Thomas D Bennett

François-Xavier Coudert
email: fx.coudert@chimieparistech.psl.eu

Stuart L James
email: s.james@qub.ac.uk

Andrew I Cooper
email: aicooper@liverpool.ac.uk

The Changing State of Porous Materials

Porous materials contain regions of empty space into which guest molecules can be selectively adsorbed and sometimes chemically transformed. This has made them useful in both industrial and domestic applications, ranging from gas separation, energy storage, and ion exchange to heterogeneous catalysis and green chemistry. Porous materials are often ordered (crystalline) solids. Order-or uniformity-is frequently held to be advantageous, or even pivotal, to our ability to engineer useful properties in a rational way. Here we highlight the growing evidence that topological disorder can be useful in creating alternative properties in porous materials. In particular, we highlight here several concepts for the creation of novel porous liquids, rationalise routes to porous glasses, and provide perspectives on applications for porous liquids and glasses.

Nanoporous materials span a fascinating array of different chemistries, ranging from classical inorganic zeolites to molecular organic and hybrid framework solids. [START_REF] Wright | The Chemistry of Microporous Framework Solids[END_REF] Their microporous and mesoporous architectures find widespread practical use [START_REF] Davis | Ordered porous materials for emerging applications[END_REF] for applications such as environmental remediation, heterogenous catalysis, medicine, and energy generation. [START_REF] Čejka | Zeolites in Catalysis: Properties and Applications[END_REF][START_REF] Furukawa | The Chemistry and Applications of Metal-Organic Frameworks[END_REF] Extensive work on the formation of crystalline inorganic zeolitic frameworks from aluminosilicate gels started in the 1940s; [START_REF] Barrer | Syntheses and Reactions of Mordenite[END_REF] that is, nearly three decades after amorphous porous solids such as activated charcoal were employed by Harrison and Zelinsky in respirators during World War 1, [START_REF] Giannakoudakis | Detoxification of Chemical Warfare Agents: From WWI to Multifunctional Nanocomposite Approaches[END_REF] and twenty years after the patenting of silica xerogel formation. [START_REF] Patrick | Silica gel and process of making same[END_REF] Those early zeolites had pore sizes that were typically below 8 Å, but the work also laid the foundations for the discovery in the 1990's of mesoporous silica solids with pores sizes approaching 100 Å. [START_REF] Yanagisawa | The preparation of alkyltriinethylaininonium-kaneinite complexes and their conversion to microporous materials[END_REF] Examples of the function-led synthesis of amorphous porous materials can also be found in the organic domain. For example, internal void space was created within so-called polymers of intrinsic microporosity (PIMs) by relying upon inefficient packing of rigid, contorted polymer units. [START_REF] Budd | Polymers of intrinsic microporosity (PIMs): robust, solutionprocessable, organic nanoporous materials[END_REF] Subsequently, order was introduced by linking organic units via covalent bonds, which ultimately gave rise to rigid, amorphous porous aromatic frameworks (PAFs) [START_REF] Ben | Targeted Synthesis of a Porous Aromatic Framework with High Stability and Exceptionally High Surface Area[END_REF] and crystalline covalent organic frameworks (COFs). [START_REF] Cote | Porous, crystalline, covalent organic frameworks[END_REF] Likewise, early work on amorphous organometallic polymers influenced the subsequent formation of ordered three-dimensional framework materials based on the self-assembly of inorganic and organic components. [START_REF] Williams | Main-chain organometallic polymers: synthetic strategies, applications, and perspectives[END_REF] More than 70,000 such metal-organic frameworks, or MOFs, have now been reported in the pure crystalline state, with their robust and ordered frameworks allowing some materials to reach specific pore volumes in excess 5.02 cm 3 g -1 . [START_REF] Honicke | Balancing Mechanical Stability and Ultrahigh Porosity in Crystalline Framework Materials[END_REF] As well as extended solids, discrete organic molecules have been fabricated that possess cage structures. These cages can assemble into either crystalline or amorphous materials, which may retain accessible porosity. [START_REF] Cooper | Porous Molecular Solids and Liquids[END_REF] Discrete cages may also take the form of inorganic compounds, such as polyoxometalates, or be formed by coordination bonding between inorganic and organic units.

Metal-organic polyhedra (MOPs), or metal-organic cages (MOCs), for example, are formed from the directed assembly of a range of inorganic and organic 'building blocks'. [START_REF] Ahmad | Metal-organic molecular cages: applications of biochemical implications[END_REF][START_REF] Carne-Sanchez | Self-assembly of metal-organic polyhedra into supramolecular polymers with intrinsic microporosity[END_REF] To date, much of the research effort to realise the potential of porous materials has focused on the rational design of the crystalline solid state. This predilection toward order has prevailed despite the utility of order-disorder transitions in hybrid solids, the potential processing advantages of disordered materials (e.g., soluble PIMs), and the success of design techniques to control porosity in amorphous polymers. [START_REF] Budd | Polymers of intrinsic microporosity (PIMs): robust, solutionprocessable, organic nanoporous materials[END_REF] This stems, in part, from the ease of characterization of crystalline solids at the laboratory scale by X-ray diffraction, which has been key to the explosive development of the chemistry of metal-organic frameworks. [START_REF] Kitagawa | Functional porous coordination polymers[END_REF] It is also manifested in a large number of highthroughput screening studies and the generation of databases of hypothetical periodic frameworks. [START_REF] Colon | High-throughput computational screening of metal-organic frameworks[END_REF] As this field has matured, the presence of defects in these crystalline structures was noted as providing an additional 'handle' to tune their properties, or to introduce extra functionality that is not otherwise present in the parent framework. The controlled introduction and characterization of elements of disorder in crystalline frameworks [START_REF] Simonov | Designing Disorder into Crystalline Materials[END_REF] was shown to be key in controlling the catalytic properties of mixed-metal framework materials. [START_REF] Abednatanzi | Mixed-metal metal-organic frameworks[END_REF] Such work also prompted studies on order-disorder phase transitions, [START_REF] Besara | Mechanism of the order-disorder phase transition, and glassy behavior in the metal-organic framework [(CH3)(2)NH2]Zn(HCOO)(3)[END_REF] and the past few years have seen increased efforts to control the most fundamental of all properties of porous materials-their physical state (Figure 1). The goal is to bridge the huge gap in behaviour between solids and liquids by introducing functional disorder in a controlled manner, while retaining some of the desirable properties of porous frameworks.

The solid state, both crystalline and amorphous, provides advantages over liquids in several respects. For example, in heterogeneous catalytic processes where the separation of catalyst from liquid phase substrate is necessary, and in the use of activated carbon with pressure-swing adsorption processes in the production of H2 from natural gas streams. [START_REF] Sircar | Purification of hydrogen by pressure swing adsorption[END_REF] It is also true that, at present, porous solids incur generally lower energy penalties than liquids in CO2 adsorptiondesorption processes. [START_REF] Darunte | Direct Air Capture of CO2 Using Amine Functionalized MIL-101(Cr)[END_REF] In other settings, however, the lack of fluidity in porous solids means that they cannot be incorporated into continuous flow processes, and the liquid state may then prove more useful. For example, liquid alkylamine or dialkylether liquid technologies are currently employed the removal of acidic gases from waste streams in the upgrading of synthesis or natural gas, and the largescale capture of CO2. [START_REF] Rochelle | Amine Scrubbing for CO2 Capture[END_REF] Such processes could prove to be conceptually easier to upgrade with porous liquid technologies, which might also offer better heat management possibilities, easier handling properties, and improved processability when compared to porous solids.

In this perspective, we focus on recent key advances in the design and introduction of topological disorder into porous materials. A dual and complementary view is emerging: rather than retro engineering topological disorder into existing ordered frameworks, we might instead search to introduce and control porosity new, heavily disordered materials, such as liquids. We discuss in particular the formation of amorphous solid and liquid states, the control over their nano-and microstructures, and efforts to tailor their physical and chemical properties. We extend the existing classification system of porous liquids, [START_REF] O'reilly | Porous liquids[END_REF] and propose strategies to populate the resulting unexplored areas of materials space. We highlight glasses as the intersection between the area of porous solids and liquids, and provide a perspective on this rapidly evolving field.

