Estelina Lora Da Silva

Sandra Galmarini
email: sandra.galmarini@empa.ch.

Lionel Maurizi
email: lionelmaurizi@gmail.com

Mario Jorge Cesar
email: mario.cesar.santos@ua.pt.

Tao Santos

David J Yang

Marco Cooke

Molinari

Santos

Tao Yang
email: yangtao@ua.pt

Tema-Nrg

David J Cooke
email: d.j.cooke@hud.ac.uk

Marco Molinari
email: m.molinari@hud.ac.uk

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

b. Adsorption spectroscopy: [START_REF] Rignanese | Dielectric properties of crystalline and amorphous transition metal oxides and silicates as potential high-κ candidates: the contribution of density-functional theory[END_REF] X-ray Absorption Spectroscopy (XASincluding Extended X-Ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES)), ( 2 2. Computational Analysis of Biocompatible Materials. This section will focus on the concept of "interface" with focus on the interactions between the surfaces of materials and the biological environment. We will explain the scientific questions and focus on the computational analytical techniques that can measures these properties at the interfaces. a. Surface properties. [START_REF] Rignanese | Dielectric properties of crystalline and amorphous transition metal oxides and silicates as potential high-κ candidates: the contribution of density-functional theory[END_REF] Segregation of defects, electrical double layer. The development and production of materials with various physico-chemical properties for specific applications, especially for medical and biological purposes, has seen a lightning growing these last decades. Among many promising functionalities, materials can be used to improve, cure or prevent human diseases or weaknesses. For instance, metallic materials are providing functionalities in antimicrobial and therapeutic compounds such as coatings on medical devices or implants.

Synthesized materials can also repair or replace defected body parts. The nanotechnologies, meanwhile, are offering promising applications in diagnoses or specific targeting. However and despite all their potential biomedical applications and their development focusing on biocompatible materials are still in their infancy.

An interplay between experimental and computational techniques is necessary to achieve a full understanding of biochemical analysis. Whereas this chapter aims to cover the Solid State Chemistry within the biochemical remit, highlighting the advantages of such computational analysis, its exploitation within the biological community is still quite limited. We therefore will cover those techniques that are currently at the forefront of the materials science, but still have not seen their full application in biochemistry. This need to be expandedat least another paragraph spelling out what we cover and why (in general terms). Marco to do it.

Computational Spectroscopy. The Interaction between matter and electromagnetic radiation.

This section will focus on some of the most relevant computational methodologies that can be applied to probe the spectroscopic properties of systems for medical and biological applications.

However before discussing such techniques, we have highlighted some relevant systems and their applications in biomedicine. Computational methodologies to study such systems will be discussed within the experimental spectroscopy data in each relevant subsection.

Biomedical Applications and Relevance of Spectroscopy

Zinc Oxide Nanoparticles

Transition metal oxides, with their incomplete valence electron of the d-shells, are responsible for forming intermediate chemical bonding. [START_REF] Rignanese | Dielectric properties of crystalline and amorphous transition metal oxides and silicates as potential high-κ candidates: the contribution of density-functional theory[END_REF] This variety of bonding configurations allows transition metal oxides to explore different crystal structures under specific temperature and pressure conditions; they may exhibit several phases including spin, charge, orbital states, which enhance further the diversity of applications. [START_REF] Godlewski | High-k oxides by atomic layer deposition-Applications in biology and medicine[END_REF] The plethora of applications can be evidenced with a simple example of nanoparticles (NPs) of ZnO, which have been shown to exhibit excellent properties for orthopaedic and dental implants, [START_REF] Memarzadeh | Nanoparticulate zinc oxide as a coating material for orthopedic and dental implants[END_REF] drug delivery, anti-cancer, anti-diabetic, antibacterial, antifungal and biological sensing applications. [START_REF] Zhang | Biomedical Applications of Zinc Oxide Nanomaterials[END_REF] Through electrohydrodynamic atomisation of ZnO NPs as a coating material, bacterial adhesion can be inhibited and osteoblast growth promoted. [START_REF] Memarzadeh | Nanoparticulate zinc oxide as a coating material for orthopedic and dental implants[END_REF] ZnO NPs have also established their capability in biological imaging, due to their high nonlinear optical coefficients; in fact, have been used for in vitro imaging of living cells. [START_REF] Urban | Bioimaging Using the Optimized Nonlinear Optical Properties of ZnO Nanoparticles[END_REF] Moreover, and since ZnO NPs possess large band-gaps (3.37eV) with high exciton binding energies (60meV), promotion of high catalytic efficiency is enabled, which is a desirable character for biosensing. [START_REF] Zhang | Biomedical Applications of Zinc Oxide Nanomaterials[END_REF] Development of novel nano-methodologies to promote alternative approaches for antimicrobial applications has led to the development of multifunctional agents with tailored physiochemical properties (shape, increased surface area and size, combined with their toxic nature towards prokaryotic organisms). [START_REF] Rai | Silver nanoparticles as a new generation of antimicrobials[END_REF] Alternatives to ZnO have been developed as dielectric films or laminar structures fabricated via atomic layer deposited of metal oxides such as HfO2, TiO2, ZrO2, Al2O3.

They have all shown surprisingly efficient antibacterial activity, comparable to the properties of ZnO. [START_REF] Godlewski | High-k oxides by atomic layer deposition-Applications in biology and medicine[END_REF] However, the advantage of low temperature layer deposition (below 100°C) has opened the possibility of coating several types of perishable substrates, including soft tissue paper, cloth, and fabric for surgical masks and wound dressing, surgical instruments, door handles, as well as synthetic and organic materials for medicine, veterinary, health care and food industry supply.

Graphene-like Materials

Carbon nanotechnology is currently at the forefront of biomedical application although generally utilized in conjunction with existing biocompatible systems. Graphene-like systems (i.e. two or more layers of graphene) have proved efficient in terms of biomedical applications. Graphene and its derivatives have excellent mechanical and lubricant properties (decreasing friction), [START_REF] Dong | Realising the potential of graphene-based materials for biosurfaces -A future perspective[END_REF] enhanced capacity for antibacterial properties and biocompatibility. [START_REF] Kumar | Comprehensive Review on the Use of Graphene-Based Substrates for Regenerative Medicine and Biomedical Devices[END_REF] Some applications include medical bone implants, mainly when coated onto ceramic biosurfaces, such as Ti surfaces embedded with SiC, [START_REF] Dong | Realising the potential of graphene-based materials for biosurfaces -A future perspective[END_REF] or Hydroxyapatite (HaP). [START_REF] Li | An overview of graphene-based hydroxyapatite composites for orthopedic applications[END_REF] HaP on its own is a biocompatible bioceramic for hard tissue repair and regeneration, due to its similarities to natural apatite. However, HaP has some drawbacks, including fracture toughness, poor tensile strength and weak wear resistance, hence reinforcement films such as graphene (or derivatives), can be implemented in order to produce biocompatible composites with increased resistance and strength. [START_REF] Li | An overview of graphene-based hydroxyapatite composites for orthopedic applications[END_REF] HaP also demonstrates favourable affinity for bacterial adhesion [START_REF] Shi | Electrophoretic deposition of graphene oxide reinforced chitosan-hydroxyapatite nanocomposite coatings on Ti substrate[END_REF] and therefore graphene-like coatings can provide the biosurface with antibacterial or bacteriostatic protection. [START_REF] Li | An overview of graphene-based hydroxyapatite composites for orthopedic applications[END_REF] Graphene has shown promising inexpensive, reliable, high-throughput sequencing with application in nanopore-based DNA sequencing. [11] [12] The monoatomic thickness of 0.35nm is similar to the DNA base spacing and graphene nanopores can be fabricated with a diameter of only 1.0 nm, which is about the size of a DNA sequence.

Further biological applications for graphene are in neuroscience. Uncoated graphene can be used as neuro-interface electrode without altering or damaging properties such as signal strength or formation of scar tissue. Graphene electrodes in the body are significantly more stable than electrodes of tungsten or silicon because of properties such as flexibility, biocompatibility and conductivity. [START_REF] Fabbro | Graphene-Based Interfaces Do Not Alter Target Nerve Cells[END_REF] When biosurfaces are coated with graphene, it is possible to generate a small electrical impulse through the piezoelectric effect, thus stimulating cellular and bone regeneration. In graphene bilayers, it is the existence of two stacking arrangements of individual layers that allows for the possibility of this electrical impulse generation. [START_REF] Tayran | Structural and electronic properties of AB-and AA-stacking bilayer-graphene intercalated by Li[END_REF] Through the 'sliding' between these layers, transitioning from the AA-phase to the AB-phase (e.g. via the movement of a joint) electrical dipoles are generated. This effect can occur due to tension and/or pressure applied between layers during the phase transition where piezoelectric effects become dominant. [START_REF] Santos | Acousto-electric transport in epitaxial monolayer graphene on SiC[END_REF] Furthermore, the application of strain between two graphene layers enables charge transfer between the layers, [START_REF] Donck | Piezoelectricity in asymmetrically strained bilayer graphene[END_REF] enhancing the intensity of dipolar interaction between the graphene and the biosurface. The variety of distortion in graphene bilayers can involve also small angular distortions, [START_REF] Li | Splitting of Van Hove singularities in slightly twisted bilayer graphene[END_REF] which generates systems known as twisted bilayer graphene. Similar to the sliding of graphene layers, the twisting enables the emergence of piezoelectric effects as the rotation of adjacent layers occurs in order to minimize the tension between the layers themselves.

