Trä är ett biologiskt material som anses vara både förnyelsebart och hållbart byggnadsmaterial vilket har gjort att det har blivit populärare att bygga i trä. En av de största utmaningarna med att använda trä som konstruktionsmaterial i större byggnader och höghus är brandsäkerheten. I det här examensarbetet har provbitar av bok (Fagus sylvatica L.) vakuumimpregnerats med fenolformaldehydharts (PF) och olika nivåer av ammoniumdivätefosfat (ADF). Provbitarna användes sedan för att testa träets dess mekaniska styrka, hygroskopiska förmåga samt brandegenskaper. Resultaten från studien visar att vakuumimpregnering med kemikalierna ammoniumdivätefosfat (ADF) och fenolformaldehydharts (PF) i trä ger ett virke som är starkare, mer formstabilt och som har ett bättre brandskydd jämfört med obehandlat trä.

Hydrogels are high water-content polymers that mimic the extracellular matrix of cells. The polymers can have many sources and be of natural origin from the extracellular matrix (ECM) of cells or be synthetically derived. Two such polymers are hyaluronic acid and gelatin, which can with the help of the release of free radicals from photoinitiators, initiated by UV light, polymerise, and form a hydrogel. In these hydrogels, cells can be encapsulated. The hydrogels can in turn be used to maintain cells as they are in the natural environment. For example, hydrogels can provide an in-vivo-like ECM for stem cells and endothelial cells by supporting “stemness” and cell-to-cell contact; respectively. We aim to establish a protocol for culturing cells in the hydrogelas a first milestone in a project focused on profiling the metabolome of cells grown in hydrogels. To accomplish this, four types of cells, namely mouse brain microvascular endothelial cells (bEnd.3), human umbilical vein endothelial cells (HUVECs), adult human lung fibroblast (hLFs) and mesenchymal stem cells (MSCs), were evaluated for growth in hyaluronic acid methacrylate (HA-ma), hyaluronic acid acrylamide (HA-am) as well as a QuattroGel composed by gelatin methacryloyl (GelMA), HA-ma, fibrinogen and thrombin. It was found that HA-masupported viability and the stemness of mesenchymal stem cells, of which the metabolome can be further studied in order to evaluate the difference between regular 2D maintenance and maintenance in 3D. No sprouting was observed for the other cells encapsulated in the hydrogel, and further experiments are needed to find the source of error.

Nearly 60 m tonnes of waste is produced annually in Europe from “plastic packaging” engendering significant challenges for legislative controls and minimisation of environmental impact. There is an increasing demand for biodegradable packaging, which can be disposed of with minimum environmental impact, but the growing market is still in its infancy predominantly due to a lack of materials having environmental, practical and economic suitability. This research project dealt with some processing challenges of environmentally friendly packaging materials from renewable resources, as a long term solution to mitigate some issues associated with oil based plastic packaging. In this work, novel Polylactic acid (PLA) and starch based composites were developed with the requisite technical properties to fill the gap in the food packaging and cosmetic packaging industry. It was found that starch can be incorporated in a PLA matrix at the 10% level without difficulty in processing in the presence of 2% methyldiphenyl diisocyante. The blend shows properties similar to pure PLA. It was also found that the elongation at break and impact properties of PLA can be increased remarkably by the addition of a biostrength impact modifier. Furthermore, mixing of PLA and starch in the blend is efficient when the PLA particle size is reduced. It was also found that flexible and tougher PLA/starch blend pellets, that can be injection moulded, can be produced by an extrusion process with a range of additives. Each additive has a maximum level that exhibits optimum properties. The blends also established that 15% starch can be incorporated into the PLA matrix to reduce the cost without any processing difficulties. Encouragingly, the presence of an impact modifier in the PLA/starch blends has shown more desirable properties. Furthermore, the mechanical properties of the pellets exposed to increased residence time in the injection moulding barrel and of the test specimens stored for 9 months at 21ºC were also satisfactory for the new blend. The overall results exhibited some attractive properties in the tri blend system, which can be easily adopted by the plastics industry for development of an injection moulded product within the scope of applications such as dry food packaging or cosmetic packaging. A further finding of this project is that biodegradation under a home composting environment can be improved by incorporating starch and certain other modifiers into PLA.