Porous liquids

The synthesis of porous liquids (PLs) stems from a desire to create materials that possess both porosity and fluidity. Classification of PLs into three categories has remained standard since their conceptualization (Figure 2). Type 1 PLs are defined as discrete, molecular 'host' materials with intrinsic porosity, which are liquid in their neat state. Initial difficulties in engineering large host molecules to form liquids in their neat states were overcome by adding flexible alkyl tails to organic cage hosts, whilst Dai and Mahurin et al have rendered hollow silica nanospheres fluid by grafting polymers onto the exterior surfaces. [START_REF] Zhang | Porous Liquids: A Promising Class of Media for Gas Separation[END_REF] This strategy requires navigation of a delicate balance; increasing alkyl chain lengths lower melting point, yet also allow occupation of the host cavity with the flexible tails, compromising porosity. [START_REF] Melaugh | Designing and understanding permanent microporosity in liquids[END_REF] The use of ionic interactions to imbue liquidity to a porous material has also proven useful. Dai et al. for example synthesized a potassium salt of a negatively charged organic cage host, before adding dicyclohexano-18-crown-6 to complex the potassium ion. [START_REF] Jie | Transforming Porous Organic Cages into Porous Ionic Liquids via a Supramolecular Complexation Strategy[END_REF] The absence of a long alkyl tail in this case meant that the cages remained empty, as indicated by both positron annihilation lifetime spectroscopy (PALS) and their high gas uptake.

Combination of the two strategies is also possible, as demonstrated by Nitschke et al. in the addition of flexible tails with positively charged end groups to a charged metal-organic cage. [START_REF] Ma | Coordination cages as permanently porous ionic liquids[END_REF] Type 2 PLs avoid the difficulties in forming pure liquid phases, by having the hosts dissolved in a solvent rather than existing in their neat state. Requirements here are (i) the host must exhibit a very high solubility to provide a high concentration of empty cavities and (ii) the chosen solvent must be too sterically hindered to fit inside the host. These considerations mean that the creation of Inorganic Type 2 species is difficult, though we suggest that the approaches taken by Akutagawa et al. in solubilizing giant Mo ring species with organic surface groups may be a transferable route forward in this area. [START_REF] Akutagawa | Nanoscale assemblies of gigantic molecular {Mo-154}-rings: (Dimethyldioctadecylammonium)(20)[Mo154O462H8(H2O)(70)[END_REF] Turning to organic liquids, an early example made use of organic cages functionalised on the outside with crown ether groups in order to provide high solubility. Here, 15-crown-5 was employed as a (somewhat unconventional) solvent, given its size and very low surface curvature.

Remarkably, using this approach clear solutions could be obtained that consisted of up to 48 wt% of the host (a cage to solvent mole ratio of only 12). Also, the uptake of methane, an industrially important gas, was found to increase by a factor of 8 due to the presence of the empty cavities. This dramatic increase in gas uptake is consistent with the prediction that the thermodynamic cost of dissolution in conventional liquids is dominated by the energy required to form a notional cavity in which solute molecules can be accommodated. [START_REF] Pierotti | A scaled particle theory of aqueous and nonaqueous solutions[END_REF] In the case of a porous liquid, the thermodynamic work to produce the empty cavities is already done during the synthesis (and/or activation) of the material, so that the solute, in a sense, has less work to do when it is dissolved. This early work in the field thus pointed to the potential of porous liquids to act as 'super-solvents' for gases.

In the aforementioned examples, substituents were grafted onto the outside of the hosts to make them highly soluble. An alternative strategy to increase solubility is to generate a mixture of less symmetrical hosts that differ subtly from each other in having substituents randomly placed at different positions. Effectively, each cage in the scrambled mixture then has a different shape, and this frustrates crystallisation of the material, making it more soluble. For example, a mixture of cage 3 (1,2-cyclohexanediamine vertices) and cage 13 (1,2-diamino-2-methyl-propane vertices), led to the scrambled cage 3 3 :13 [START_REF] Čejka | Zeolites in Catalysis: Properties and Applications[END_REF] as the dominant component in the mixture, in which 3 cyclohexane vertices of each cage were replaced with a propyl group. The products proved to be highly soluble in 2-hydroxyacetophenone and exhibited permanent porosity. Later, similar materials were identified involving more scalable solvents by using a robotic screening technique. [START_REF] Kearsey | Accelerated robotic discovery of type II porous liquids[END_REF] The need for low melting points and/or high solubilities is removed altogether in Type 3 porous liquids, since this these take the form of suspensions rather than neat liquids or solutions. Specifically, particles of porous solids (e.g., silica, zeolites, MOFs etc.) are agitated until they form a suspension in a liquid whose molecules are unable to enter the pores. However, the nature of the solid-liquid interactions and/or the particle size may need to be controlled if a highly stable suspension is to be obtained. For example, Moro et al. have formed suspensions of silica nanoparticles in water, though surface hydrophobization was necessary to prevent the ingress of solvent into the porous cavities. [START_REF] Moro | Hydrophobization of Silica Nanoparticles in Water: Nanostructure and Response to Drying Stress[END_REF] Size excluded dispersions have also been investigated, first by Liu et al., who suspended ZIF-8 in a mixture of liquid glycol and 2-methylimidazole to form a slurry.

Although there was no direct evidence that the ZIF-8 pores remained unoccupied by the solvent, this slurry exhibited unusually high CO2 sorption capacity and selectivity. [START_REF] Liu | A hybrid absorption-adsorption method to efficiently capture carbon[END_REF] It has been noted that the gas uptakes of Type 3 PLs are predictable -typically being simple weighted averages of the uptakes of the solid and liquid in their pure states. [START_REF] Shan | New Class of Type III Porous Liquids: A Promising Platform for Rational Adjustment of Gas Sorption Behavior[END_REF] Very recently, several extended metal-organic framework species with intrinsic porosity have been isolated in the liquid form; that is, reported to melt at temperatures lower than their decomposition point. The zeolitic imidazolate family consists of over 100 different known frameworks based on tetrahedral metal nodes connected by imidazolate based linkers. [START_REF] Tian | The silica-like extended polymorphism of cobalt(II) imidazolate three-dimensional frameworks: X-ray single-crystal structures and magnetic properties[END_REF] Several species undergo partial coordination bond (Zn-N) breakage at ca. 400 °C, followed by rapid interchange of metal-ligand coordination partners. Interestingly, this results in a liquid which possesses 95% accessible porosity, compared to 74% in the microporous solid form. [START_REF] Gaillac | Liquid Metal-Organic Frameworks[END_REF] The absence of a second component in such systems, coupled with the fact that they are not discrete molecular species, leads us to propose that these species belong to a new category of porous liquid: Type 4. In effect, they are solid materials of extended connectivity in 3 dimensions which, in the liquid state, retain intrinsic porosity due to the strong constraints of their instantaneous coordination (Figure 2); that is, the local order imposed by the associated nature of the liquid.

Supercooled Porous Liquids and Glasses

The move towards fluid porosity provides an intriguing opportunity to look deeper into possibilities in an area that bridges both liquid and solid states: that is, supercooled liquids, or glasses (Figure 3). Cooling a liquid causes an increase in viscosity, and a corresponding decrease in molecular motion of the components present in the system. Slow cooling (compared to molecular motion) results in the first order phase transition known as crystallisation, though relatively high rates of cooling may result in a slowdown of molecular motion, until no further changes in movement on observable timescales are observed. [START_REF] Ediger | Supercooled liquids and glasses[END_REF] The range over which this slowdown in molecular motion occurs is a general kinetic phenomenon, referred to as the glass transition Tg (Figure 3a). We therefore suggest the possible existence of porous glasses corresponding to the categories of the porous liquids in Figure 2.

In the strictest sense, Figure 3a only provides a route to form glasses from Type 1 and Type 4 porous liquids, in which the liquid state can be regarded as pure. Whilst reports of the latter exist (formed by quenching liquids from the ZIF family), the extension in the case of Type 1 is less clear.