The underlying idea of generating the piezoelectric effect generated by sliding or rotation of the graphene layers, can also be applied when graphene is adsorbed on biosurfaces, e.g. graphene deposited on a Si/Si SiO2 surface. [START_REF] Da Cunha Rodrigues | Strong piezoelectricity in single-layer graphene deposited on SiO2 grating substrates[END_REF] At the nanoscale, the electric dipole moments (piezoelectric effect) are generated due to the strain induced by the surface corrugations and the difference between the lattice topology of the two materials surfaces. [18] [19] Moreover, the addition of graphene to a host biomaterial has the potential to increase the conductivity if uniformly incorporated, even at low vol% due to its high intrinsic conductivity; unique properties of graphene can be transferred to the host surface for biomechanical applications. [START_REF] Ahmad | Enhanced thermoelectric performance of Bi2Te3 based graphene nanocomposites[END_REF]

Bulk vs Nanoparticle

The importance of the properties that can be exploited for biomedical applications imposes the gathering of a complete characterisation of the nanodevice systems. This should be applied to both bulk and nanostructures, as they possess such different properties from those of bulk materials (e.g. the confinement excitonic effects strongly affects the optical properties), by probing the corresponding structural, electronic, optical, magnetic and dynamical properties. This characterisation includes the study of the most common and abundant impurities and chemical defects found in these systems, i.e. hydrogen impurities and native defects (i.e. vacancies), since these alter the chemical properties of interest. An interesting example is observed for Cerium Oxide (ceria) which can exist in two forms in the bulk state: CeO2 and Ce2O3, due to the transformation of Ce 4+ to Ce 3+ being intermediated by oxygen vacancies. However in the nanostructure form, a mixture of 3+ and 4+ states of Ce exist on the surface of the nanostructure. When the diameter of the nanostructure decreases, the number of 3+ sites increase, as well as the O vacancies, enabling the NPs to absorb and release O due to the redox-cycling between the two charged states. This property ensures that ceria NPs can be used in pharmacological and biological applications. [START_REF] Dhall | Cerium Oxide Nanoparticles: A Brief Review of Their Synthesis Methods and Biomedical Applications[END_REF] A more complete description of these nanosystems and computational techniques to study such systems will be detailed on Section 3.3.

Absorption Spectroscopy for the Evaluation of Opto-Electronical Properties

Adsorption computational spectroscopy can provide insights into the mechanisms underlying the excitation processes at the atomistic level, and providing fundamental understanding to direct the design and optimisation of materials for biomedical applications. This is generally done using abinitio calculations within the framework of density functional theory (DFT). [2] [22] Such level of theory can be applied to both quantities related to the electronic ground-state (time-independent DFT) and to excited states (time-dependant DFT).

Computational spectroscopy allows for the prediction of accurate values of fundamental optoelectronical properties (gap, absorption spectra, excitons) and simulate structural and dynamical properties of materials with interest for biomedical application (nanostructured systems, large unitcells, defects, doping, interfaces). For examples, vibrational spectroscopy such as IR absorption and Raman scattering has served as a fundamental tool for determining the weak interactions between guanine (DNA base adsorption) on ZnO model clusters (g-ZnnOn) and comparison performed between DFT data. Adsorption of guanine with a ZnO cluster has been theoretically probed in terms of geometry, binding energies, electronic and spectral properties, HOMO-LUMO charge distribution and Mulliken charges. Guanine favour physisorption with weak Zn-N bonds tend to form on the active Zn 2+ site. [START_REF] Chandraboss | Experimental and first-principles study of guanine adsorption on ZnO clusters[END_REF]

A Brief Overview of the Theory

Based on first-principles calculations, a system of interacting electrons and nuclei in the presence of time-dependent external fields can be calculated by employing several different methods, depending on their accuracy. The most widely used are Density based methods, such as the Time-Dependent extension of DFT to access neutral excitations, [START_REF] Marques | TIME-DEPENDENT DENSITY FUNCTIONAL THEORY[END_REF] Green's function based methods, the many-body perturbation theory (GW [START_REF] Hedin | New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem[END_REF] and BSE [START_REF] Salpeter | A Relativistic Equation for Bound-State Problems[END_REF]). Time-dependent (TD-)DFT allows the computation of excited state properties, since the respective Kohn-Sham scheme obeys a one-particle Schrödinger time-dependent equation. Within this approach, the absorption spectra is obtained through a linear change of the density produced by a small change in the external potential, which is the linear response theory. However, and similarly to the ground-stated DFT, the time-dependent exchange-correlation (xc) and its first derivative, the exchange-correlation kernel (fxc), encompass all non-trivial many-body effects, which have to be obtained by different approximations [START_REF] Marini | yambo: An ab initio tool for excited state calculations[END_REF]. The most common approximation to the fxc kernel is the adiabatic local-density approximation (ALDA), where it is assumed that at time t, the kernel is equal to the ground-state LDA potential, obtained with the density n(r,t). ALDA fails to describe the absorption spectra of extended systems, especially for wide band-gap semiconductors. ALDA, does not satisfy the divergence of 1/k 2 for small wave-vectors, and instead converges to a constant value. Some successful kernels have currently been implemented (long-range corrected kernel, bootstrap kernel), which account for the correct divergence behaviour, however, these fail to capture excitonic effects. [START_REF] Rigamonti | Estimating Excitonic Effects in the Absorption Spectra of Solids: Problems and Insight from a Guided Iteration Scheme[END_REF] Many-body perturbation theory (MBPT) is a method based on the Green's function method, and provides a more accurate approach to obtaining excited state properties. [START_REF] Marini | yambo: An ab initio tool for excited state calculations[END_REF] The one-particle Green's function, G(r,t;r',t'), can be thought of being the probability amplitude for the propagation of an additional particle from (r',t') to (r,t) in a many-body interacting system, thus taking into account an ensemble consisting of a particle interacting with surrounding opposite chargesquasiparticle (QP). [START_REF] Marini | yambo: An ab initio tool for excited state calculations[END_REF] Quasiparticle energies are calculated within the GW approximation, in which the expansion of the self-energy, Σ, in terms of G and screened Coulomb interaction W, Σ = GW, is truncated after the first term. Since the GW approximation considers the addition and/or removal of an electron (one-particle G) the one-particle excitation spectra can be computed. The experimental observable is related to direct or inverse photoemission, [START_REF] Marini | yambo: An ab initio tool for excited state calculations[END_REF] which provides information regarding the band-gap widths and characters of the valence and conduction band states.

Within MBPT, a method to compute the optical response is through the Bethe-Salpeter equation (BSE). Since the BSE is a process involving two-particle excitations (two-particle G), [26] [28] this method accounts for electron-hole interactions (excitonic effects), therefore prevailing over the noninteracting TD-DFT methodology. Since optical absorption experiment creates this electron-hole interaction (the exciton), good agreement between theory and experiment can be achieved by taking into account the exciton. This effect is mainly important when considering small-gap semiconductors and metals, since these materials screen excitons. [START_REF] Salpeter | A Relativistic Equation for Bound-State Problems[END_REF] However, to obtain such theoretical accuracy, one has to consider that the two-particle nature of the BSE makes the calculations computationally expensive, since a four-point equation (due to the propagation of two particles, starting and end points) has to be solved. [START_REF] Salpeter | A Relativistic Equation for Bound-State Problems[END_REF] The GW method, combined with the solution of the Bethe-Salpeter equation (BSE), is currently the most reliable approach to calculate optical response functions.

Optical Properties of Materials and Dependence on their Dimensionality

The optical properties of macroscopic (bulk) materials emerge from the induced polarisation when the material is subject to an external time-dependent electromagnetic field and macroscopic susceptibilities. By expanding the induced polarisation, the linear term becomes the macroscopic spontaneous polarisation and the non-linear effects come about from the second, third and higher order terms of the expansion. [START_REF] Milne | Enhancement of nonlinear optical properties in late group 15 tetrasubstituted cubanes[END_REF] For extended systems the equations of motion and the coupling of the electrons with the external electric field are derived from the Berry-phase formulation of the dynamical polarisation. [START_REF] Attaccalite | Nonlinear optics from an ab initio approach by means of the dynamical Berry phase: Application to second-and third-harmonic generation in semiconductors[END_REF] It is then possible to calculate the second-and the third-harmonic generation of systems under interest. This formulation is developed upon the Green's function method. However within TD-DFT, it is also possible to evaluate the second harmonic generation (SHG) in semiconductors which also takes into account the crystal local-field and excitonic effects. [START_REF] Luppi | Ab initio second-order nonlinear optics in solids: Secondharmonic generation spectroscopy from time-dependent density-functional theory[END_REF] However, the later method is limited to the treatment of the electron correlation of systems with weakly bound excitons.

TD-DFT has been successfully applied to ZnO clusters to probe respective optical properties (and validated by employing and MBPT). [START_REF] Balasaheb | Study of electronic and optical properties of ZnO clusters using TDDFT method[END_REF] The absorption spectra has shown an enhancement in the intensity with a blueshift of the spectral lines occurring with an increase in the cluster size. The observed optical gap was closely dependent on the size, geometrical shape, symmetry and dimensionality of the structures. From inspection of molecular orbitals and eigenvalues, it was shown that the electronic transitions occur between the non-bonding O p-states and unoccupied Zn sphybrid orbitals.