Ce travail s’inscrit dans un contexte favorable au développement de nouveaux bétons dans le domaine du génie civil. Il consiste en la mise au point et la caractérisation d un béton renforcé de fibres obtenues à partir des déchets de bois de palmiers dattiers. Une première partie est consacrée à l’étude expérimentale des propriétés thermophysiques des fibres naturelles du palmier dattier. On montre que les facteurs essentiels affectant la conductivité thermique sont la variété du palmier dattier et l’orientation des fibres et que le bois de pétiole de palme est la partie la plus intéressante en tant qu’isolant thermique. les fibres végétales du bois de pétiole constituent, donc une alternative intéressante aux fibres inorganiques et synthétiques .Afin de remédier aux problèmes de stabilité dimensionnelle et de dégradation, on optimise la concentration du prétraitement alcalin nécessaire pour nettoyer et modifier la surface des fibres. Les effets du traitement sont étudiés au moyen d’un microscope électronique à balayage. Les conséquences sur les propriétés mécaniques du traitement alcalin sont également mises en évidence. L’analyse des résultats conduit à choisir une concentration optimale de 0,75 % pour l’hydroxyde de sodium.On s’intéresse ensuite au comportement du matériau composite obtenu à partir de chaux et de fibres de bois de palmier. On propose une démarche expérimentale et théorique originale sur la conductivité thermique, basée sur l’homogénéisation, de différentes formulations du béton de bois de pétiole de palmier ainsi que sur l’influence de la porosité. Finalement ce béton présente d’excellentes performances de point de vue isolation thermique.Finalement, on a procédé à une simulation numérique des phénomènes de transfert de chaleur au sein du béton de pétiole afin de valider le modèle de prédiction théorique choisi. nous avons, en effet refléchi à un modèle numérique inspiré de la modélisation théorique auto-cohérente (HAC) pour prédire la conductivité thermique numérique, basé sur des sphères concentriques d’air et de bois de pétiole occupant le centre de la matrice chaux, afin de balayer numériquement toutes les possibilites de dispositions de charges dans le composite. La dernière partie propose une validation des résultats expérimentaux obtenus à partir du développement d’un modèle tridimensionnel / The growing interest in new concrete and their use in many fields of civil engineering was that we wanted to bring a new approach to the design of a new product consisting of a reinforced concrete with basel end frond palm fibers. This led us to conduct the experimental study of thermal properties of natural fibers of date palm (Phoenix dactylifera L.). The analysis of experimental results showed that the essential factors affecting the thermal conductivity are the variety of date palm and the fiber orientation and that the basel end of the frond palm is the most interesting part as thermal insulation. However, the main problem encountered when using plant fibers as reinforcement is cohesion, bonding with the matrix and dimensional instability so the composite loses its mechanical properties. In this context, an alkaline pretreatment of palm fibers was envisaged to clean and modify the fiber surface to address the problems of dimensional stability of the fibers and degradation before their use as reinforcement in the cement matrix. We also studied the influence of chemical treatment with sodium hydroxide on the mechanical properties of processed samples, they were subjected to the tensile test to estimate the fracture strength for each treatment concentration, the Young's modulus and elongation at break corresponding. Subsequently, we conducted experimental and theoretical research on the thermal conductivity of different formulations of basel end palm wood concrete composite. The study of the theoretical apparent thermal conductivity was based on an approach that relies on a process whereas the material consists of a solid matrix combined with a fluid phase (air). Finally, we performed a numerical simulation of heat transfer phenomena to assess the thermal conductivity of basel end frond palm concrete composite and validate subsequently the theoretical prediction model selected. The results showed that the numerical approach based on the isotropic orientation of the particles in the composite coincides and approaches the physical reality