Here, iminospherand-based (non-porous) liquids have been demonstrated to possess reversible glass transitions at around 50 °C, with the glasses produced retaining the high transparency of their liquid phases upon cooling, and possessing the ability to be drawn into fibres. [START_REF] Giri | Alkylated organic cages: from porous crystals to neat liquids[END_REF] However, the occupation of cage pores by the externally functionalized long alkyl species in the liquid state is also likely to persist in the glass, given the enthalpic stabilization afforded to the system by long chain -pore wall dispersive interactions. Interestingly, liquids formed from similar cages functionalized with shorter alkyl chains possess 30% empty cages, though their glass forming ability has not yet been investigated, [START_REF] Giri | Alkylated organic cages: from porous crystals to neat liquids[END_REF] whilst the crown-ether anionic covalent cages highlighted in Figure 2 also form a glass, though only below room temperature. [START_REF] Jie | Transforming Porous Organic Cages into Porous Ionic Liquids via a Supramolecular Complexation Strategy[END_REF] The prospect of a Type 1 liquid possessing a glass temperature Tg above room temperature, while retaining porosity in the glass state, is therefore exciting, though for now elusive.

Unlike the other types described above, extending this approach to form Type 2 porous glasses is significantly more complicated. For example, highly concentrated porous liquids are most sought after for the purposes of application; however, these will be the most vulnerable to precipitation of the discrete organic as temperature is lowered and solubility decreases. Moreover, the presence of solvent has been observed to decrease the Tg in the case of both discrete organic molecules, [START_REF] Hancock | The Relationship between the Glass-Transition Temperature and the Water-Content of Amorphous Pharmaceutical Solids[END_REF] and inorganic systems. [START_REF] Hancock | The Relationship between the Glass-Transition Temperature and the Water-Content of Amorphous Pharmaceutical Solids[END_REF][START_REF] Angell | Liquid fragility and the glass transition in water and aqueous solutions[END_REF][START_REF] Sare | Glass-Forming Composition Regions and Glass Transition Temperature in Nonaqueous Electrolyte Solutions[END_REF] A detailed study on the effect of concentration on Tg in Type 2 porous liquids formed from a variety of solvents would thus be highly informative in perhaps identifying a useful trade-off between concentration of cage, and the stability of the glass at room temperature.

The absence of a fixed stoichiometry means that the compositional variance of glasses is huge compared to crystalline solids, allowing control over the resultant material properties. Even in a straightforward case, such as the ternary calcium aluminosilicate system CaO-Al2O3-SiO2 which is useful for display applications, a database of 231 different compositions predicts Young's moduli values which span from 60 to 160 GPa (Figure 3b). [START_REF] Yang | Predicting the Young's Modulus of Silicate Glasses using High-Throughput Molecular Dynamics Simulations and Machine Learning[END_REF] Taking a broader perspective, the freezing of colloidal suspensions occurs naturally in a variety of processes such as sea ice growth, and has been utilized to generate controlled porosity in a variety of materials including alloys, silica, water-soluble polymers, clays, and bone substitutes. [START_REF] Lasalle | Particle redistribution and structural defect development during ice templating[END_REF][START_REF] Zhang | Aligned two-and three-dimensional structures by directional freezing of polymers and nanoparticles[END_REF] Deville et al. have shown extensively that such processes can be harnessed in structuring complex composite materials (Figure 3c) [START_REF] Deville | Freezing as a path to build complex composites[END_REF] . Such methods should also prove applicable to other porous liquids, where they would lead to the generation of tuneable hierarchical porosity combining intrinsic and ice-templated porosity.

The glass phase analogy of polymorphism, called polyamorphism, may also be harnessed to effect transformations between different glasses of identical chemical composition but different physical and chemical properties. [START_REF] Mcmillan | Polyamorphic transformations in liquids and glasses[END_REF] The transit between two glass states commonly occurs through the application of pressure, and results in sudden changes in material density and properties; this has been demonstrated in a host of different systems including Y2O3-Al2O3, [START_REF] Mcmillan | POLYAMORPHISM AND LIQUID-LIQUID PHASE TRANSITIONS IN AMORPHOUS SILICON AND SUPERCOOLED Al2O3-Y2O3[END_REF] GeO2 and molecular organics. [START_REF] Ha | Supercooled liquids and polyamorphism[END_REF] The existence of different amorphous states of the ZIF-62 glass forming system has already been probed (Figure 3d), though the different properties of the amorphous states have not been explored.

Proposed Applications

Many of the suggested applications for porous liquids thus far centre on chemical separation technologies. Currently, acid gas separations are performed using scrubbing agents such as ethanolamines and polyethylene glycol dialkyl ethers that absorb a target gas, and are later regenerated though typically energy intensive processes. [START_REF] Sporer | The Linde Solinox process: Gypsum-free flue-gas desulphurization Gas Separ[END_REF] The use of organic cage-based liquids for key separations of soluble gases 51 would require higher selectivities than available at present, but could be advantageous in terms of reductions in the energy required for recycling due to improved heat management.

Several important problems still need to be addressed in using porous liquids for such processes.

Greenaway et al. demonstrated appreciable gas uptake in a range of porous liquids, notably through scrambling techniques (Figure 4a), but also found that the dynamic equilibria between bound and unbound guest molecules led to leaching of the guest over several days. [START_REF] Greenaway | Understanding gas capacity, guest selectivity, and diffusion in porous liquids[END_REF] The synthesis of porous liquids of lower volatilities may prove particularly beneficial in overcoming this loss through regular thermal or pressure swing processes.

Overall, Type 3 PLs in particular have some attractive aspects with regard to real world applications: i. they can be prepared economically by forming a dispersion of two commerciallyavailable components, ii. they have predictable gas uptakes, and iii. they are a diverse and modular platform technology consisting of thousands of potential variants, with a correspondingly wide range of tuneable properties. PLs might even be drop-in replacements for existing solvent-based gas separation processes, if they are found to be superior in terms of economics and performance.

Examples have been tailored toward gas separations such as CO2/CH4 separation, which is of interest for natural gas sweetening and biogas upgrading, thus demonstrating their potential for application. In this regard, a dispersion of the MOF Al(OH)(fumarate) in polydimethylsilicone oil was found to have greater CO2 capacity than the industrially used solvent Genosorb. A further exciting possibility is that PLs can be tailored toward gas separations for which no selective solvent currently exists, such as ethane/ethane separation. [START_REF] Cahir | Type 3 porous liquids based on non-ionic liquid phases -a broad and tailorable platform of selective, fluid gas sorbents[END_REF] In such applications, the liquid state could allow manufacture of free-standing or supported liquid membranes. [START_REF] Fu | Ultra-thin enzymatic liquid membrane for CO2 separation and capture[END_REF] Applications in gas separations may also be opportunities for Type 4 glasses, such as those formed from ZIFs. For example, Jiang et al. have recently utilized the glass forming process by first forming a crystalline ZIF-62 layer upon an Al2O3 substrate, before melt-quenching (Figure 4b). [START_REF] Wang | A MOF Glass Membrane for Gas Separation[END_REF] Interestingly, they found separation factors for H2/CH4, CO2/N2 and CO2/CH4 mixtures exceeding those for the crystalline material. Although the molecular mechanism is still unclear, the high selectivities reported for the ZIF-62 glass membrane should promote much further exploration into the guest capture and selectivity properties of porous glass materials in general.

Porous liquids may find application beyond carbon capture and storage -for example, in the subsequent utilization of the captured feedstock. Electrochemical reduction and catalytic conversion processes have been observed to produce a range of value-added chemicals such as formic acid, methanol and ethylene. [START_REF] Whipple | Prospects of CO2 Utilization via Direct Heterogeneous Electrochemical Reduction[END_REF] A range of electrolytes have been investigated, including KOH/MeOH mixtures, and ionic liquids. [START_REF] Kunene | Selective CO2 Reduction over Rose's Metal in the Presence of an Imidazolium Ionic Liquid Electrolyte[END_REF] Porous liquids might present a unique opportunity to overcome problems of low CO2 solubility while at the same time acting as a catalyst for the reductive processes.