It is also possible to express the optical properties of finite systems, such as atoms, molecules, or clusters, within the dipole approximation (as the field-induced dipole polarisation [START_REF] Milne | Enhancement of nonlinear optical properties in late group 15 tetrasubstituted cubanes[END_REF]), where the microscopic polarisability is defined by the linear term and the first and second hyperpolarisabilities are the non-linear contributions to the optical properties. [29] [33] At the microscopic level the quadratic dependence on the field means that the magnitude of the quadratic hyperpolarisability tensor must be enhanced in order to produce improved SHG characteristics. This effect is produced when two photons create a single photon of twice the energy of the original two photons. [START_REF] Urban | Bioimaging Using the Optimized Nonlinear Optical Properties of ZnO Nanoparticles[END_REF] Materials displaying non-linear optical (NLO) properties are important not only for optoelectronics applications but also for sensing and bioimaging. ZnO NPs have shown efficient NLO properties which enables efficient applications for in vitro imaging of living cells. [START_REF] Urban | Bioimaging Using the Optimized Nonlinear Optical Properties of ZnO Nanoparticles[END_REF] Moreover, it has been shown that ZnO NPs display pronounced nonlinear doubling effect (SHG). [START_REF] Urban | Bioimaging Using the Optimized Nonlinear Optical Properties of ZnO Nanoparticles[END_REF] Graphene provides a similar functionality for biosensing applications and has been successfully exploited for protein binding sensor platforms. [START_REF] Peña-Bahamonde | Recent advances in graphene-based biosensor technology with applications in life sciences[END_REF] In graphene, a further advantage is the tenability of the nonlinear third-harmonic generation (frequency tripling) using an electric gate voltage. [START_REF] Jiang | Gate-tunable third-order nonlinear optical response of massless Dirac fermions in graphene[END_REF] This technique has particular promise in biomedicine as this provides an alternative avenue for real-time imaging of histopathological quality; examples include the characterisation of tumor tissue via realtime optical biopsies. [START_REF] Kuzmin | Third harmonic generation imaging for fast, label-free pathology of human brain tumors[END_REF] The conventional technique that has been applied successfully to detect brain tumor tissue is stimulated Raman microscopy. However, such a technique is based on subtle differences in the vibrational spectra of the tumor tissue and healthy tissue, thus requiring extensive comparison of experimental spectra against libraries of reference spectra. [START_REF] Kuzmin | Third harmonic generation imaging for fast, label-free pathology of human brain tumors[END_REF]

Inelastic scattering: Lattice Dynamics and Raman Spectroscopy

Carbon nanotechnology have shown great promise in biomedical applications. All from nanotubes to fullerenes passing through graphene have been shown to be promising nanozymes. Here we show the computational application of Raman spectroscopy applied to graphene, which conceptually can be extended to any biochemical system that contains graphene. The application of Raman spectroscopy allows for the identification of monolayer or multi-layered graphenes in the Bernal (AB) configuration. [START_REF] Malard | Raman spectroscopy in graphene[END_REF] As graphene samples are produced in bulk both via exfoliation or epitaxial methods, with both techniques giving a variety of graphene rotational disorder, [START_REF] Malard | Raman spectroscopy in graphene[END_REF] each of these permutations will impact on the biochemical property of the systems. Hence, the characterization of such configurations becomes of paramount importance to control selectively graphene behaviour in biomedical systems.

Within the Harmonic Approximation, lattice dynamics enables the computation of the vibrational modes (phonons) at the zone-centre, which can be directly compared with experimentally derived Raman spectroscopy. Bilayer graphene consists of two coupled monolayers of carbon atoms, each with a honeycomb crystal structure. Although, we focus on biomedical applications, the very basic of this technique resides in the physics at the atomistic scale that describes the vibrational motion of the structure. In order to satisfy the translational and symmetry properties of the Bravais lattice, the honeycomb graphene lattice can be seen as two sublattices, mathematically labelled as inequivalent A and B lattices, each containing two atoms. Since in bilayer graphene there are two lattices (A and B), then there are 4 inequivalent carbon atoms that need a description within the unit cell, this leads to three acoustic (A) and 9 (3N-3) optical (O) lattice vibrations or phonon branches. [START_REF] Tayran | Structural and electronic properties of AB-and AA-stacking bilayer-graphene intercalated by Li[END_REF] Comparison between LDA calculated graphene phonon dispersions with the in-plane phonon dispersion of graphite obtained from inelastic X-ray scattering displays reasonable agreement (Figure 1), although a small shift of the higher-frequency transverse optic (TO) and longitudinal optic (LO) modes is observed. LDA calculations often overestimate the energies of higher-frequency phonons, but despite this difference the characteristic features of the phonon dispersion are well reproduced. At low q-vectors, the in-plane transverse acoustic (TA) and longitudinal acoustic (LA) modes show linear dispersions. While the doubly-degenerate LA mode has zero frequency at the Γpoint, the TA mode, also known as the shear-mode (Figure 2), has a non-zero frequency at the zonecentre (ν=0.82 THz). [START_REF] Popov | Two-phonon Raman bands of bilayer graphene: Revisited[END_REF] The ZA mode is the flexural acoustic mode (Figure 2), which corresponds to out-of-plane, in-phase atomic displacements. In contrast to the TA and LA modes, the ZA branch shows a parabolic dispersion close to the Γ-point, indicating low group velocity and being a characteristic feature of layered structures. [START_REF] Popov | Two-phonon Raman bands of bilayer graphene: Revisited[END_REF] The existence of a flexural mode is also a signature of 2D systems, and in particular it is a mode which is typically found in graphene-like systems. Since the long-wave flexural mode has the lowest frequency, it is the easiest to excite. [START_REF]A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance[END_REF] The flexural mode is relevant for the understanding the intrinsic properties of graphene (i.e. electrical resistivity and thermal expansion coefficient). For example, for monolayer graphene, the high thermal conductivity is due to the vibrational morphology of the flexural mode. [START_REF]A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance[END_REF] When graphene-like systems are adsorbed on biosurfaces, this flexural mode tends to hybridize with the substrate, therefore making it possible to estimate the substrate induced changes of the thermal expansion coefficient and the temperature dependence of the electrical resistivity. [START_REF] Amorim | Flexural mode of graphene on a substrate[END_REF] At slightly higher frequencies, the out-of-plane ZO' mode can be observed (Figure 2), which corresponds to interlayer motion along the z-axis (a layer-breathing mode). The other out-of-plane optic modes are characterised by the doubly degenerate ZO branch. At the Γ-point, the interlayer coupling causes the LO and TO modes to split into two doubly-degenerate branches, both of which correspond to in-plane relative motion of atoms. With the exception of the ZA and ZO' modes, all the frequency branches have symmetry-imposed degeneracy at the zone-center (Figure 1). To correctly describe the dispersion of the LO and the in-plane TO phonon branches near the Γand K-points, it is important to consider the renormalization of the phonon energies, associated with a process in which a phonon can create an electron-hole pair. [START_REF] Malard | Raman spectroscopy in graphene[END_REF] These very consideration will need to be taken into account whether graphene is studied within materials science or in biochemistry. In order to understand the effects of the electron-phonon coupling one should resort to methodologies that go beyond the framework of the Born-Oppenheimer and density-functional approximations. One of the effects of the coupling interaction is the emergence of the Kohn anomaly, [START_REF] Kohn | Image of the Fermi Surface in the Vibration Spectrum of a Metal[END_REF] causing the softening of certain Γand K-point phonons, leading to a discontinuity in its derivative. This effect can be caused by the strong inhomogeneities in the screening of lattice vibrations by the conduction electrons. It is shown that Kohn phonon vibrations cause the Fermi level oscillations and therefore a tunable band gap opening. [START_REF] Milošević | Kohn anomaly in graphene[END_REF] For functionalised graphene (with group-IV elements and different functional groups, such as F, Cl, H3C-, and H2N-) the combination of an out-of-plane symmetrybreaking defect and a soft infrared-active phonon mode induces a large out-of-plane piezoelectric response into functionalized graphene. [START_REF] El-Kelany | Piezoelectricity of Functionalized Graphene: A Quantum-Mechanical Rationalization[END_REF] It is therefore expected that the emergence of the Kohn anomaly on gated-graphene systems, will also affect the piezoelectric impulses, mentioned above, which are induced by the sliding and rotation of the adjacent graphene layers.

Regenerative medicine is currently a field of intensive interest, and thus the study of biodegradable and biocompatible materials with piezoelectric effects, such as graphene-type materials, is important. Not only can piezoelectric biomaterials be applied for bone and cartilage regeneration, [START_REF] More | Piezoelectric material -A promising approach for bone and cartilage regeneration[END_REF] but also these effects have other biological applications, namely for diagnostic ultrasonography, [START_REF] Chapelon | New piezoelectric transducers for therapeutic ultrasound[END_REF] immunological biosensors [START_REF] Ferreira | Acoustic wave biosensors: physical models and biological applications of quartz crystal microbalance[END_REF] and pulmonary drug delivery system. [START_REF] Rodzinski | Targeted and controlled anticancer drug delivery and release with magnetoelectric nanoparticles[END_REF] In fact piezoelectric effects may occur naturally in the tissues, playing a significant role in regulating and stimulating the continuous stress-induced modifications of the tissue (i.e. collagen). [START_REF] Bassett | Generation of Electric Potentials by Bone in Response to Mechanical Stress[END_REF]

Coherent or resonance spectroscopy

A complete characterisation of the biomaterials includes, not only the study between bulk and nanosized structures as mentioned above, but also the study of the most common and abundant impurities and chemical defects found in these systems, i.e. hydrogen impurities and native defects (i.e. vacancies), since these alter the chemical properties of interest. The following sections will therefore highlight two major resonance spectroscopy techniques with interest for biomedical applications, focusing on the analysis of hydrogen impurities and vacancies (small voids) of biomaterials.

One such experimental technique is Muon Spin Spectroscopy (μSR), a well-demonstrated technique to study several fields of sciences, which include atomic-level studies in condensed matter, molecular, chemical, biological, geological and engineering materials. μSR enables direct measurements of intrinsic electron spin relaxation rates in spin based electronics with relevancy for several applications, including biotechnology. [START_REF] Nuccio | Muon spin spectroscopy: magnetism, soft matter and the bridge between the two[END_REF] In biosciences, μSR has been applied for the imaging of human brain to study new brain functions. [START_REF] Nagamine | Muon Application to Advanced Bio-and Nano-Sciences[END_REF] Due to the sensitive nature of the muon as a magnetic probe [START_REF] Dehn | Communication: Chemisorption of muonium on gold nanoparticles: A sensitive new probe of surface magnetism and reactivity[END_REF] and the selective positioning nature of the positive muon (light proton with shot lifetime) at negatively charged sites, muon spectroscopy can detect and identify the magnetism of blood cells, namely hemoglobin (nonmagnetic oxy-hemoglobin and magnetic deoxy-hemoglobin and met-hemoglobin). [START_REF] Nagamine | Muon Application to Advanced Bio-and Nano-Sciences[END_REF] The advantage of using such a technique as compared to magnetic resonance imaging (MRI), or positron-emission tomography (PET), is that μSR can detect the function of the brain more efficiently (deeper probing, smaller volume, and short time-scale measurements) without the need of applying high magnetic fields. Moreover muon spectroscopy can provide new aspects of the oxygenation reactions of hemoglobin since it can detect triplet excited states of oxy-hemoglobin. [START_REF] Nagamine | Muon Application to Advanced Bio-and Nano-Sciences[END_REF] Implanted muons can sometimes bind to an electron to form a light isotope of hydrogen called muonium. By analysing the muonium behaviour inside a material one can learn about proton and hydrogen behaviour, which is important since the chemical and structural properties of the biomaterial will be affected.