The objective of this master s thesis is the preparation and characterization of ribonucleic acid (RNA)/inorganic material interfaces by electrospray deposition and photoemission spectroscopy. This was done through investigation of the chemical and electronic structure of the surface of Highly Ordered Pyrolytic Graphite (HOPG) and gold before and after multiple steps of RNA thin film deposition by electrospray. Great interest has been shown by researchers into RNA due to its self-assembling ability. A series of experiments was conducted depositing RNA Poly adenosine, RNA Poly cytidine, and (for control purposes) DI water on HOPG. RNA Poly adenosine was also deposited on Gold. Gold is a more practical surface for use with RNA, but HOPG is useful for this study because it allows the precise determination of the density of states (DOS) of RNA. X-ray photoemission spectroscopy (XPS) and ultraviolet photoemission spectroscopy (UPS) were used to characterize the RNA-interfaces. The work function, high binding energy cutoff, and HOMO energies were determined. The clean, in-vacuum deposition of RNA was carried out using an electrospray thin film deposition device. The HOPG and gold substrates were prepared by in-situ cleavage and sputtering respectively. The electrospray method can be used for many different types of molecules including Polymers, metal-organics, crystals, and biological materials including RNA or DNA. These measurements provided data that will be helpful in determining the electronic properties of biological and substrate interfaces.

In pharmaceutical development cell cultures are used as in vitro models to evaluate the function of drug candidates. In such research it is vital to have models that resemble the in vivo environment to get reliable results. In 3D models with hydrogels ECM like scaffolds are supporting the cells in a more in vivo like environment than flat 2D cultures. In this project PEG-peptide based hydrogels with cell binding RGD incorporated on one PEG-peptide type has been evaluated for culturing of HepG2 cells. Structure and viscoelastic properties were evaluated with techniques like circular dichroism spectroscopy, dynamic light scattering and rheology. Sterilisation impact was also evaluated for PEG-peptides. For cell culturing, observations in light microscope and evaluation with Live/Dead assay and albumin assay were performed. A few companies were interviewed regarding 3D culturing and interest in mechanically tuneable hydrogels. The HepG2 cells grows and forms spherical clusters in the 3D environment with hydrogels, percentage of RGD seems to not impact cell adhesion, growth or albumin secretion. UV irradiation was the most suitable sterilisation method for gel components. The most rigid gel combination formed had storage modulus of around 230 Pa. Mechanically tuneable hydrogels is interesting for the industry. The PEG-peptide based gels are suitable tor growing cells but too soft to closely resemble the in vivo rigidity of hepatocytes.

Nedbrytbara metaller utgör en ny klass av biomaterial med potential attersätta permanenta material i tillfälliga applikationer. Detta för att minskarisken för långvariga biverkningar. I den pågående forskningen för att utvecklanya nedbrytbara metaller är screening av nya material genom in vitro testmetoderett attraktivt alternativ för att undvika onödiga, tidskrävande ochdyrbara djurstudier.Denna avhandling fokuserar på in vitro-testning av zink- och magnesiumbaserademetaller. Inverkan av faktorer såsom sammansättningen av testlösningen,buffersystemet, belastning samt mikrostruktur hos legeringar undersöktes.Genom att använda elektrokemiska in situ tekniker såsom impedansspektroskopi(EIS) är det möjligt att studera gränssnittet mellan metall ochlösning och karakterisera egenskaperna hos den korroderande ytan. Ex situytkaraktäriseringstekniker som svepelektronmikroskopi och infraröd spektroskopianvändes sedan för att komplettera resultaten av de elektrokemiskamätningarna.Korrosionen av zink i Ringer’s lösning fanns vara närmare in vivo korrosionän korrosionen i fosfatbuffrad saltlösning (PBS). Ringers lösning är därför denföredragna testmiljön för långsiktig utvärdering av zinkbaserade metallerDet biologiska buffersystemet (CO2/H2CO3) bör företrädesvis användasför att stabilisera pH-värdet på