More speculatively, many crystalline framework materials have shown that their strong local order can lead to stimuli-responsive properties, making them "smart materials" whose chemical properties may be switched through stimulation with, for example, temperature, pressure, or light.

The switching of physical structure through application of external stimuli is also a concept widely used in information storage. [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] We predict this may be extended to porous materials. For example, the design glasses and liquids by incorporating photoresponsive moieties, such as an azobenzene backbone, would render it possible to change the physical and chemical properties using light.

Mochida et al. have provided proof of concept in controlling the reversible transition of a rutheniumbased solid coordination polymer to an ionic liquid of identical composition (Figure 4c). [START_REF] Funasako | Reversible transformation between ionic liquids and coordination polymers by application of light and heat[END_REF]

Novel Materials Discovery

The relative novelty of the field of porous liquids and glasses compared to corresponding solidstate studies promises much excitement in the area of new materials discovery. Here, it is already clear that we need to move from serendipity-based discovery of new states of porous materials to an era of designability and the creation of new materials with targeted properties. Motivation to guiding research into improved Type 1, 2 and 3 materials will for example be improvements in the concentration of pore generators. This might be pursued in Type 1 inorganic and inorganic-organic liquids for example by borrowing from the strategy used in Type 1 organic liquids, [START_REF] Zhang | Porous Liquids: A Promising Class of Media for Gas Separation[END_REF] with porous counter-ions such as crown ethers in place of long alky chains or smaller, non-porous counterions such as NTf2. Improvements in the capacity of Type 2 and Type 3 liquids on the other hand clearly necessitate an increase in solubility of the porous component. The results of Greenaway et al., [START_REF] Greenaway | Understanding gas capacity, guest selectivity, and diffusion in porous liquids[END_REF] provide some directions on this. The field may pay particular attention to scrambled, achiral cages and asymmetrical porous materials which exist in topologically disordered solid states, and link the higher solubilities observed to the same logic employed in amorphous pharmaceuticals. Further research into the creation of Type 3 PLs through the heating of (low Tg) MMMs may also be of interest.

Such experimental efforts would be made more efficient from the development of computational techniques to accurately predict the structures and properties of hypothetical porous liquids.

Extending the plethora of high-throughput computational studies focusing on the uptake capacities and separation abilities for different gas species, to topologically disordered liquid and glasses would therefore present an interesting challenge. [START_REF] Wilmer | Large-scale screening of hypothetical metal-organic frameworks[END_REF] This should, however, also go hand in hand with the adaptation and application of theoretical tools for systematic characterization of molecular cages and porous molecular materials, [START_REF] Evans | Application of computational methods to the design and characterisation of porous molecular materials[END_REF][START_REF] Greenaway | High-throughput discovery of organic cages and catenanes using computational screening fused with robotic synthesis[END_REF] such as crystal structure prediction. [START_REF] Pulido | Functional materials discovery using energy-structure-function maps[END_REF] Type 4 liquids present an entirely different problem, which at the outset is one of first developing some guiding principles to allow their formation across different chemical families (Figure 2). Far less work has been performed in this area, though we would suggest that controlling the hierarchy of bond energies within porous materials is a key requirement to the formation of Type 4 liquids, regardless of chemistry. Specifically, clear differences in the strength of bonding leads to the possibility of selective bond breaking at sufficiently high temperatures while maintaining some local order, which seems to be crucial to obtain a porous liquid. Considerations in each case would be the residual diffusivity of framework components after melting, limiting the size of the rigid unit which may be used, lest the molten fluid be too viscous or glassy; and also the stabilization of the ionic components after the initial decoordination (in the case of salts).

For example, the ADOR process in zeolites relies upon the chemical destruction of mixed metal zeolites, followed by chemical structuring and reconfiguration of the components into a different framework. [START_REF] Eliasova | The ADOR mechanism for the synthesis of new zeolites[END_REF] Similarly, hydrogen-bonded organic frameworks (HOFs) such as triptycene trisbenzimidazolone are also formed from rigid organic molecules that crystallize through supramolecular interactions based on hydrogen bonding, which is typically an order of magnitude weaker than covalent bonds. [START_REF] Mastalerz | Rational Construction of an Extrinsic Porous Molecular Crystal with an Extraordinary High Specific Surface Area[END_REF] The design of Type 4 associative liquid HOFs may be challenging, however, because of the typically very high melting points of these materials, their inherent propensity to crystallize, or because of sublimation/decomposition before melting.

Finally, we also note that non covalent interactions with strong local order (i.e., preferential coordination) have been observed to play a critical role in excellent glass forming systems such as B2O3. [START_REF] Ferlat | van der Waals forces stabilize low-energy polymorphism in B2O3: Implications for the crystallization anomaly[END_REF] There, the strongly associated nature of the trigonal BO3 units, combined with the large number of possible three-connected networks energetically quasi-degenerate, favours the vitrification and the formation of a macroscopically disorder material. Such systems, modified to feature a larger and bulkier motif, are also good candidates for Type 4 porous liquids.

Understanding and Designing

There are substantial gaps in our fundamental understanding of existing porous liquids and glasses, which must be filled at a fundamental level if we are to make progress in their applications.

Further research into how kinetic factors such as cooling rates and sample sizes influence their melting/vitrification behaviour is likely to yield pathways to accurately controlling the density (and therefore porosity) of all porous glass categories, while a combination of simulated thermodynamic energy landscapes with experimental pressure-temperature diagrams would allow significant control to be exerted over new structure discovery in a parameter space of larger dimension with tuneable variables such as chemical composition, pressure, and temperature.

The nature of the transitions between ordered and disordered states is a second area in which our current knowledge is lacking. We have highlighted here the routes to forming porous liquids, and speculate on routes to novel porous glasses. Many interesting questions also lie in the reversibility of the transition from liquid to glass, and also the transition from ordered crystalline materials to topologically disordered states. For example, fast interchange between ordered crystalline chalcogenide domains and topologically disordered glasses form the basis of research into improved data storage. [START_REF] Zhang | Designing crystallization in phasechange materials for universal memory and neuro-inspired computing[END_REF] This is facilitated by significant differences in electrical resistance between ordered and disordered states, which we note has been observed within examples of amorphous and crystalline MOFs. [START_REF] Tominaka | Topochemical conversion of a dense metal-organic framework from a crystalline insulator to an amorphous semiconductor[END_REF] It is possible that the chemical complexity of such systems provide more shallow energy landscapes, and the existence of a plethora of degenerate states which allow for increased storage capacity.

One may also consider direct transitions between the crystalline and liquid states, particularly within low Tm systems such as those in Type 1 and Type 2 categories. The latent heat of the solidliquid phase transition in both inorganic and organic systems is used to store, and release, thermal energy near the transition temperature. [START_REF] Macfarlane | Energy applications of ionic liquids[END_REF] The use of hybrid crystalline systems has (very recently) been proposed, [START_REF] Chen | Metal-Organic Framework-based Phase Change Materials for Thermal Energy Storage[END_REF] as have crystalline-liquid transitions in metal-organic systems. [START_REF] Mcgillicuddy | Metal-Organic Phase-Change Materials for Thermal Energy Storage[END_REF] Other uses may also be found for such transitions, for example in gas storage where we borrow inspiration from ionic liquids. [START_REF] Seo | Phase-Change Ionic Liquids for Postcombustion CO2 Capture[END_REF] Here, the reaction of room temperature solids with guest molecules results in the reduction of their inherent Tm, and the subsequent ability to use the enthalpy of fusion to offset energy losses in absorbent regeneration.