Muon Spin Rotation/Relaxation/Resonance Spectroscopy: Hydrogen Impurities

Impurities and/or dopants may appear in materials from initial growth conditions to aging of fully developed devices, [54] [55] affecting the device properties and reliability. Among such defects are impurities, such as hydrogen species that can be unintentionally incorporated during the growth environment. [54] [56] Depending on the respective behaviour, Hydrogen can be amphoteric, where it counteracts the electric conductivity by passivating defective levels or, it can enable a donor level close to the conduction band, thus inducing n-type conductivity. [54] Hydrogen may indeed influence the electrical, magnetic, optical and thermal properties of the host, [54] thus altering the respective properties and hence functionality. In graphene samples a variety of functional groups can be bound to the carbon network, however the most common chemisorbed specie is found to be the atomic Hydrogen. Hydrogen impurities can generate localized spin states causing spin-half paramagnetism. [57] [58] Due to computational simplicity and efficiency, it is still ground-state electronic structure DFT calculations that are mostly applied to obtain several properties and extrapolate to provide insights to experimental spectroscopy data. Examples are studies of defect chemistry of solids to obtain defect formation energies and electronic configurations, which ultimately describe the electrical behaviour. The position of defect levels within the band-gap can also be examined through density of state calculations, which may provide insights if the defect level is located deep in the band-gap (amphoteric) or if it is a shallow defect and therefore being resonant with the conduction states and positioned above the conduction band minimum. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] First-principles studies of Hydrogen in a wide range of oxides have been achieved [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] by employing mostly (semi-)local functionals within Density Functional Theory (DFT). However, it is well known that these functionals provide poor accuracy of the solids band-gaps, and are also inadequate to treat strongly correlated systems, namely d-and f-electron systems, because the incomplete cancellation of the Coulomb self-interaction favours delocalisation. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] Non-local hybrid functionals, have received increased interest providing reasonably good solutions for the band-gap problem. [START_REF] Park | Hybrid functional study on structural and electronic properties of oxides[END_REF] This is owed to the mixing of a fraction of the GGA exchange-energy with the exact Hartree-Fock exchange. These functionals also have the advantage of being able to partially correct the selfinteraction error, providing reasonably good descriptions for the electronic structure of the f-electron systems. Another approach that can correct the severe self-interaction error of the (semi)-local functionals is to introduce a local Hubbard-U potential, characterized by the on-site Coulomb repulsion among the localised electrons. If the Hubbard correction is applied to spin-polarized GGA calculations, good agreement for lattice parameters and band gap can be achieved with a small value of U. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] GW is another alternative to DFT for calculating the electronic properties of materials from firstprinciples, and can improve on the band-gaps of insulators and semiconductors, hence correcting the systematic DFT underestimation. Most computationally affordable GW calculations employ the LDA eigenfunctions, as the starting point, to generate the self-energy (G0W0) from the LDA polarisation (or dielectric constant) one obtains the screened interaction, W0. [START_REF] Salpeter | A Relativistic Equation for Bound-State Problems[END_REF] When employing G0W0 it has been demonstrated that the fundamental band-gaps in sp 3 covalent materials show an improvement over LDA. [START_REF] Hybertsen | Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies[END_REF] In spite of this, the one-shot GW band-gaps are still underestimated, when compared to experimental, even for weakly correlated semiconductors. [START_REF] Van Schilfgaarde | Quasiparticle Self-Consistent $GW$ Theory[END_REF] One-shot GW approaches are rather unsatisfactory, since the QP levels are closely related to the quality of the ground-state wave-functions (DFT exchange-correlation functional).

Quasiparticle self-consistent GW (QSGW) applies a Hamiltonian that is found by optimisation and therefore it is expected that calculations will predict more reliable ground-and excited-states properties for a large number of weakly and moderately correlated materials. [START_REF] Van Schilfgaarde | Quasiparticle Self-Consistent $GW$ Theory[END_REF] Calculations result in reliable quasi-particle (QP) levels for a wide range of materials: not only in the description of the fundamental gaps in semiconductors but also for the majority of the energy levels. Even in strongly correlated d-and f-electron systems, errors are somewhat larger than experimental evidences, but these are still systematic. [START_REF] Van Schilfgaarde | Quasiparticle Self-Consistent $GW$ Theory[END_REF] Despite the increased accuracy of QSGW, this method tends to slightly overestimate semiconductor band-gaps and underestimate dielectric constants. [START_REF] Hybertsen | Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies[END_REF] The reason for this is because W does not include electron-hole correlation; the inclusion of the correlation energy would reduce the pair excitation energy in its intermediate states. [60] [61] Therefore and in order to obtain a more precise position of the defect levels inside the band-gap, care has to be taken to employ the correct functional or methodology. Since a hybrid functional, or even (QS)GW will increase the band-gap width, the position of the defect levels will be more consistent and more reliable to compare to experimental data. Examples concern the case of Y2O3, [START_REF] Cox | Oxide muonics: II. Modelling the electrical activity of hydrogen in wide-gap and highpermittivity dielectrics[END_REF] which is a promising material for biological imaging applications. [63] [64] Calculations have been performed with the hybrid non-local functional (HSE06). Results demonstrated the existence of metastable minimum-energy sites of which amphoteric behaviour was found for Hydrogen after considering the lowest-energy structures for each charge state. For all neutral and negative configurations, localised defect levels were found inside the gap. The calculated acceptor transition level is observed to be near midgap, and is consistent with experimental data. [START_REF] Cox | Oxide muonics: II. Modelling the electrical activity of hydrogen in wide-gap and highpermittivity dielectrics[END_REF] However, for the case of lanthanide oxides, relevant for applications such as magnetic resonance imaging, X-ray computed tomography and fluorescence imaging, [START_REF] Xu | Biomedical Applications of Lanthanide Oxide Nanoparticles[END_REF] the f-states enter into play. It therefore becomes difficult to perform many-body perturbation calculations, or even non-local calculations within DFT. Therefore DFT+U can aid in localising the correlated f-states of the metal, and hence increase the band-gap width to slightly higher values when compared to the performance of (semi-)local functionals. The DFT+U approach is computationally as efficient as conventional DFT, and is well suited for defect studies, which require a large number of atoms, and has also proved reliable in recent studies of defects in f-electron solids. Examples of this approach can be found in studies of Hydrogen impurities on Lu3O3 by employing the effective Hubbard-type potential to treat the onsite 4f-electron correlations [START_REF] Nagamine | Muon Application to Advanced Bio-and Nano-Sciences[END_REF]. By considering the lowest-energy configurations to obtain the charge-transitions, results predict that Hydrogen is an amphoteric impurity in Lu2O3, in accordance to experimental results. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] Several experimental techniques exist that may extend the search for new information regarding the Hydrogen impurities. These include, electron paramagnetic resonance (EPR), where Hydrogen is studied in the paramagnetic state or under non-equilibrium conditions (because interstitial Hydrogen is not stable in the neutral charge state). Such a technique provides insights into redox biochemistry research, due to its ability to distinguish and quantify the hydroxyl radicals and hydrogen atoms. [START_REF] Spasojević | Electron Paramagnetic Resonance -A Powerful Tool of Medical Biochemistry in Discovering Mechanisms of Disease and Treatment Prospects[END_REF] Nuclear magnetic resonance (NMR) is yet another method that can gather information about the bonding configurations of Hydrogen and which is widely applied to biomedical and pharmaceutical research.

In spite of the advantages, the use of microscopic techniques, like EPR or infrared (IR) vibrational spectroscopy, show some drawbacks when gathering microscopic information about Hydrogen configurations and electric defect levels, since these are limited to systems where Hydrogen is usually present in high concentrations.

Moreover, since isolated Hydrogen impurities are very difficult to study experimentally, because they possess high mobilities and thus tend to pair with other defects, [START_REF] Silva | Hydrogen impurity in yttria: Ab initio and $\ensuremath{\mu}$SR perspectives[END_REF] [67] muon spin resonance is a relevant technique to study Hydrogen in biomaterials, [START_REF] Li | Behaviour of hydrogen in wide band gap oxides[END_REF] providing very similar results to EPR. It is an experimental technique performed on muonium, which is an electron bound to a positive muon, being a pseudo-isotope of Hydrogen with similar chemical behaviour. From this spectroscopy technique it is possible to exploit the muon spin rotation, relaxation and resonance. [START_REF] Cox | Oxide muonics: II. Modelling the electrical activity of hydrogen in wide-gap and highpermittivity dielectrics[END_REF] The short lifetime (2.2 μs) of muonium reflects short time-scale measurements under non-equilibrium conditions, thus favouring observation of the isolated defect centers, modeling exactly those centers that are responsible for the electrical activity of Hydrogen. [START_REF] Cox | Oxide muonics: II. Modelling the electrical activity of hydrogen in wide-gap and highpermittivity dielectrics[END_REF] Although the muon is only one ninth the mass of the proton, it is still possible to compare the respective properties to those of Hydrogen in a wide range of materials. These properties include electronic structure, thermal stability and charge-state transitions, [START_REF] Cox | Oxide muonics: II. Modelling the electrical activity of hydrogen in wide-gap and highpermittivity dielectrics[END_REF] often in a parallel approach with ab-initio studies.