testlösningen vid magnesiumnedbrytning. NärHEPES användes för att stabilisera pH ökade korrosionshastigheten på grundav bildning av mindre skyddande skikt av korrosionsproduktMöjligheten att använda helblod och plasma som mer kliniskt relevantatestmiljöer utvärderades och befanns producera reproducerbara resultat.Bildning av ett korrosionsskikt bestående av både organiskt och oorganisktmaterial detekterades på zink i både plasma och helblod.När zink prover i helbod utsattes för belastning förhindrade korrosionsskiktetbildningen av mikrosprickor och förtidigt brott av provet. Det varvidare möjligt att detektera tidig sprickbildning på grund av belastning avMagnesium AZ61-legering med EIS.Adsorption av organiska species på zinkytan under anodisk polariseringökar yttäckningen av Zn-joner i helblod. Den ökade yttäckningen leder sedantill utfällningen av ett skyddande skikt av zinkfosfater och en minskadkorrosionshastighet vid högre potentialer.Korrosion av Zn-Mg och Zn-Ag legeringar i Ringers lösning befanns skevia selektiv upplösning. Lokal utfällning av korrosionsprodukter och bildningav ett poröst, mindre skyddande skikt av korrosionsprodukter hittades påZn-Mg legeringar. Den selektiva upplösningen av Zn-Ag legering orsakade enanrikning av AgZn3 vilket kan påverka biokompatibiliteten av ett implantatmed tiden. / Degradable metallic implants are a new class of biomaterials with potentialto replace permanent materials in temporary applications to reduce therisk of long term adverse effects.This thesis focuses on in vitro testing of zinc and magnesium based metals.As new degradable metals are developed screening of new materials within vitro test methods is an attractive option to avoid unnecessary, time consumingand expensive animal studies. The influence of factors such as ioniccomposition of the test solution, buffer system, strain and alloy compositionwas investigated. By employing electrochemical in situ techniques such asimpedance spectroscopy it is possible to study the metal-solution interfaceand determine the properties of the corroding surface. Ex situ surface characterizationtechniques such as scanning electron microscopy and infraredspectroscopy were then used to complement the results of the electrochemicalmeasurements.The importance of appropriate selection of the test solution is highlightedin this work. Zinc was found to corrode in Ringer’s solution by a mechanismcloser to in vivo corrosion than in a phosphate buffered saline solution(PBS).Ringer’s solution is therefore the more appropriate test environment for longterm evaluation of zinc based metals.When evaluating the corrosion of Zn-Mg and Zn-Ag alloys in Ringer’ssolution selective dissolution was found to occur for both types of alloys. Localprecipitation and formation of a porous, less protective, layer of corrosionproducts was found for Zn-Mg alloys. The selective dissolution of Zn-Agalloy caused an enrichment of AgZn3 on the surface which may affect thebiocompatibility of the alloy.The use of HEPES to maintain the pH of the test solution increasedthe corrosion rate of magnesium due to formation of a less protective layerof corrosion products. Magnesium corrosion should therefore preferably bestudied in solutions where the pH is maintained by the biological buffer systemCO2/H2CO3.In addition to saline solutions human whole blood and plasma were evaluatedas more clinically relevant in vitro environments. They were found toproduce reproducible results and to be suitable for short term experiments.Formation of a corrosion product layer comprised of both organic and inorganicmaterial was detected on zinc in both plasma and whole blood.During anodic polarization the adsorption of organic species on the zincsurface was found to increase the surface coverage of Zn ions in whole blood.The increased surface coverage then allowed for precipitation of a protectivelayer of Zn5(PO4)3 and a subsequent decrease in corrosion rate at higherpotentials.When subjecting zinc samples to strain the organic/inorganic corrosionproduct formed in whole blood was observed by impedance spectroscopy toprevent micro cracking and premature failure.The cracking of magnesium alloy samples under applied strain was alsocharacterized by impedance. Changes in surface properties due to crack initiation / <p>QC 20171019</p>