The complexity of topologically disordered porous solids and liquids presents significantly greater challenges in both fundamental and applied domains when compared with their crystalline counterparts, which are themselves difficult systems to understand in detail -for example, in terms of the effects of defects. However, topologically disordered porous solids and liquids also provide new opportunities to engineer processability and to harness significant, reversible changes in both chemical and physical properties that simply cannot be attained in porous crystalline frameworks. PIMs, [START_REF] Budd | Polymers of intrinsic microporosity (PIMs): robust, solutionprocessable, organic nanoporous materials[END_REF] COFs, [START_REF] Cote | Porous, crystalline, covalent organic frameworks[END_REF] POCs, [START_REF] Tozawa | Porous organic cages[END_REF] porous liquids, [START_REF] Giri | Liquids with permanent porosity[END_REF] organometallic polymers, [START_REF] Williams | Main-chain organometallic polymers: synthetic strategies, applications, and perspectives[END_REF] extended networks, [START_REF] Kinoshita | The Crystal Structure of Bis(Adiponitrilo)Copper(I) Nitrate[END_REF][START_REF] Hoskins | Design and Construction of a New Class of Scaffolding-like Materials Comprising Infinite Polymeric Frameworks of 3D-Linked Molecular Rods. A Reappraisal of the Zn(CN)2 and Cd(CN)2 Structures and the Synthesis and Structure of the Diamond-Related Frameworks [N(CH3)4][Cu1Zn11(CN)4]and CUI[ 4,4"4[END_REF] MOFs & PCPs, [START_REF] Yaghi | Selective Binding and Removal of Guests in a Microporous Metal-Organic Framework[END_REF]78 liquid MOFs, [START_REF] Gaillac | Liquid Metal-Organic Frameworks[END_REF] functionalized silica spheres, [START_REF] Zhang | Porous Liquids: A Promising Class of Media for Gas Separation[END_REF] linked MOPs, [START_REF] Carne-Sanchez | Self-assembly of metal-organic polyhedra into supramolecular polymers with intrinsic microporosity[END_REF] aluminosilicate gels, [START_REF] Kistler | Coherent expanded aerogels and jellies[END_REF] clays, [START_REF] Bergaya | Handbook of Clay Science[END_REF] microporous carbons, 81 synthetic zeolites. 5 Figures: PIMs, [START_REF] Song | Controlled thermal oxidative crosslinking of polymers of intrinsic microporosity towards tunable molecular sieve membranes[END_REF] COFs, [START_REF] Cote | Porous, crystalline, covalent organic frameworks[END_REF] POCs, [START_REF] Tozawa | Porous organic cages[END_REF] porous liquids, [START_REF] Giri | Liquids with permanent porosity[END_REF] extended networks, [START_REF] Izatt | Macrocyclic and Supramolecular Chemistry[END_REF] MOFs & PCPs, [START_REF] Rosi | Hydrogen storage in microporous metal-organic frameworks[END_REF] liquid MOFs, [START_REF] Gaillac | Liquid Metal-Organic Frameworks[END_REF] functionalized silica spheres, [START_REF] Zhang | Porous Liquids: A Promising Class of Media for Gas Separation[END_REF] linked MOPs, [START_REF] Carne-Sanchez | Self-assembly of metal-organic polyhedra into supramolecular polymers with intrinsic microporosity[END_REF] aluminosilicate gels, [START_REF] Comas-Vives | Amorphous SiO2 surface models: energetics of the dehydroxylation process, strain, ab initio atomistic thermodynamics and IR spectroscopic signatures[END_REF] [START_REF] Gaillac | Liquid Metal-Organic Frameworks[END_REF] Categories shaded in blue are discussed in the outlook section. We note that the example in I Type 1 posed a problem for us in classification terms. We placed this in the inorganic category, rather than the inorganic-organic category because although functionalisation with an organic is necessary for the liquid state, the main body of the material is inorganic in nature. [START_REF] Ueda | Photogeneration of Microporous Amorphous Coordination Polymers from Organometallic Ionic Liquids[END_REF]

Figure 1 .

 1 Figure 1. The evolution of atomic arrangement in porous materials science. This figure highlights the evolution in focus from selected amorphous solids, through to the crystalline state, and onwards to the liquid state, spanning organic, inorganic and hybrid materials. References:

4 Figure 2 .

 42 Figure 2. Updated classification of porous liquids. The 1 st row shows a schematic depicting PL types. Type 1 PLs consist of intrinsically porous hosts (hollow circles). In Type 2 PLs, these are dissolve in sterically hindered solvents (solid circles). Type 3 PLs consist of microporous hosts (square grids) within a sterically hindered solvent. Type 4 PLs are neat microporous hosts which form transient, strongly associated liquids. Examples of known materials are given, alongside suggestions (in blue), for some categories not yet populated, on which discovery of the first examples may be based. Figure references. Schematics. 25 I Type 1 (adapted). 26 O Type 1. 28 IO Type 1. 29 I Type 2. 30 O Type 2. 32 IO Type 2. 87 I Type 3 (adapted). 33 O Type 3. 10,53 IO Type 3. 34 I Type 4. 64 O Type 4. 65,88 IO Type 4.[START_REF] Gaillac | Liquid Metal-Organic Frameworks[END_REF] Categories shaded in blue are discussed in the outlook section.

Figure 3 .Figure 4 .

 34 Figure 3. Solid-Liquid Transformations. (a) Schematic representation of enthalpy as a function of temperature for a liquid state capable of both crystallisation and vitrification, depending on cooling rate.[START_REF] Debenedetti | Supercooled liquids and the glass transition[END_REF] The glass transition is dependent upon rate of cooling -faster cooling leads to lower Tg values than slower cooling rates. Tg is however commonly defined using heating and cooling rates of 10 K/min for standardization between materials. (b) Ternary diagram showing the Young's modulus values predicted by high-throughput molecular dynamics simulations as a function of composition in the CaO-Al2O3-SiO2 glass system.[START_REF] Yang | Predicting the Young's Modulus of Silicate Glasses using High-Throughput Molecular Dynamics Simulations and Machine Learning[END_REF] (c) Ice-templated mesostructure of alumina (scale bar = 500 μm).[START_REF] Deville | Freezing as a path to build complex composites[END_REF] (d) The pressure-temperature (P, T) phase diagram of ZIF-62. Blue: stability domain of crystalline ZIF-62, tracing the results of the phase transition analysis from PXRD (blue and red diamonds). Red: two distinct amorphous phases with high (dark red) and low (light red) densities relative to each other.Yellow: domain of liquid ZIF-62, defined by melting points from the crystalline ZIF-62 (observed optically at high P and using DSC at ambient P). Crosses indicate conditions from which samples were quenched for morphological analysis.[START_REF] Widmer | Pressure promoted low-temperature melting of metal-organic frameworks[END_REF]

Acknowledgements

TDB acknowledges the Royal Society for a University Research Fellowship (UF150021), the Leverhulme Trust for a Philip Leverhulme Prize, and the University of Canterbury Te Whare Wānanga o Waitaha, New Zealand, for a University of Cambridge Visiting Canterbury Fellowship. FXC acknowledges funding by the Agence Nationale de la Recherche (ANR-18-CE29-0009-01). AIC acknowledges the Leverhulme Trust for funding through the Leverhulme Research Centre for Functional Materials Design.

Author Contributions

All authors contributed equally to the writing of the manuscript.

Competing Interests

The authors declare no competing interests.


V Vardakastani

Dominique Saletti

W Skalli

P Marry

Jean-Marc M Allain

C Adam

Increased intra-cortical porosity reduces bone stiffness and strength in pediatric patients with osteogenesis imperfecta

Keywords:

Increased intra-cortical porosity reduces bone stiffness

and strength in pediatric patients with osteogenesis imperfecta

Introduction

Osteogenesis imperfecta (OI) is a heritable disease that appears in one in 20,000 births. The disease is caused by a mutation of Type I collagen, and seven subtypes of OI have been identified [START_REF] Glorieux | Osteogenesis imperfecta[END_REF]. The symptoms and severity of the disease vary between patients, but the main shared characteristic of OI is bone fragility, leading to a high risk of fracture. As human specimens of OI bone are difficult to obtain, limited information is available in existing literature regarding the mechanism of this decrease in bone mechanical integrity. A number of previous studies have performed nanoindentation testing on human OI bone specimens [START_REF] Albert | Bone properties by nanoindentation in mild and severe osteogenesis imperfecta[END_REF][START_REF] Fan | Mechanical properties of OI type III bone tissue measured by nanoindentation[END_REF][START_REF] Fan | Comparison of nanoindentation measurements between osteogenesis imperfecta type III and type IV and between different anatomic locations (femur/tibia versus iliac crest)[END_REF][START_REF] Weber | Pamidronate does not adversely affect bone intrinsic materials properties in children with osteogenesis imperfecta[END_REF][START_REF] Imbert | Mechanical and mineral properties of osteogenesis imperfecta human bones at the tissue level[END_REF] and each of these studies has concluded that both the elastic modulus and hardness of the bone tissue itself are only marginally different to typical values for healthy cortical bone, despite the fact that it is known that OI significantly degrades the macroscopic mechanical behavior of the bone [START_REF] Weber | Pamidronate does not adversely affect bone intrinsic materials properties in children with osteogenesis imperfecta[END_REF].

