guinier region (i.e. for qRg 51), where the

0.04

0.03 Intensity (a.u.)

and technology [14–16]. On the other hand Small-angle X-ray scattering patterns do not give morphological information directly. The SAXS pattern is essentially given by the intensity of the Fourier transform of the electron density. In this respect a suitable model is necessary to correctly describe and interpreted the morphology of the investigated system [17–20]. In this study we describe the modeling of the scattering particle form factor in a water solution of a Polyamidoamine (Pamam) dendrimer, a highly branched biopolymers of interest in the field of biotechnology and material science [21–27]. The experimental inter-dendrimers structure factor S(q), obtained from the X-ray Scattering data, was analyzed in the framework of the Ornstein–Zernike integral equation, by using the hypernetted chain approximation (HNCA) as closure relation [28,29]. The effective inter-dendrimer interaction, modeled as a screened Coulombic plus hard-sphere repulsion potential, allows the estimation of the dendrimers’ effective charge. The performed analysis strongly supports the findings that the effective intra- and inter-dendrimer charge interactions, as well as the dendrimer solution environment conditions, are crucial parameters for the modulation of the degree of structural organization in solution. We finally describe the X-ray scattering form factor characteristics of the nanoaggregates obtained during the growth process of Zeolite 13X in presence of the polyamidoamine dendrimer template.

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G G G

0.02

≡ -N< ≡ -CH2-CH2-CO-NH-CH2-CH2 ≡ -COO-Na+

0.01

0.0

0.1

0.2 q (Å-1)

0.3

0.4

Fig. 1. Small Angle X-ray Scattering profile of a water solution of sodium carboxilate poliamidoamine dendrimers (generation 2.5) at the concentrations of C¼ 10 wt%. In the inset a schematic representation of soft core nanoparticles employed as scattering objects.

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diameter D. According this model we have investigated the observed inter-dendrimer structure factors S(q), obtained by SAXS experiments, by means of the solution of the Ornstein–Zernike equation, in terms of the hypernetted chain approximation (HNCA) closure relation [35]. More specifically the structure factor for a system of interacting particles can be written as Z 1 sinðqrÞ SðqÞ ¼ 1þ dr ð4Þ 4p2 rC ½gðrÞ1 ðqrÞ 0

Intensity (a. u.)

-2.0

ln I(q) -2.5

0.01 -3.0

-3.5 0.000

0.002

0.01

0.004

0.006

0.1 q (Å-1)

Fig. 2. Analysis of the scattering form factor for the water solution of G2.5 PAMAM dendrimers at the concentration of C¼ 0.5 wt%. In the inset the Guinier analysis of data is reported.

particle form factor can be expressed as P(q)¼P(0)exp 2 ( q2Rg/3) [14], as reported in the inset of Fig. 2. Besides the dendrimer dimension, it is of fundamental importance to obtain details on the inter-dendrimer interaction in their solution environment. This tunable interaction due to the presence of dendrimers chargeable groups promises the possibility of controlling the molecular conformation by varying the conditions of solutions in a manner much like the polyelectrolytes systems [30–34]. In order to obtain information about the interdendrimer interaction potential the charged dendrimers can be approximated as impenetrable spheres of radius R whose charge Ze is distributed on the surface. Those spheres are immersed in the uniform neutralizing background of the solvent molecules which participates with its dielectric constant and which produces also a screening effect in the system. According to this model the repulsive potential between two identical spherical objects (macroions) of diameter s ¼2R placed at a distance r (center to center distance) is given by [27–28] UðrÞ ¼

ekðrsÞ r 4peð1þ ksÞ Z 0 e2

2

This equation provides a way to relate the structure factor S(q) with the radial pair correlation function g(r) (i.e. the probability that two particles stay at distance r in the system), and then, by means of the HNCA scheme, to the interparticle potential U(r) [35,36]. Although the structural properties of dendrimers have been the subject of various experimental and theoretical structural studies, the problem of charge effects in solution still remain an open question [21–24]. For example a Monte Carlo simulation study of dendrimers with flexible spacers [25–27] indicate the backfolding of the terminal groups toward the molecules’ interior. In our case the choice of the an effective interparticle interaction composed of a screened Coulombic plus hard-sphere repulsion potential, represent a useful first approximation that allow us to estimate the dendrimer effective charge Zeff. As we will show later, this charge promote the growth of the zeolite directly on the dendrimer surface, with the formation of a porous barriers of zeolites cavities around the dendrimers. In Fig. 3 the numerical structure factor S(q) computed according the HNCA scheme has been compared with the experimental structure factor obtained from SAXS spectra at the dendrimer concentration of C¼10 wt%. From the figure it is clear how the adopted model reproduces quite satisfactorily the experimental results with the same average dendrimer effective charge of Zeff¼15 e (in units of electron charge 9e9). From the obtained results we can