The aim of this project was to address the food waste problem, particularly bread waste, to some extent by producing monofilaments obtained from wet spinning of fungal hydrogel through the cultivation of Rhizopus delemar on bread waste. The project had two phases. Firstly, the possibility of production of chitosan fiber with wet spinning (using different acids) was evaluated, the process was optimized, and then applied to the production of fungal fiber. Regarding first stage of the project, adipic acid, a non-toxic solvent with two carboxyl groups, was used as acting physical crosslinker between the chitosan chains, resulting in improving properties of the monofilaments. Adipic acid performance was compared with conventional solvents, such as citric, lactic, and acetic acids. By injecting chitosan solutions into a coagulation bath (EtOH or NaOH 1M or EtOH-NaOH or H2SO4-EtOH), monofilaments were formed. Scanning electron microscopy showed that uniform chitosan monofilaments with smooth surface were formed using adipic and lactic acids. In general, fibers obtained from adipic acid displayed higher mechanical strength (Young’s modulus of 4.45 GPa and tensile strength of 147.9 MPa) than that of monofilaments produced using conventional solvents. Fiber dewatering with EtOH before drying led to greater fiber diameter and lower mechanical strength. As the second stage of this study, Rhizopus delemar was cultivated on bread waste in shake flasks and 1.3 M3 bioreactor. While different combinations of ground bread and K2HPO4 was used as the substrate for shake flask cultivations, white bread waste without K2HPO4 was utilized for scaling up the process, mostly due to the Glucosamine (GlcN) and N-acetyl-glucosamine (GlcNAc) content in the fungal cell wall. GlcN and GlcNA content obtained from ground bread was remarkably higher than that of obtained from combinations of ground bread and K2HPO4 as the substrate. Cultivation in 1.3 M3 bioreactor resulted in about 36 kg wet biomass with a mean of 14.88% dry weight, indicating 5.95 g biomass/L. The biomass yield of 0.15 g dry biomass/g dry bread was achieved. Alkali insoluble material (AIM) was obtained by alkali treatment of biomass. Fungal hydrogel was prepared by adding adipic and lactic acid to AIM, followed by grinding treatment. While hydrogels treated with lactic acid showed better spinnability and gelling ability, the one from adipic acid was not uniform to be wet spun. Considering hydrogels treated with lactic acid, the optimum grinding cycle for more spinnable hydrogel was 6 negative cycles, contributing to the fibers with the tensile strength of around 82 MPa. Such fibers showed antibacterial property against Escherichia coli, making them as a good option for suture applications. However, further in vitro and in vivo trials are essential to test the fungal fiber for such applications.

81% of the population in sub-Saharan Africa relies on charcoal and firewood to cover their energy needs for cooking. In Africa charcoal is usually produced by burning tree in a traditional kilns and then the food is cooked with a carbon-fired stoves indoors. All that links to three problems; deforestation, health issues and overpopulation, all of which can be reduced with a pellet cooking stove. Zambia in sub-Saharan Africa consumes charcoal equivalent to 6,089,000 tons of firewood each year. The total consumption of firewood being 13,967,000 tons per year. That leads to harvesting rate between 250,000 and 300,000 hectares each year making Zambia having one of the world’s fastest deforestation rates. Deforestation can be reduced by using the energy from the wood more efficient. In charcoal production and heating with charcoal about 72-86% of the produced energy is released to the atmosphere resulting the efficiency rate of only 14-28%. In comparison pellet production efficiency rate is 70-83%. Therefore if fuel pellets are used for cooking purposes energy instead of charcoal efficiency increases by 42-69% leading to lower need of wood material to cover equal energy demand. In this study five hardwood species and a softwood reference material from Zambia has been evaluated for fuel pellet production purposes. Evaluated hardwood species are Umsafwa, Umupundu, Umusamba, Umwenge and Umutondo. Reference material is already in use for pellet production in Zambia. Evaluation includes pellet production in a single pellet press, post production testing