The fact that OI bone exhibits essentially normal stiffness and strength at the nanoscale suggests that the cause of the degraded macroscopic mechanical properties occurs at scales above that of the collagen/apatite nanostructure. That is to say, micro-morphological factors may contribute to the abnormal macroscopic behavior of OI cortical bone. For instance, there are suggestions in previous studies that abnormal collagen orientation and lamellar architecture affect bone mechanical integrity in OI, and decreased lamellar thickness and osteonal size have been reported in OI [START_REF] Nyman | Effect of ultrastructural changes on the toughness of bone[END_REF][START_REF] Davis | Increased susceptibility to microdamage in Brtl/+mouse model for osteogenesis imperfecta[END_REF][START_REF] Rauch | Static and dynamic bone histomorphometry in children with osteogenesis imperfecta[END_REF][START_REF] Marotti | A new theory of bone lamellation[END_REF]. Moreover, the formation of micro-cracks and accumulation of micro-damage can also degrade mechanical behavior. Previous mouse studies [START_REF] Davis | Increased susceptibility to microdamage in Brtl/+mouse model for osteogenesis imperfecta[END_REF][START_REF] Dong | Collagen mutation causes changes of the microdamage morphology in bone of an OI mouse model[END_REF] indicate that OI bone shows a greater propensity to accumulate micro-damage and to form linear micro-cracks than normal bone. Bulk degradation of bone properties due to micro-cracks would not necessarily be detected by nanoindentation, whereas in a macroscopic mechanical test they would behave as material defects. Thirdly, there is the observation that cortical bone in OI becomes 'trabecularized' [START_REF] Jones | The microscopic structure of bone in normal children and patients with osteogenesis imperfecta: a survey using backscattered electron microscopy[END_REF], so that although the matrix itself may not be mechanically compromised, the increased porosity could degrade macroscopic mechanical properties.

Given the apparent importance of microstructural alterations in OI, the aim of this study was to examine the microstructure of OI cortical bone in a series of biopsy specimens from human subjects using polarized light microscopy. Collagen fiber organization was qualitatively assessed, and areal intra-cortical porosity was calculated. Porosity was then compared to micro-mechanical stiffness and strength measured during previously performed compression tests on a subset of the specimens.

Materials and methods

Specimen acquisition

The human OI cortical bone specimens used in this study were harvested during surgical rodding procedures for the fixation of femoral and tibial fractures undertaken at Hospital Armand Trousseau in Paris, France. The study protocol was approved by the Hospital ethical committee and written parental consent was obtained for each patient. After harvest, the biopsy specimens were wrapped in saline soaked gauze and frozen at -18 °C prior to transport to the laboratory.

Group assignment

A subset of the specimens described in the present study had been subjected to mechanical compression testing after harvest as part of a prior (unpublished) study. These specimens were assigned to Group 1. Group 2 comprised the remaining specimens which had not been previously compression tested, thereby allowing assessment of microstructure in untested specimens (since mechanical compression to failure could potentially affect microstructure, even though the final compressive strain was generally only a few percent). Since the protocol for the mechanical compression tests mentioned above has not been previously published, it is described below. The reader is referred to [START_REF] Antherieu | Mechanical characterization of child cortical bone for the study of osteogenesis imperfecta[END_REF] for further detail of the compression tests from the unpublished thesis. After mechanical compression testing of the specimens in Group 1, all specimens from both groups were prepared for polarized light microscopy as described in the section 'Resin embedding' below.

Mechanical compression testing of Group 1 specimens

Unconfined compression tests were performed on the specimens assigned to Group 1 in the present study using a uniaxial RAITH® testing device [START_REF] Houssen | Monitoring micrometer-scale collagen organization in rat-tail tendon upon mechanical strain using second harmonic microscopy[END_REF]. Since the surgically harvested biopsy fragments were of irregular size and shape, prior to testing each specimen was thawed and cut under constant irrigation into a parallelepiped shape using a diamond saw (Isomet Low Speed Saw, Buehler, USA). Due to the variation in size of the biopsy fragments, the resulting parallelepipeds also varied in size. Dimensions of the prepared specimens varied from 1.3 to 4.3 mm in width and thickness, and from 5.0 to 6.9 mm in length. When biopsy fragments were too thin to be securely held for cutting with the diamond saw, specimen preparation was achieved using manual polishing with successively finer polishing disks until a flat surface had been achieved. For each specimen, the cutting direction was chosen such that the faces of the parallelepiped test specimen were approximately parallel and perpendicular to the fabric direction of the host bone tissue respectively, as ascertained by visual inspection of the microstructure of the harvested fragments prior to cutting. Each specimen was then oriented in the uniaxial testing apparatus such that the applied loading was approximately aligned with the fiber direction (primary loading axis) of the bone in vivo. Prior to each compression test, black ink dots were applied to the side of the specimen to aid in subsequent image analysis using digital image correlation for strain determination, then the sample was preloaded with three cycles of compression to a maximum force of 20 N. Preloading helps to remove any artifacts due to minor asperities on the specimen surfaces. Compression tests were then performed at a strain rate of 0.001 s -1 until failure. During testing, force was measured using a 1 kN load cell, and specimen deformation was imaged using a digital camera (Canon EOS, Canon Inc., Japan). After testing, successive images were processed to derive compressive axial strain using custom-written digital image correlation post-processing software [START_REF] Antherieu | Mechanical characterization of child cortical bone for the study of osteogenesis imperfecta[END_REF]. Using the apparent stress vs. strain data thus derived, the apparent level Young's modulus was identified by least-squares fitting of the middle third of the linear region of the apparent stress vs. strain curve. The ultimate stress was identified as the maximal nominal stress obtained during each test. Note that when reporting mechanical test results, we use the terms 'apparent' elastic modulus and 'apparent' ultimate strength, to refer to the fact that the scale being tested is above that of the tissue level (as would be interrogated by nanoindentation), therefore the apparent properties are a function of both tissue material properties and microstructure.

Resin embedding

Prior to specimen preparation for microscopy, all specimens in both tested and untested groups were fixed in 10% phosphate buffered formalin (Electron Microscopy Sciences, USA) at room temperature for 24 h. Specimens were placed under vacuum at -300 mbar in order to assist formalin penetration. During fixation, the volume ratio of fixative to tissue was kept at or above 10:1. After fixation, all specimens were rinsed under running tap water for 1 h. Specimens were then dehydrated in increasing concentrations of acetone (50%; 75%; 100%), at 24 h per step based on the specimen size [START_REF] An | Handbook of histology methods for bone and cartilage[END_REF]. Specimens were then embedded in epoxy resin (Spurr Low Viscosity Embedding Media, Electron Microscopy Sciences, USA) using the corrected formulation of Ellis [START_REF] Ellis | Corrected formulation for Spurr low viscosity embedding medium using the replacement epoxide ERL 4221[END_REF]. Resin impregnated specimens were mounted by placing them inside small rings of plastic which had been pre-glued onto standard 25 × 75 mm microscopic slides, and then filling the space around the specimen with resin. After placement, specimens were degassed under vacuum for 15 min at -300 mbar, and were then polymerized overnight at 60 °C.