ð2Þ

where k is the Debye–Huckel inverse screening length which is determined, at a given temperature T, by the ionic strength I of the solvent (in mol/l), according to the following relation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8pe2 N a I k¼ ð3Þ eK B T  103 where e is the unit of electron charge, KB the Botzmann constant, Na the Avogadro number. We also assume an hard sphere type repulsive component for the potential to represent the close contact inter-dendrimer interaction. According to this approach the equilibrium structural properties of a macroion solution are computed by numerical methods starting from the knowledge of some structural parameters, such as the particles concentration (in mol/l), the effective charge in Ze and the particle

1

S(q)

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0 0.0

0.1

q (Å-1)

0.2

0.3

Fig. 3. Comparison between the experimental structure factor S(q) obtained by scattering experiments and one computed by means of the modeling of the interparticle interaction (by using the HNCA closure scheme) for the nanoparticle at the concentration of C¼ 10 wt%.

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deduce that the sodium carboxilate terminal groups of Pamam dendrimers in water solution are ionized and an average number of 15 over the 32 terminal groups per dendrimer realize this ionization. (i.e. a degree of ionization near to 50%). A different result has been obtained in a SAXS investigation in water solution of half integer Pamam generation g¼3.5 containing COO þ –Na  terminal groups [37]. In that case, in fact, analysis coming from SAXS experiments revealed a dendrimer effective charge of Zeff ¼24 e (i.e. a degree of ionization near 40%). We finally describe the X-ray scattering form factor evolution during the growth process of Zeolite 13X in presence of the dendrimers acting as template. The synthesis solution for zeolite 13X crystallization was prepared according an hydrothermal synthesis [38,39] starting form the following formulation (molar composition): 2.7Na2O:1Al2O3:2.8SiO2:90H2O. In order to slow down the relevant self-assembly process the mixture was diluted in water (of about a factor of 10) and then added with a water solution of generation G2.5 PAMAM dendrimers at the concentration of c¼2 wt%. Finally, to obtain direct information of the morphological features of the generated aggregates during nanoparticles formation the small angle x-ray scattering measurements have been performed 20 min after the mixing of the main reactants, at the constant temperature of T¼90 1C. Fig. 4 shows the SAXS intensity profile for the generation 2.5 Pamam dendrimers in water solution at different elapsed times after the mixing. The increase of scattering intensity in the small q region is indicative of a growth process within the system. A log–log plot of the SAXS spectra of Fig. 4 (inset of Fig. 4) evidences the presence of a linear region that can be connected with the fractal nature of the generated supramolecular aggregates. More specifically, the fractal dimension of a particle can be determined analyzing the power-law regime of the scattered intensity I(q)p  a [40], were the exponent a is related to the fractal dimension of the scattering structures. For a mass fractal

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we have a ¼Dm and 1o a o3 in a three-dimensional space, while for surface fractals a ¼6 Ds. By measuring the exponent a it is possible to determine, then, the nature of the structure of scattering particles. The typical curves obtained by the SAXS measurements are presented in Fig. 4 in log–log scale. The slope of log I(q) vs log q curves in the linear region (see inset of Fig. 4) furnished a slope a respectively of 3.28, 3.46, 3.42, for the different elapsed time of 20 min, 60 min, 120 min respectively. This corresponds to a surface fractal dimension of Df ¼2.6 (assuming average slope of 3.4) and furnishes an indirect confirmation of the fractal nature of the surface of the generated aggregates. These results suggest that the long-range electrostatic repulsion of the dendrimer previously detected decreases as zeolite components begin to grow on the charged dendrimer’s surface. This causes dendrimers aggregation with the rapid formation of aggregates whose dimension is bigger than the typical SAXS resolution. The formation of large supramolecular assemblies at the final stage was finally verified by the scanning electron microscopy (SEM) analysis, as shown in Fig. 5. The figure shows the presence of a large aggregate, wich is probably obtained by a secondary aggregation process between dendrimers. Molecular driving force for the aggregation of dendrimers can be traced back to the condensed charge (Na þ cations from the carboxylic dendrimer terminal groups and from the mother liquid of zeolite components) from the diffuse double layer at the surface of the dendrimer. This condensed charge, acting as an effective structuredirecting agent, casted the growth of the zeolite nanoporous structures directly on the dendrimer surface, thus producing a screening of the electrostatic repulsive interaction between dendrimers. The presence of the inorganic porous barriers, composed of zeolites cavities, may be used to promote selective reactions or selective incorporation of key features of specific enzymes, thus stimulating the development of mesoporous particles capable of mimicking the enzyme functions.