Muonium spectroscopy has yet another advantage since this technique can provide detailed information about the electronic structure of muonium/Hydrogen through the hyperfine interaction (refers to small shifts and splittings in the energy levels due to the interaction between nuclei spins and electron density). [START_REF] Szász | Hyperfine coupling of point defects in semiconductors by hybrid density functional calculations: The role of core spin polarization[END_REF] Such information is difficult to obtain for isolated Hydrogen from any other technique. The calculations of the hyperfine tensors proved useful information in characterising the neutral impurity centers, thus allowing a direct comparison with the experimentally obtained hyperfine constants measured by μSR. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] It is important to be aware that when providing ab-initio results for comparison of the hyperfine tensors at the atomic sites, one needs to be aware of the exchange-correlation functional employed to compute the hyperfine tensor. It is well known that a pure PBE approach tends to delocalise the spin density of defect centers. [START_REF] Szász | Hyperfine coupling of point defects in semiconductors by hybrid density functional calculations: The role of core spin polarization[END_REF] Hybrid functionals provide reasonably good results in comparison to the experimental data, since the defect centers will result in more localised centers. For the case of the studies performed on Lu2O3, calculations of hyperfine constants for the neutral interstitial configurations show a isotropic hyperfine interaction with two distinct values of 926 MHz and 1061 MHz for the Fermi-contact term which correspond to two interstitial positions of hydrogen in the lattice. These high values are consistent with the muonium spectroscopy measurements, which also reveal a strongly isotropic hyperfine signature for the neutral muonium fraction with a slightly larger magnitude of 1130 MHz. [START_REF] Da Silva | Electronic structure of interstitial hydrogen in lutetium oxide from $\text{DFT}+U$ calculations and comparison study with $\ensuremath{\mu}\mathrm{SR}$ spectroscopy[END_REF] From a theoretical point-of-view, through DFT calculations, the higher energy configurations (metastable states) that may exist for the different Hydrogen charges, should be considered in order to compare with μSR. This will allow defining the charge transition levels for each structural configuration that Hydrogen can adopt in a system. This procedure is more realistic when comparing to non-equilibrium muonium measurements since, and due to the short life-time of muonium (~2.2 μs), it is not possible to obtain full equilibrium measurements. Instead higher energy metastable states can also be accessed together with their acceptor and donor levels individually.

The material thermodynamics depends on the formation energies of different types of defects and therefore the stable charge states and their transitions can be determined from this quantity. [START_REF] Risto | Issues in first-principles calculations for defects in semiconductors and oxides[END_REF] For the case of the Hydrogen impurity, the formation energies are hence evaluated to obtain the properties of interstitial Hydrogen in the host material and this is defined as being the energy required to incorporate the impurity in three charge states (H -, H 0 , H + ) in the host lattice. [67] [69] Having determined an adequate number of minimum-energy Hydrogen configurations it is also important to identify representative pathways for the impurity migration that connect initial and final ionic configurations. This type of study can be carried out by employing the nudge-elastic band (NEB)

method. [START_REF] Jónsson | Nudged elastic band method for finding minimum energy paths of transitions[END_REF] From this method it is possible to compare the proton/muon sites and the activation energies between equivalent sites. [START_REF] Marinopoulos | Protons in cubic yttria-stabilized zirconia: Binding sites and migration pathways[END_REF] Polarised muons have proved to be reliable and sensitive probes of local magnetic fields in matter and an important tool for the investigation of Hydrogen reactions in low electron density materials (i.e. graphene). In defective graphene, muon spectroscopy aids in answering two debated questions:

the possible onset of magnetism and the interaction with Hydrogen.

It is possible to observe clear muon spin precession in graphene samples, contrary to the behavior of graphite, and this has been demonstrated to originate from a localised muon-Hydrogen nuclear dipolar interactions, rather than to a hyperfine interaction with magnetic electrons, and reveals the formation of an extremely stable CHMu states (analogous to CH2). These results rule out the formation of magnetism in chemically synthesized graphene samples. Moreover, in μSR spectroscopy electronic states of edges and defect sites have revealed radically different signals with respect to the standard case of graphite, or even of the pristine graphene plane. [START_REF] Riccò | Muons Probe Strong Hydrogen Interactions with Defective Graphene[END_REF]

Positron Lifetime Spectroscopy: Vacancies

Vacancies are an example of one of the most common defects found in graphene and can be induced by proton irradiation. [START_REF] Riccò | Muons Probe Strong Hydrogen Interactions with Defective Graphene[END_REF] When a C atom is removed from the lattice, breaking of the symmetry of the system induces a band-gap and the three σ-dangling sp 2 bonds introduce localised states in the mid-gap, which split due to the crystal field effects and a Jahn-Teller distortion. [START_REF] Nanda | Electronic structure of the substitutional vacancy in graphene: density-functional and Green's function studies[END_REF] While two of the electrons bind to each other to form a pentagonal ring, the third dangling bond becomes a paramagnetic center. One impurity may induce magnetisation in the graphene lattice due to formation of spin-polarised localised states. However, the presence of several vacancies may affect the magnetisation of the system due to correlation of the impurity position. Also, since the presence of only one vacancy allows symmetry breaking of the lattice (inducing a band-gap), two identical vacancies, located at the same sub-lattice, will increase asymmetry, therefore increasing the gap width. Therefore breaking of the symmetry may define the magnetic properties of the lattice, allowing for the defects to interact with each other as being ferromagnetic or antiferromagnetic, depending on the extension of the asymmetry. The Fermi level of graphene is quite sensitive to perturbation, and alterations may occur due to the mismatch and subsequent strain at surfaces or interfaces or due to impurities at the interface of graphene. [START_REF] Nanda | Electronic structure of the substitutional vacancy in graphene: density-functional and Green's function studies[END_REF] not sure which interface one refers to-spell it out.

It is therefore important to investigate the defects or chemical impurities at the interface of the multilayer or single layer graphene with biosurfaces. The choice of the substrate on which graphene is deposited plays an important role in the electronic, magnetic and chemical properties of the film.

It is relevant to employ a non-destructive probe, which can investigate graphene over layers on various substrates without extensive sample preparation or probe modification of its chemical or physical properties.

A well-developed non-destructive experimental technique suited in probing point defects, mainly vacancy-type defects, is positron annihilation spectroscopy. By measuring positron lifetimes and momentum distributions during the annihilation process, it is possible to obtain information on the electronic structure in solids, mainly the open volumes and the chemical environments of the defects, i.e vacancy-type defects. [START_REF] Makkonen | First-principles calculation of positron states and annihilation at defects in semiconductors[END_REF] The bound state of a positron and an electron is analogous to a Hydrogen atom, where the proton is replaced by the positron. The annihilation radiation contains information on the electron momentum distribution at the annihilation site due to conservation of momentum during the annihilation process. Though there is the tendency for the electron and positron to annihilate when close to each other, under certain conditions these can form a bound state before annihilation occurs. If the thermalised positron is in the vicinity of an electron, the two charged particles will be attracted by their electrostatic charges instead of being annihilated, hence forming a positronium. [START_REF] Akmalova | Positron Lifetime Spectroscopy of Silicon Nanocontainers for Cancer Theranostic Applications[END_REF] From a computational point of view, it is possible to employ a two-component generalization of the Density Functional Theory (TCDFT), to probe the positron state and annihilation characteristics. The positron-electron correlation-energy functional is usually calculated on the limit of the vanishing positron density. For a delocalised positron the respective density is small at every point of the lattice, not influencing the electronic structure, and hence the electronic structure of the perfect lattice is solved separately from the positron density. When the positron and electron densities are known, then the positron annihilation rate can be calculated. [70] [75] When a positron is localised at a lattice defect, one has to take into account the fact that the positron attracts electrons, and the average electron density increases near the defect. The short-range screening effects have hence to be taken into account by correlation functionals which depend on both the electron and the positron densities. Nevertheless, in most applications for positron states at defects, the full scheme is simplified by using the same procedure as that for delocalised positrons.

This means that the zero-positron-density correlation energy and enhancement factors are used.

The simplified scheme can be well justified by arguing that the positron, and the respective screening cloud, forms a neutral quasiparticle that enters the system without changing the average electron density. On the other hand, the two-component calculations also support the use of a conventional schemes within the LDA or GGA approximations. [START_REF] Puska | Theory of positrons in solids and on solid surfaces[END_REF] In order to investigate two dimensional materials like graphene, it is essentially important to trap the positrons on the surface state. If positrons are implanted at energies less than 10 eV then it is possible to obtain the relevant information from the top atomic layers of the nanoscaled sample as there is greater probability for trapping the positrons into the surface state. [START_REF] Chirayath | Investigation of graphene using low energy positron annihilation induced Doppler broadening spectroscopy[END_REF] Recently, measurements using a low energy positron beam have been reported and applied for the study of multilayer graphene adsorbed on a polycrystalline Cu sample. [START_REF] Chirayath | Investigation of graphene using low energy positron annihilation induced Doppler broadening spectroscopy[END_REF] The efficient trapping of positrons on the surface state of graphene at kinetic energies as low as 2 eV has been used to obtain the respective Doppler broadened spectra. This is the first ever measurement of graphene thin-films

(2-3 nm of thickness) adsorbed on a substrate with a depth resolved Doppler broadening spectroscopy at positron kinetic energies below 10 eV, to have been reported so far. These findings open the possibility of employing positron beam spectroscopy to characterise defects and chemical structure in nanometre 2D materials.

Computational Techniques for Biocompatible Materials

Biological reactions are mainly induced by interactions between the surrounding environment and the surfaces of the materials. Thus, the key parameter to focus on in order to reduce or at least control the influence of a material at the bio-interface is its surface. Biological reactions are not always well understood and this chapter will describe how computational analysis can provide excellent tools to explain the interactions of materials surfaces with biological media. We will explain the scientific questions and focus on the computational analytical techniques that can measure these properties at the interfaces. In a first part, we will discuss which properties of the surface are crucial.

We will discuss the importance of the chemistry or the roughness biocompatible materials and present the computational techniques that can be used to investigate these surface characteristics.

The biological behavior of surfaces is controlled in a large part by interactions between a specific surface (with specific properties as will be discussed in the first part of the chapter) and different (bio-)molecules present in the surrounding media. This will be the subject of the second part, where techniques able to study and predict surface interactions with bio-molecules such as polymers or proteins will be presented. The last part will finally discuss the importance of size in the case of nanoparticles bio-interactions, which has a large influence on colloidal stability, the formation of the so-called corona of proteins or other molecules or on the formation of micelles.