Computer numerically controlled milling

After embedding in epoxy resin, a custom built computer numerically controlled (CNC) milling system based on a Proxxon MF70 milling machine (Proxxon Ltd, Germany) was used to mill the mounted OI bone specimens down to the desired thickness for transmitted polarized light microscopy using natural birefringence (200-300 μm). A 3 mm diameter, 4-flute milling bit was used in all milling processes in order to achieve surface finishes in the order of 5-10 μm, which is less than the depth of field of the microscope at the magnifications used for imaging bone microstructure. This system allows preparation of large sections of mineralized bone at thicknesses of several hundred microns, suitable for polarized light imaging of interference colors in unstained specimens.

Polarized light microscopy and image analysis

Since structured arrays of collagen molecules are birefringent, collagen fibers in bone generate interference colors between crossed polarizers, with the color (or intensity in a single wavelength illumination system) containing information about specimen retardation, which can in turn be related to collagen orientation. Although we note that previous studies have quantitatively linked polarization colors to collagen orientation in bone [START_REF] Bromage | Circularly polarized light standards for investigations of collagen fiber orientation in bone[END_REF][START_REF] Spiesz | A quantitative collagen fibers orientation assessment using birefringence measurements: calibration and application to human osteons[END_REF], in this study polarized light imaging was used qualitatively to provide an indication of the degree of organization of collagen in the bone, and quantitatively in the sense of providing unstained contrast between bone and background for the measurement of intra-cortical porosity.

For each specimen, several microscope images were taken (with the number of images being dependent on the dimensions of the specimen) using an XJP300 polarizing microscope (Kozo Optics, China) with either 4× or 10× strain free objectives, and a five megapixel CMOS color camera (DCM-510, ScopeTek, China). A full wave retarder plate was used to enhance interference color generation on the unstained specimens. All images were saved in TIFF format, and, with the exception of background thresholding to change the first order red background induced by the waveplate to a black background, no post-processing or color modification was performed on any of the images.

Following image acquisition, the ImageJ software (version 1.48, National Institutes of Health, USA) was used in order to measure areal intra-cortical porosity on the polarized light microscopic images. Total specimen surface area was measured first using the ImageJ area measuring tool, then the outline of each pore in the bone was manually traced and its area measured. Note that using either 4× or 10× microscope objectives limits the optical resolution of the microscope to approximately 3 μm, therefore the porosity measure did not include pores smaller than several tens of microns in diameter, as these cannot be adequately segmented at the magnifications used. The areal porosity for each acquisition was then calculated as the total area of pores divided by the total bone area (including pores).

Results

Twenty six biopsy specimens from three children were included in the study. Of these, eight had previously undergone compression testing and were assigned to Group 1, and the remaining eighteen specimens were assigned to Group 2. However, three of the Group 1 specimens failed to provide reliable mechanical compression results (two specimens were so fragile that they failed during the preconditioning cycles, and the third specimen displayed excessive surface roughness and was eliminated from the test group). Therefore five biopsy specimens were successfully tested in Group 1. Patient demographics and biopsy sites are given in Table 1. Note that all patients had undergone bisphosphonate therapy prior to specimen harvest.

Fig. 1 shows four representative polarized light images of OI bone. Note that in one of these images, the bone structure appears well aligned, but even in this image there is a region of disordered, trabecularized tissue beside the lamellar bone. Although the interference colors do not provide quantitative collagen fiber orientation in this study, the relative differences between colors in an image can be used to infer the generally high degree of disorganization in the specimens. The uneven distribution of pore sizes and shapes in the bone is evidenced by the images in Fig. 1 and also by the large variation in areal porosities measured between specimens from the same patient as shown in Table 2, which gives the mean and range of intra-cortical areal porosity measurements for all specimens from a particular biopsy site. For each of the three patients, cortical areal porosity is substantially higher than literature values for healthy cortical bone, with even the lowest porosity (Patient III) being nearly double the expected porosity value of ~5%. It is also interesting to note that Patient III was the only ambulant patient, and the mean porosities for the other two nonweight bearing patients are 40-50% higher again. Fig. 2 shows a stitched reconstruction of the entire cross-section of a biopsy specimen from Patient II. This particular specimen displays large, interconnected directional pores and an overall porosity of 29%, which is indicative of the highest porosities found in the sample group (refer to maximum porosity values in Table 2). Fig. 3 shows a series of fissures in the bone cross-sections. It is unclear whether these existed in vivo or are a result of biopsy removal and/or processing, therefore we refer to them as fissures rather than micro-cracks.

Figs. 4 and 5 plot the apparent level mechanical response (elastic modulus and ultimate strength respectively) versus the measured areal porosity of the specimen in question for each of the five specimens which were mechanically tested. Although the number of tested specimens is too low to permit meaningful statistical analysis of the results, these plots show a striking relationship between apparent level mechanical properties and areal porosity, with R 2 N 0.9 in both cases. Furthermore, Fig. 6 plots apparent ultimate strength vs. apparent elastic modulus for the five specimens which underwent compression testing, and again there appears to be a strong linear relationship between these two measures.

Discussion

Given the findings of previous nanoindentation studies in which both human and murine OI bone tissue have been found to exhibit similar mechanical properties to normal bone, the aim of this study was to investigate OI bone at the microstructural level using polarized light microscopy, and in particular to qualitatively assess collagen fiber organization, and to quantitatively assess areal porosity. To our knowledge, this is the first assessment of OI bone microstructure and its relation to micro-mechanical properties in human tissue.

Given the difficulties in obtaining bone biopsy from pediatric human subjects at the time of surgery, only three patients could be recruited for this study. From these three patients, we attempted to process and image all clinically harvested bone fragments where the fragments were at least a few millimeters in size. For the previously performed mechanical testing study however, only those fragments which could be reliably cut into parallelepiped blocks were tested, and so the number of mechanically tested specimens is small.

As expected, the polarized light images showed a generally high degree of collagen disorganization, with some regions in which disorganized collagen and organized collagen exist side by side in the same biopsy fragment. One limitation of the study is that the polarized light imaging used here only provided qualitative information on collagen organization, whereas it is possible to use more specialized approaches to quantitatively measure collagen alignment in bone (e.g. [START_REF] Spiesz | A quantitative collagen fibers orientation assessment using birefringence measurements: calibration and application to human osteons[END_REF]). However, given the uncertainties in biopsy location and orientation implicit in obtaining fragments of bone removed at the time of surgery, we did not believe that the significant additional effort and resources required to obtain quantitative collagen fiber orientation were justifiable at this stage. The observations of regions of highly disorganized collagen in human OI tissue are in line with the prior histological observations [START_REF] Rauch | Static and dynamic bone histomorphometry in children with osteogenesis imperfecta[END_REF]. Taken together with the previously mentioned nanoindentation studies by other authors [START_REF] Albert | Bone properties by nanoindentation in mild and severe osteogenesis imperfecta[END_REF][START_REF] Fan | Mechanical properties of OI type III bone tissue measured by nanoindentation[END_REF][START_REF] Fan | Comparison of nanoindentation measurements between osteogenesis imperfecta type III and type IV and between different anatomic locations (femur/tibia versus iliac crest)[END_REF][START_REF] Weber | Pamidronate does not adversely affect bone intrinsic materials properties in children with osteogenesis imperfecta[END_REF][START_REF] Imbert | Mechanical and mineral properties of osteogenesis imperfecta human bones at the tissue level[END_REF], the presence of disorganized collagen alone does not seem to adversely affect tissue-level (i.e. nanoscale) mechanical integrity.

With regard to the areal cortical porosities measured in this study, the mean porosities found (between 10 and 15%) were two to three times higher than those previously reported for healthy adult cortical bone (e.g. 0.0456 ± 0.01 in [START_REF] Feik | Age-related changes in cortical porosity of the midshaft of the human femur[END_REF]). This phenomenon, previously named 'trabecularization' of OI bone [START_REF] Jones | The microscopic structure of bone in normal children and patients with osteogenesis imperfecta: a survey using backscattered electron microscopy[END_REF], consists of a gradual loss of cortical bone's compact form leading to a structure resembling trabecular microarchitecture. In this study, trabecularization was noted in all specimens to varying extents. We note that the increased porosity found here does not appear to occur in murine OI, with a recent study finding no significant difference in porosity between OI and wild type mice [START_REF] Carriero | Altered lacunar and vascular porosity in osteogenesis imperfecta mouse bone as revealed by synchrotron tomography contributes to bone fragility[END_REF]. Although healthy pediatric bone has been previously reported to exhibit higher porosity in both cortical and trabecular bone than adult bone [START_REF] Schnitzler | Cortical bone development in black and white south African children: iliac crest histomorphometry[END_REF][START_REF] Rauch | Intracortical remodeling during human bone developmenta histomorphometric study[END_REF], the mean porosity levels in OI bone reported here appear to be higher again. Furthermore, the apparent level mechanical properties measured here are substantially lower than normal values for cortical bone [START_REF] Ohman | Compressive behaviour of child and adult cortical bone[END_REF]. Most striking is the relationship between areal porosity and mechanical properties displayed in Figs. 4 and5.