10

2

1 Intensity (a.u.)

Intensity (a.u.)

4

α = 3.4

0.1 0.01 1E-3 1E-4

q (Å-1)

0.1

0 0.02

0.04

0.06

q (Å-1) Fig. 4. SAXS intensity profile of G2.5 poliamidoamine dendrimers in presence of the mother liquor for the 13X zeolite synthesis, at different elapsed time after the mixing (20 min squares, 60 min hollow triangles, 120 min circles). The log–log plot of the SAXS intensity profiles is also reported in the inset.

Fig. 5. Image of the generated fractal aggregates during the dendrimer template directed growth of the 13X zeolite by scanning electron microscopy (SEM).

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4. Conclusion We present the modeling of the scattering structure factor in highly branched bio-inspired polymers in solution. The presence of interference peaks in the small angle X-ray scattering spectra of a water solution of generation 2.5 Pamam dendrimers has been ascribed to the longrange intermolecular electrostatic interaction caused by the presence of chargeable moieties in the system. The analysis of the experimental inter-dendrimer structure factor S(q) in the framework of the Ornstein–Zernike integral equation, allows us to adopt a suitable model for the charged dendrimer systems in solution. More specifically, the modeling of the inter-dendrimer interaction potential in terms of a screened coulomb potential allows us to obtain important information about the dendrimer effective charge Zeff (degree of ionization). The obtained results point out the important role of the dendrimer charge in regulating, through the modulation of the electrostatic interaction, main part of their structural properties in solution. Moreover we investigated the long-range assembly conditions during the growth of the intermediate nanoaggregastes generated by the inclusion of aluminosilicate components of zeolite 13X on the surface of dendrimers. Dendrimer charged terminal groups, in fact, acting as an effective structure-directing agent, casted the growth of the zeolite components directly on the dendrimer surface inducing a surface fractal morphology on the generated aggregates. The construction of supra-molecular organic-inorganic nanostructured materials based on porous materials has been drawing increasing attention for its ease of use and high efficiency to create mesoporosity [41–43]. It can be concluded that the development of appropriate models for the description of the main spectral features in scattering experiments results in a suitable interpretation of the molecular conformation as well as furnishing important information about the interaction of (nano-) particles in solution in the field of soft condensed matter. References [1] Volino F. Spectroscopic methods for the study of local dynamics in polyatomic fluids. In: Dupuy J, Dianoux AJ, editors. NATO ASI-series B, 33. New York: Plenum Press; 1978. [2] Lindner P, Zemb T. Neutron, X-rays and light: scattering methods applied to soft condensed matter. Delta S Amsterdam: NorthHolland; 2002. [3] Kahnert FM. Numerical methods in electromagnetic scattering theory. J Quant Spectrosc Radiat Transfer 2003;79–80:775–824. [4] Mishchenko MI, Tishkovets VP, Travis LD, Cairns B, Dlugach JM, Liu L, et al. Electromagnetic scattering by a morphologically complex object: Fundamental concepts and common misconceptions. J Quant Spectrosc Radiat Transfer 2011;112:671–92. [5] Berne BJ, Pecora R. Dynamic light scattering; with application to chemistry, biology and physics. John Wiley and Sons; 1976. [6] Triolo A, Lin JS, Triolo R. Combined SANS and SAXS experiments in polyolefins-hydrogenated oligocyclopentadiene (HOCP) blends. Physica A 1998;249:362–8. [7] Magazu S. NMR, static and dynamic light and neutron scattering investigations on polymeric aqueous solutions. J Mol Struct 2000;523:47–59. [8] Hovenier JW. Lights scattering by non-spherical particles. J Quant Spectrosc Radiat Transf 1996;55:535–694. [9] Chen SH, Mallamace F, Faraone A, Gambadauro P, Lombardo D, Chen WR. Observation of a re-entrant kinetic glass transition in a

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