An Overview of Surface Properties

As generally most interactions between biocompatible materials and any biological system happen at the surface of the material, the surface properties are of paramount importance. From an experimental point of view, despite accurate control of synthesis processes, understanding the phenomena at the interface is often neglected leading to biased observations and conclusions. The types, number and arrangement of chemical groups at the surface will determine what species adsorb [77] [78] [79] [80] [81] and what surface reactions can take place. [82] [83] In this section, we will discuss therefore how computational solid state techniques can help define those properties of the surfaces likely to be exploited in biomedicine. We will discuss the equilibrium properties of pure materials and how to study them using different computational techniques. Then we will focus on the influence of defects, the environment and non-equilibrium structural features, such as growth features.

Amorphous Solids

Surfaces cost energy. The lowest energy (equilibrium) arrangement of the atoms is disturbed, leading to a higher energy of the atoms/molecules at the surface. The energy contribution of the surface is more important for small structures than for large, due to the different scaling of the surface (d 2 ) and the volume (d 3 ) with the typical dimension d. Therefore the shape of small (typically submicrometric) structures are often dominated by the minimization of the surface energy. For amorphous solids, where the surface energy is independent of the orientation of the surface, this typically means a spherical shape, optimizing the surface to volume ratio. For larger structures of amorphous solids, where the contribution of the surface energy becomes minimal, the chemical groups present at the surface are those that will minimize surface energy.

Ionic and Covalent Crystals

For the crystalline phases the energy of an interface depends on the orientation with respect to the crystalline lattice. The reason for this is that the orientation of the interface will determine the nature of "bonds" present in the original crystal structure that will be broken in forming the surface. The dependence of the interfacial energy on the interface orientation with respect to the crystal lattice means that the shape, minimizing the total interfacial energy of a finite sized crystal, is no longer a sphere. Wulff developed a general method to predict the equilibrium morphology of a finite sized crystal based on the interfacial energy per unit area 𝛾(𝜙, 𝜃) as a function of the orientation. [START_REF] Wulff | Zur Frage der Geschwindigkeit des Wachstums und der auflösung der Krystallflächen[END_REF] fact Wulff showed that, in order to minimize the overall interfacial energy, the distance of an interface from the center of mass should be proportional to 𝛾(𝜙, 𝜃) (Figure 1). The Wulff construction demands knowledge of the interfacial energy with respect to the interface orientation. However 𝛾(𝜙, 𝜃) is not easily accessible with experimental methods. [START_REF] Xu | Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies[END_REF]. These are generic images, what about changing them slightly so that there is no need of citation and no probs with copyright.

In the case of ionic crystals, the low energy interfaces are usually parallel to a crystal plane (h k l), where h, k and l are the Miller indices of the plane indicating its orientation of the plane with respect to the crystal lattice (Figure 1b). For a crystalline plane, h, k and l are inversely proportional to the intercept of the plane with the vectors of the crystal lattice and for most lattices are equivalent to the indices of the surface normal. The continuous function 𝛾(𝜙, 𝜃) can thus be reduced to a certain number of surface energies of different crystallographic planes (h k l). Atomistic simulation techniques can be used to determine the enthalpic contribution to the surface energy of different atomistic planes, taking into account the relaxation of the position of the atoms at the surface. This can be done either using DFT [85] [86] [87] or classical atomistic force fields (potentials). [88] [89] The energy of a surface is calculated by comparing the energy of the relaxed surface to that of the bulk crystal structure. Usually crystals are represented by periodic boundary conditions, or in other words by a small part of the crystal that is thought to repeat in all three dimensions to build up a much larger bulk structure. However in direction of the surface normal, the periodicity of the crystal is disrupted and periodic boundary conditions can no longer be applied in this direction. There are two main methods to deal with this 1D lack of periodicity. ( 1) If an energy minimization or structural relaxation technique is used to find the lowest enthalpy structure, the bulk structure is often represented by a region with pre-relaxed, fixed atomic positions adjacent to the surface layer which is allowed to relax. [START_REF] Tasker | SURFACE TENSIONS AND SURFACE-STRUCTURE OF THE ALKALI-HALIDE CRYSTALS[END_REF] (2) If molecular dynamic calculations are performed instead, the surface is often represented by a slab of material, terminated on both sides by a surface. [START_REF] Galmarini | Changes in portlandite morphology with solvent composition: Atomistic simulations and experiment[END_REF] While the surface energy 𝛾(𝜙, 𝜃) depends on the surface directions, there might be different surface terminations to take into account, resulting from the different nature of the broken bonds through the crystal at different depths, which share the same surface normal. To get the correct surface energy, the termination with the lowest energy has to be considered. [START_REF] De Leeuw | Surface Structure and Morphology of Calcium Carbonate Polymorphs Calcite, Aragonite, and Vaterite: An Atomistic Approach[END_REF] Additionally some surfaces might present large surface restructuration (local rearrangement of the atoms close to the surface), something that will have to be considered explicitly. [START_REF] Schardt | Crystallography of the $(3\ifmmode\times\else\texttimes\fi{}3)$ surface reconstruction of $3C\ensuremath{-}\mathrm{SiC}(111),$ $4H\ensuremath{-}\mathrm{SiC}(0001),$ and $6H\ensuremath{-}\mathrm{SiC}(0001)$ surfaces retrieved by low-energy electron diffraction[END_REF]

Metals

So far we only discussed the enthalpic contribution to the surface energy. For ionic crystals this is generally by far the dominant contribution to the surface energy, justifying the estimation of the surface energy directly from energy minimization or molecular dynamics. For metals however the surface free energy is often important. Consequently different methods have been developed to calculate the surface free energies of metals: One being a thermodynamic integration technique [START_REF] Broughton | Molecular dynamics investigation of the crystal-fluid interface. VI. Excess surface free energies of crystal-liquid systems[END_REF] [94] [START_REF] Grochola | Exact" surface free energies of iron surfaces using a modified embedded atom method potential and λ integration[END_REF] and the other based on the characterization of fluctuations at the surface. [96] [97] [98] [99] Again the aim of these techniques is to determine the anisotropy of the surface energy to be able to predict growth, morphology and the surface properties of the final material.

[100]

Influence of the Environment

The environments (melt, solution, gas phase) around the solid both during the formation/synthesis and in the end application also have a significant influence on the surface properties. While the solid is growing, the interactions with the species from e.g. a melt or a solution can change the relative surface energies and consequently the equilibrium shape. [78] [90] The same if the material is surrounded by an aqueous environment. For calcium hydroxide, the stronger interaction of water with the higher energy surfaces compared the low energy basal plane is likely to be the reason why particles precipitated from pure, supersaturated Ca(OH)2 solutions do have the shape of hexagonal platelets that is observed for naturally occurring minerals. [START_REF] Galmarini | Changes in portlandite morphology with solvent composition: Atomistic simulations and experiment[END_REF] As these interactions are generally transient and changing constantly, as well as the fact that liquids in contact with surfaces generally show density variations perpendicular to the surface in the length scale of 0.5-1 nm, [START_REF] Galmarini | Atomistic simulation of the adsorption of calcium and hydroxyl ions onto portlandite surfaces -towards crystal growth mechanisms[END_REF] [101] only simplified systems with the adsorption of few molecules are generally studied with DFT or ab-initio methods, [82] [86] [102] [103] while for the study of the larger scale systems, the preferred method being classical atomistic simulations. [START_REF] Galmarini | Changes in portlandite morphology with solvent composition: Atomistic simulations and experiment[END_REF] [101] If the surface is reacting with species from the environment, on the other hand DFT is more frequently used in these studies, as chemical reactions are more easily described by DFT. For oxides for example, DFT in combination with thermodynamic calculations allow the prediction of the conditions, under which surfaces are likely to be hydrogenated or hydroxylated, [82] [85] [86] or it can be used to estimate the acidity of surface groups.

[104]

Especially for metals, surface reactions, such as oxidation, can lead to the formation of surface layers, which again can be studied using atomistic methods. Defects and species in solution can have a higher or lower affinity to the interface region than to the bulk (Erreur ! Source du renvoi introuvable.a), leading to a concentration gradient within the material normal to the surface. The energetics of this segregation of defects or adsorption of surrounding species can be estimated by atomistic simulations. [78] [81] [106] The easiest is to calculate the adsorption or segregation enthalpy, by comparing the energy of the bulk and the interface positions. However care has to be taken to consider all relevant positions at the interface.

To estimate the free energy difference more advanced methods, such as nudged elastic band, metadynamics or other free energy methods are needed. [80] [81] An additional complexity is the distribution and equilibrium concentration of defects. For the estimation of this, additional methods are needed. In the case of weak surface adsorption from solution, direct molecular dynamics simulation of the system over long enough times allows the estimation of the distribution of the species in solution.

[107] However due to the limited possible size and length scale of the simulations, this approach is limited to systems with weak adsorption and fast dynamics as well as to large concentrations (~>1 mol/L). This is of particular interest for biological interactions as biological fluids interacting with materials are usually highly concentrated. For other systems, either additional thermodynamic calculations [108] or grand canonical (or Metropolis) Monte Carlo calculations [109] are needed. Within this context single surfaces are also often extended to porous media. A special case arises, when the species considered are charged which is the norm in biological media. In this case the adsorption/segregation will lead to a spatial separation of charges normal to the interface.

In the case of solids one generally speaks of a space charge region, in the case of adsorption from a solution of an electrical double layer. For the latter a charge separation can also be caused by surface reactions such as acid/base reactions of surface groups. For both segregation [110] [111] and adsorption [112] [113] the distribution of the charges is often calculated using continuum methods (that is approximating the distribution of discrete charges by a continuous charge distribution), often using the results of atomistic methods However in the case of the electrical double layer, Monte

Carlo methods are also frequently used. [104] [114] [115]

Non-Equilibrium Effects

In the discussion above, we assume that equilibrium properties determine the surface properties.