These preliminary findings on a small number of specimens point to the hypothesis that the increase in bone fragility in human OI bone is due to increased intra-cortical porosity.

Although porosity and apparent mechanical properties appear to be strongly related at the level of individual biopsy specimens, the wide range of porosity values shown in Table 2 indicates that there was a highly uneven distribution of pores between biopsy fragments from the same anatomical site. Some of this variability may be attributable to radial variations in porosity between the outer and inner cortex, although the variation in cortical porosity from approximately 9% at the outer cortex to 6% at the inner cortex reported in [START_REF] Schnitzler | Cortical bone development in black and white south African children: iliac crest histomorphometry[END_REF] does not fully account for the much wider range of values reported here.

An essential remark concerning the mechanical behavior of the specimens used in this study is that all patients had been treated with bisphosphonates prior to surgery. The extent to which bisphosphonate therapy has affected the microstructure (including the porosity) of the biopsy specimens is not known, however we note that according to [START_REF] Weber | Pamidronate does not adversely affect bone intrinsic materials properties in children with osteogenesis imperfecta[END_REF] this treatment has no significant effect on the mechanical behavior of the OI bone. Furthermore, since two of the patients in this study were non-ambulant, the risk of bone loss due to inactivity is high and therefore there is a possibility that the measured values for OI bone porosity were due to a combination of OI and disuse osteoporosis. This coexistence of the two diseases is reported to be common in OI patients and thus the results given here can be considered reflective of a realistic clinical situation for an OI patient [START_REF] Glorieux | Osteogenesis imperfecta[END_REF]. As pointed out in the Results, the areal porosity for the single male ambulant patient was substantially (50%) lower than for the two non-ambulant patients (one male and one female). The irregular shape of the pores in the OI bone is also noteworthy. In healthy pediatric cortical bone, cortical remodeling causes the formation of large Haversian canals inside osteons [START_REF] Rauch | Intracortical remodeling during human bone developmenta histomorphometric study[END_REF], and Haversian porosity would be expected to be primarily responsible for the micro-porosity measured at the length scales reported here. However, the images in Figs. 1 and 2 display clear trabecularization, in which the increased porosity is not just due to the enlargement of Haversian canals, but due to the creation of new pores and fissures within the bone. These pores are often several hundred microns in size. An important implication of the large pore sizes found here is that existing high resolution in vivo imaging modalities such as pQCT may be able to adequately resolve increased micro-porosity in OI subjects. If increased intra-cortical porosity is indeed responsible for bone fragility in OI, then it may be possible to develop clinically useful subject-specific assessments of bone strength based on in vivo pQCT imaging.

There are a number of limitations to this study. Firstly, due to the nature of the resin embedding and sectioning process for polarized light microscopy, we were only able to measure porosity after mechanical testing had been performed (in the case of the Group 1 specimens). This means that some change in the microstructure of the bone could have occurred due to the compression tests, although we believe that any effect of compression on micro-porosity would be minimal due to the small (b1%) apparent compressive strains required to reach ultimate strength. In the future it would be desirable to perform nondestructive micro-CT evaluation of the specimens prior to mechanical testing. This would also have the advantage of providing 3D porosity measures, although due to the small biopsy fragment thicknesses and large pore sizes in OI bone, 3D porosity measurement would require careful consideration of the concept of a representative elementary volume for assessment.

A second limitation was that no assessment of micro-damage was performed in this study. Therefore neither the effect of micro-cracks on apparent mechanical properties, nor the role which any partially open micro-cracks may have played in increasing intra-cortical porosity could be assessed. It is likely that the surgical procedure induces substantial surface micro-damage in the biopsy fragments at the time of removal, however differentiating pre-existing micro-damage from that induced by surgical removal and specimen preparation would have required in vivo labeling which was beyond the scope of this study.

A third limitation is that due to the nature of biopsy specimen collection during surgery, the orientation and location of the retrieved bone fragments relative to the orientation of the patient's femur or tibia was not well known. As mentioned in the Materials and methods, it was generally possible to visually estimate the bone fabric direction prior to cutting the parallelepipeds for compression testing, however detailed orientation and location information for each small fragment (e.g. inner vs. outer cortex) was not obtainable. Given the high local variability in OI bone porosity and the frequent appearance of directional pores (Fig. 2), improved orientation information would be valuable in future studies.

In conclusion, the polarized light microscopy performed in this study indicates that pediatric OI bone exhibits extensive collagen disorganization and trabecularization, with increased porosity and reduced mechanical integrity compared to healthy bone. Importantly, micromechanical properties tentatively appear to be driven by increased intra-cortical porosity. Large pores in OI bone highlight the possibility of in vivo pQCT imaging for patient-specific bone fragility assessment in the future. We hope that the initial results given here will lead to further investigation of the role of micro-porosity in OI bone fragility by research groups with clinical access to human OI bone tissue.

Fig. 1 .

 1 Fig. 1. Typical polarized light images of human OI biopsy specimens. Note that the first order red background induced by the waveplate has been thresholded to convert it to black; no other image alteration has been performed. Top left, Patient I left femur showing a region of aligned bone (arrow A) which has been partially trabecularized (arrow B). Top right, Patient I left femur again showing collagen disorganization as evidenced by the strong differences in interference colors in close proximity to each other (arrow D). Bottom left and bottom right, two different biopsy fragments from Patient II left tibia, both showing the presence of large irregular pores. Arrow C shows manual outlining of a pore as an example of how areal porosity was determined.

500µmFig. 2 .

 2 Fig. 2. Stitched polarized light image of an entire biopsy specimen from Patient II left tibia.Again the first order red background induced by the waveplate has been thresholded to convert it to black; no other image alteration has been performed. The patient was nonambulant, and this image has an areal porosity of 29%; therefore it is representative of the most porous samples found in this study. Extensive trabecularization of tibial cortical bone is evident with interconnected pores and pore sizes of hundreds of microns.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Polarized light images with 10× objective, with the top two images showing fissures in biopsy specimens which had been subjected to prior compression testing (Patient I top left and Patient II top right), and the bottom row showing fissures in biopsy specimens which had not been subjected to prior compression testing (bottom left is Patient III and bottom right is Patient II). All specimens contain visible fissures, and since in vivo staining was not performed in this study it is not possible to differentiate between pre-existing, surgery-induced, and compression-induced microdamage in this study. Note some machining artifacts are visible in the bottom right image.

Fig. 5 .Fig.

 5 Fig.5. Plot of apparent ultimate strength (as measured by compression testing of Group 1 specimens) vs. areal porosity (as determined by manual measurement of polarized light images of the same specimens).

Table 1

 1 OI biopsy specimen details.

	Patient	Age	Gender Treatment prior	Ambulant Biopsy location and
	ID	(years)		to surgery		number
	I	4.5	M	Bisphosphonate No	R. femur (n = 4)
						L. femur (n = 8)
	II	3	F	Bisphosphonate No	L. tibia (n = 7)
	III	6	M	Bisphosphonate Yes	R. tibia (n = 7)

Table 2

 2 Areal cortical porosity for all specimens measured using polarized light microscopy.

	Patient ID		N	Mean	Range (min, max)
	I	Right	4	0.145	0.031	0.292
		Left	8	0.160	0.039	0.271
	II		7	0.142	0.046	0.278
	III		7	0.092	0.034	0.306