However, for crystals growing from a solution, the prevalence of a surface is often also controlled to a larger or lesser extent by the speed of growth in the direction of the surface normal. Control of the growth is also one method to control the surface roughness which is an important parameter for cellular attachment and proliferation.

[116] The main method is to grow nanostructures at the surface of the materials to provide specific properties such as anti-biofouling. [117] In order for the crystal to grow, the atoms have to move first from the bulk solution to the interfaces.

Schematically one can imagine different types of surfaces for which the adsorption process can be different: atomically flat surfaces which run parallel to a certain crystal plane, stepped surfaces which only one direction in common with a crystal plane and finally kinked surfaces that have no direction in common with any crystalline plane (Erreur ! Source du renvoi introuvable.b). An atom that adsorbs at a kink site will immediately become part of the crystal and indistinguishable from other surface sites. An atom that adsorbes at a step site still retains a certain mobility in one direction, due to the reduced number of bonds formed with the surface compared with a kink site. In order to definitely become part of the crystal it would have to associate with one or more other atoms, forming a one dimensional nucleus, terminated on both ends by a kink site that can then grow easily.

Alternatively an atom adsorbed at a step site can move along the step until it finds a kink site where it can be integrated into the crystal. An atom adsorbed at a flat surface is even less strongly bound to the surface and even more mobile. It can undergo 2D surface diffusion until it either encounters a step or a kink site or other surface atoms to form a 2D layer nucleus. Generally the relative surface energies also give an indication of the relative growth rates as they are governed by similar properties: a kinked surface will clearly grow faster than a stepped and much faster than an atomically flat surface and at the same time can be expected to have a much higher surface energy.

Similarly solvent or solute species adsorbing at flat, stepped or kinked surfaces preferentially will slow down growth in that direction, due to the competition of the adsorbed species with growth species, and will lower the relative surface energy. However there are a few exceptions where kinetic effects should be considered.

First of all for a growth species to adsorb, it will have to move through the electrical double layer and through the structured water layers [101] [118] and it will have to lose its hydration shell. These processes are often associated with an energetic barrier which can vary from surface to surface.

Such effects can be studied by the same free energy methods that can be used to study the adsorption of other species from solution. [START_REF] Galmarini | Atomistic simulation of the adsorption of calcium and hydroxyl ions onto portlandite surfaces -towards crystal growth mechanisms[END_REF] Additionally the changing diffusion coefficient of species in the structured water layers close to the surface[101] as well as the surface diffusion coefficient[119] can be of importance for growth. Diffusion coefficients can either be estimated form activation energies [120] or from direct molecular dynamics calculations, however especially for the latter great care has to be taken to take into account the correct time scale that allows for large scale diffusion and not to be limited to fast, local movements. [121] [122] Growth in a certain direction can be accelerated by the presence of defects at the surface, namely screw dislocations. A screw dislocation is a line defect where, at a certain line in the crystal, the atomic planes are partially shifted by an interatomic distance parallel to the defect line. If the screw dislocation reaches a surface, step sites will be created over part of the crystal (Erreur ! Source du renvoi introuvable.c). This step can now grow in a spiral fashion without ever reaching the edge of the surface and being annihilated. This means that due to the presence of screw dislocations, a flat surface oriented parallel to an atomic plane can grow continuously without needing to periodically go through a layer nucleation step. This process is well known to influence growth [123] and to be of big importance for the growth of nanoscale structures such as nanorods or nanotubes. [124] [125] The energetics and the atomic structure and even the kinetics (using coarse grained kinetic Monte Carlo) of the growth of these dislocations can be studied using atomistic simulation. [126] [127] Finally growth can also happen by ordered attachment or aggregation of preformed nanocrystalline building blocks, especially if mediated by organic molecules,[128] a process that can also lead to the formation of screw dislocations that will promote further growth [129] and that has already been studied using atomistic simulation.

[130]

Example of Application

After having discussed in detail different ways in which computational solid state methods can and have been used to understand the properties of surfaces relevant for biocompatible systems, let us look at a specific application and how the different techniques were applied for that system. A good example of application of the techniques described above is the study of TiO2 for photocatalytic water treatment. TiO2 is one of the most promising candidates for "Advanced Oxidation Processes (AOPs)", which are based on the generation of highly reactive oxygen species (i.e. H2O2, OH, O2 -, O3) at the surface of particles suspended in the water via photocatalysis. These reactive species then lead to the mineralization of refractory organic compounds, water pathogens and disinfection by-products, without creating any secondary pollution. However, photocatalytic processes will improve the production of reactive oxygen species (ROS) leading to potential environmental toxicity.

[131] It is crucial to have a good understanding of the surface properties to understand, predict and improve the efficiency of the surface reactions in order to decrease their potential undesired side effects with living environment. Thus computational methods, in combination with experimental techniques, have been used extensively to know which surfaces are low-energy and thus present on the particles, [132] [133] how these surfaces are modified by restructuration [134] or surface reactions [START_REF] Arrouvel | Effects of morphology on surface hydroxyl concentration: a DFT comparison of anatase-TiO2 and γ-alumina catalytic supports[END_REF] and defects [135] and finally how the photocatalytic synthesis of reactive oxygen species is happening at the different surfaces. [START_REF] Tilocca | Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of TiO2-anatase[END_REF] [83]

Surface Adsorption and Surface Functionalization

As discussed above, the properties of surfaces are of great paramount importance for biological In addition to this steered or voluntary adsorption, in biological media the interaction between the surface and the media generally leads to the formation of a layer of adsorbed bio-molecules.

Recently it has become clear that, to understand the final behavior of bio-interfaces, the adsorption of proteins onto the surface plays a crucial role, something that is still being studied intensively. [141] [142] [143] [144] Thus whether steered or unsteered, the adsorption of organic molecules is a very important process for biocompatible materials. In this chapter, we will discuss different phenomena that are important for the interaction between surfaces and organic molecules and we will discuss different computational methods that can be used to study them.

Influence of the functional groups of adsorbed molecules

The organic molecules in question possess different functional groups, the molecules (polymers or proteins) can be very large and they are often charged. These three aspects are often studied with different techniques. The interaction of different functional groups with the surface are generally studied for small molecules, peptides or oligomers with either classical atomistic methods [145] [146] [147] or DFT[148] [149], (Figure 3a), although with increasing computational time, the system sizes are also increasing.

Influence of the conformation of adsorbed molecules

To study the conformation of polymers or large proteins adsorbed or grafted to a surface different techniques are used. Closely related to the atomistic methods discussed above are coarse grained methods where instead of taking into account each atom, only positions of and interactions between groups of atoms are described. [152] [153] Additionally the solvent is not always considered explicitly but can be approximated by adapting the interactions between and the dynamics of the coarse grained entities. Approaches to adapt the dynamics of a system taking into account an implicit solvent are Brownian dynamics [154] [155] and Langevin dynamics. [156] [157] [158] The advantage of this approach is not only the fewer number of entities within the system but also the fact that, due to the larger mass and slower dynamics of the coarse grained entities, a larger timestep can be used and thus larger timescales become accessible. Such coarse grained simulations have for instance been used to study end-grafted polymers under shear flow to understand their tribological properties.

Influence of the charges of adsorbed molecules

In theory both the full atomistic and coarse grained methods mentioned above take into account charges on the molecules. However a further complexity arises when looking at charged molecules adsorbing onto a charged surface within an electrolyte solution. In this case the conformation and adsorption of the organic molecules is influenced by the distribution of the charges in the electrolyte and the resulting electrical potential which in turn is influenced by the presence of the molecules.

This phenomenon is most commonly studied using coarse grained Metropolis or Grand Canonical Monte Carlo methods, where the organic molecules are treated as polyelectrolytes [167] [168] or using mean field theory.

An example of field of study is the development of anti-fouling surfaces. The anti-fouling surfaces are specifically designed to avoid unwanted cellular adhesion and proliferation as well as the unspecific adsorption of biomolecules. A common strategy to render a surface non-biofouling is the formation of a hydrophilic or zwitterionic polymer-layer either through adsorption, coating, chemical grafting or the formation of a self-assembled monolayer.

[169] The first theoretical studies into the effectiveness of these layers used mean field theories to study the effect of surface density and polymer length.

The Special Case of Nanoscale Materials

Nanotechnology is a research area which has seen its interest growing for the last twenty years. The possibility to use the singular properties of nanomaterials to solve long standing problems is becoming more and more promising. Nanoparticles (NPs) have become the most important components in nanotechnology. Their size (usually below 100nm) with specific physico-chemical characteristics, opens the way for the development of new solutions for catalysis, food industry, medicine or other applications. [179] [180] [181] The small size of the particles has different effects than those of the bulk solid, as already mentioned above. The physical solid state properties of a nanoscale structure can be different from that of larger structures due to nano-confinement, additionally the surface properties can be different due to the influence of the higher concentration of edges and kinks. Also the specific geometry of the surface (Figure 4) changes both the mechanisms of adsorption of large molecules and, in case of charged particles in the presence of electrolytes, the charge distribution close to the surface. Finally for any application of nanoparticles dispersed in aqueous environment such as most biological media, thus for biomedical applications in particular, the small size and change in adsorption behaviors influence the stability and colloidal interactions of nanoparticles. Thus in this chapter we will discuss the special case of nanoparticles and other nanoscale materials as well as their interaction and will present computational methods that can be used to study them, as well as their current limitations.

Nanoparticles

Many nanostructures exhibit interesting electrical, optical or magnetic properties which are directly linked to their size. These properties are either the effect of the high surface to volume ratio and the ensuing high influence of the surface (e.g. lower melting temperature, different phase diagram etc.)

or due to the intermediate nature between molecule and continuous 3D solid (e.g. band structure, optical properties etc.). For the latter quantum mechanics methods (e.g. DFT) are of most interest; however, the systems cannot be treated using methods used for bulk solid-state materials such as periodic boundaries. On the other hand many of the nanostructures used are too large to be studied The small volume of nanoparticles has a significant effect on the volume available to adsorbed species and thus influences the adsorption notably of macromolecules (Erreur ! Source du renvoi introuvable.). Mean field theories on the adsorption of linear molecules can take this effect into account to some extent.

[161] However for atomistic methods, already the adsorption of larger molecules on flat surfaces is a challenge, as discussed in the previous section. For nanoparticles now the systems to be studies are even larger, as periodic boundary conditions cannot be applied in the same way as for flat surfaces. Consequently in the vast majority of studies on polymer/protein adsorption on nanoparticles, coarse grained methods are applied. [156] [188] [189] [190] [191] In addition most of the time oligomers rather than larger molecules have been studied, [188] [192] [193] or the nanoparticle has been simplified. [189] [190] [194] Other coarse grained studies specifically deal with the adsorption of a single charged polyelectrolyte. [195] [196]

Other nanoscale materials

There are two related fields that do look at similar phenomena as the adsorption of large organic molecules on nanoparticle surfaces. One is the study of polymer nanocomposites, [197] [198] [199] [200] looking at changes in the conformation of polymers in a polymer melt around a nanoparticle.

While this phenomenon is also about the interactions of the polymers with nanoparticles, the difference between these systems and surface adsorption is that the polymer are confined in the polymer melt as well as close to the nanoparticle surface. For the study of polymer nanocomposites, generally coarse grained methods similar to the once mentioned above are used. A second field of study which has many similarities to surface adsorption is the formation of micelles, which, depending on the size, are nanostructures as well. However instead of being confined by a surface, the systems are confined by hydrophilic/hydrophobic forces acting on different parts of the molecules. As there are only the organic molecules to simulate and not both the organic molecules and a nanoparticle, many all-atom (or united atom, treating all but the hydrogen atoms explicitly) simulations of micelles can be found, [201] [202] although coarse grained simulations on larger micelle structures exist as well. [203] [204]

Interactions of Nanoscale Structures

In most applications, nanostructures and particles have a tendency to interact, agglomerate and even coalesce or sinter, thus changing their properties and behavior. This process has been studied by several authors for the case of gaseous phase synthesis where the influence of the surrounding phase on the interaction between particles is negligible and the interaction between small nanoparticles can be simulated in vacuum. [130] [205] Other systems, such as nanoparticles in suspension, are more complicated. Typical biological media for instance are complex electrolytes containing a high concentration of organic molecules. Thus, the interaction between nanoparticles are not only the result of van der Waals and, depending on the material, magnetic forces, mitigated by the surrounding media, but also of electrostatic forces including the electrical double layer and the contribution of any organic molecules adsorbed at the nanoparticle surface. Due to lack of alternatives, the electrical double layer and the electrostatic interaction of nanoparticles in an electrolyte is often described by analytical theories developed for large particles where the surface can be considered to be flat locally. [112] [113] [206] [207] However both mean field calculations [208] [209] and coarse grained Monte Carlo simulations [210] [211] have shown that the ionic distribution around a nanoparticle can differ significantly from that of a flat surface. Nevertheless only two of the studies mentioned above also look at how the changes in the ionic distribution around the nanoparticle effect the interparticle forces [208] and there are still no readily available models that would be generally applicable to describe the electrostatic forces between nanoparticles. The situation is similar in for the effect of adsorbed organic molecules on the interparticle forces. There are some models available,[112] however they have been developed for larger particles and it is unclear how this is applicable to nanoparticles. The coarse grained studies that exist in literature about the interaction of polymer decorated nanoparticles, [156] [212] while very interesting, do not permit a general view of the contribution of adsorbed organic molecules on the interaction of nanoparticles.

Summary and Conclusions

In summary we can say that the interaction between materials and biological systems are mainly controlled by surface properties. Here computational methods can be used to clarify the surface properties of different materials, such as the morphology and the type of species and surface groups present in different environments. Typically biological media are strong electrolyte with large organic molecules, such as proteins, in suspension. The adsorption of proteins and other biomolecules at the surface will largely determine the biological interactions and there understanding is therefore of primordial importance. The adsorption of large molecules is determined by the interactions between the surface and different functional groups of the molecules, confinement and entanglement effects of the large molecules at the surface as well as by electrostatic forces. The computational study of the first two aspect is quite well established, using e.g. atomistic methods for the first and coarse grained for the second. However the interdependence between the electrical double layer and the surface adsorption of large biological molecules is often neglected. To take this into account there are two main methods (1) coarse grained Metropolis or Grand Canonical Monte Carlo methods, where the organic molecules are treated as polyelectrolytes, and (2) mean field theory.

These are the method of choice as, due to the complexity and size of the system to study, atomistic methods are not adapted. Instead a multiscale approach to study different aspects with different computational techniques is the way to get a complete picture. Finally nanoscale systems will often behave differently from bulk systems and thus have to be studied especially.

Conclusions

In summary one can say that, although the field of solid-state computational chemistry of nanoscale biomaterials has a high potential and is rapidly growing, it is still a comparatively young field and a lot of issues still need to be addressed for a better fundamental understanding of these systems.

Marco to sort out

  ) UV/Vis, (3) IR c. Inelastic scattering: (1) Raman Spectroscopy, (2) Electron Energy Loss Spectroscopy (EELS) d. Elastic scattering: X-ray diffraction e. Coherent or resonance spectroscopy: (1) Nuclear Magnetic Resonance (NMR) or Magnetic Resonance Spectroscopy (MRS): observe local magnetic fields around atomic nuclei, (2) Electron Spin Resonance (ESR) or Electron Paramagnetic Resonance (EPR): study materials with unpaired electrons, (3) Muonium spectroscopy (μSR): local environments, (4) Positron Annihilation Spectroscopy: study voids, vacancies, poresby employing two-component DFT (available in ABINIT and a VASP interface MIKKA Doppler)

( 2 )

 2 Restructuration/Hydroxylation etc. (3) Growth/dissolution (surface roughness) b. Surface adsorption and surface functionalization (molecules) (1) Surface functionalization by grafting or voluntary adsorption of molecules. (2) Adsorption of biomolecules in biological media. (3) Nanoparticles: Size, Aggregation/Agglomeration c. Influence of size at the bio-interface (1) Agglomeration / Colloidal forces -Brownian motion, vdW, electrostatic, magnetic. (2) Micelle formation 1 Introduction

Figure 1 .TAFigure 2 .

 12 Figure 1. Phonon dispersion of AB-stacked bilayer graphene computed within the harmonic approximation (solid purple line). The unit cell contains four carbon atoms, leading to three acoustic (A) and nine optical (O) phonon branches. The calculated dispersions are compared to the in-plane phonon dispersion of graphite obtained from inelastic X-ray scattering (red dots). The phonon branches are marked with the labels assigned to the Γ-point phonons. Is there a point in negative numbers in Y?

Figure 1 .

 1 Figure 1. a) Schematic illustration of the Wulff construction in 2D: The interfacial energy curve is shown in blue, the perpendicular lines to the ϴ-direction at the position of γ(ϕ) used for the Wulff construction in black and the resulting equilibrium morphology corresponding to the inner envelope to all perpendicular lines in red. b) Schematic illustration of the cell parameters a ⃗ , b ⃗ , c and α, β, γ. Also shown is the (101) surface with the surface normal (101), where the numbers in parenthesis are the Miller indices indicating the orientation of the plane. Illustrations adapted from[START_REF] Xu | Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies[END_REF]. These

Figure 2 .

 2 Figure 2. Schematic illustration of possible influences on the morphology of solids a), different types of surface sites and surface diffusion b) and defect growth mechanisms c). Adapted from (11).

  systems and are often tailored to selectively control the materials properties. Within this context surface properties are modified by the steered adsorption or grafting of organic molecules providing additional surface functionalities. Typical examples are implants, stents or antibacterial surfaces, which are often specifically functionalized to tailor their biological interactions. For example, surface functionalizations can prevent, on different engineered surfaces (Silica-, Titanium-or polymericbased for example), the proliferation of micro-organisms such as bacteria or fungi.[136] The functionalizations can also change the charges at the surface. The surface functionalization is mainly done by adsorption of small chemical groups providing new charges or new surface groups without completely masking the material surface properties. For example, small molecules containing amino (-NH2) and/or carboxylic (-COOH) groups are often used to charge the surface respectively positively or negatively, or to be able to graft further functional molecules.[139] [140] Another approach consists in adsorbing large molecules such as polymers onto the material surfaces to change their biological interactions or protect the integrity of the bulk material. Polyethyleneglycol (PEG) or Polyvinylalcohol (PVA) are used to protect the surfaces of materials from biofouling to colloidally stabilize particles. In the special case of particles to be injected or added to biological systems, either in vitro or in vivo, the surface properties will determine amongst other things the cellular uptake and their biodistribution.[137] [138]

Figure 3 .

 3 Figure 3. Different aspects of surface adsorption of organic molecules: a) atomistic interactions between surface groups and functional groups of the organic molecule; b) confinement effects due to the restricted space available within an adsorbed layer of molecules; c) entanglement effects partially pinning the different molecules and restricting its free movement; d) interdependence of the adsorption of charged molecules and the ionic distribution within an electrolyte.

[

  154] [157] In addition to molecular dynamics, Monte Carlo approaches are also used frequently to study the conformation of adsorbed polymers.[159] [160] Finally, due to the complexity of polymeric systems, a number of thermodynamics and mean field theories have been developed to describe the adsorption of polymers on surfaces and, at least for linear polymers[155] [161] [162] and some well-defined more complex systems[163] [164] give valuable first insight into the phenomenon governing their conformation and behavior. As an example these theories have been used to explain the mechanisms of thermoresponsive cell culture substrates.[165] [166]

  [170] [171] Further atomistic[172] [173] and DFT calculations[174] showed the importance of the hydration layer on the polymer surface to understand the non-fouling properties, something that is consistent with experimental observations[175] [176] and significantly increased the theoretical understanding of these systems. Subsequent studies looked at the influence of the conformation and arrangement of the molecules in the non-fouling layer.[177] [178]

Figure 4 .

 4 Figure 4. Schematic comparison between volume available to macromolecules adsorbed on a) a planar surface (large particle), b) on a nanorod and c) on a nanoparticle.