and X-ray examinations for tree different moisture contents; 8%, 10% and 12%. Pellet production includes friction energy, maximal friction energy and compression energy measurements. Post production testing includes density and hardness testing as well as X-ray examinations that indicate the amount of produced ash in the combustion process. High compression energy means higher energy cost in production so low compression energy is a desired property. Umupundu was the only wood species whose moisture content had no effect on the amount of compression energy. Umsamba and Umutondo gave the lowest and Umupundu and Umsafwa the highest compression energies of the tested hardwood pellets. Almost all of the friction energies of the tested materials were close to one another. The biggest exception was Umsafwa with 8% moisture content which had 38% higher friction energy than the reference material on average in this study. The values of the friction energy are low compared with other studies but within the reasonable limits compared with the reference material. A clear linear relationship was found between the friction energy and Fmax, so the friction energy directly implies the magnitude of the force of Fmax. A high hardness value is desirable because high hardness links directly to pellets high durability. All hardwood species tested were harder than the reference material. Ash significantly shortens the service life of the pellet stove, therefore it is desirable to produce as little ash as possible. Umsafwa and Unwenge has the lowest amount of metals that indicates the smallest amount of ash formed when burning pellets. Umsafwa with MC of 12% and Umwenge with MC of 10% are the best mix based on this study. / 81% av befolkningen i Afrika söder om Sahara är beroende av träkol och ved för att täcka sitt energibehov för matlagning. I Afrika produceras träkol vanligtvis genom att träden bränns i en traditionell ugn och sedan tillagas maten med en koleldad spis inomhus. Det leder till tre problem; avskogning, hälsoproblem och överbefolkning, allt detta kan minskas med en pellets spis. I Zambia förbrukar träkol motsvarande 6 089 000 ton ved varje år, och den totala förbrukningen av ved är 13 967 000 ton per år. Det leder till en avverkningstakt på mellan 250 000 och 300 000 hektar varje år vilket gör att Zambia har en av världens snabbaste avskogningshastigheter. Avskogningen kan minskas genom att energin från veden används mer effektivt. Vid produktion och användning av träkol frigörs cirka 72-86% av den producerade energin till atmosfären, vilket resulterar i en användningsgrad på endast 14-28%. Vid pelletstillverkning är motsvarande värde mycket högre, 70-83%. Om bränslepellets används istället för kol för matlagningsändamål ökar därför energieffektiviteten med 42-69%, vilket leder till lägre behov av trämaterial för att täcka lika energibehov. I denna studie har fem lövträslag och ett referensmaterial av barrträd från Zambia utvärderats för produktion av bränslepellets. De utvärderade lövträslag är Umsafwa, Umupundu, Umusamba, Umwenge och Umutondo. Referensmaterialet används redan för pelletstillverkning i Zambia. Utvärderingen inkluderar pelletsproduktion i enpetarpress, efterproduktionstestning och röntgenundersökningar för trädens olika fukthalter; 8%, 10% och 12%. Pelletsproduktion omfattar friktionsenergi, maximal friktionsenergi och mätningar av kompressionsenergi. Testning efter produktion inkluderar densitets- och hårdhetstestning samt röntgenundersökningar som indikerar mängden producerad aska i förbränningsprocessen. Hög kompressionsenergi innebär högre energikostnad i produktionen alltså låg kompressionsenergi är en önskad egenskap. Umupundu var det enda träslag vars fukthalt inte hade någon effekt på mängden kompressionsenergi. Umsamba och Umutondo gav de lägsta och Umupundu och Umsafwa de högsta kompressionsenergierna av de testade lövträpellets. Nästan alla friktionsenergier för de testade materialen låg nära varandra. Det största undantaget var Umsafwa med 8% fukthalt som hade 38% högre friktionsenergi än referensmaterialet i genomsnitt i denna studie. Värdena på friktionsenergierna är låga jämfört med andra studier men inom de tillåtna gränserna jämfört med referensmaterialet. Ett tydligt linjärt beroende hittades mellan friktionsenergin och Fmax, således friktionsenergin antyder direkt storleken på kraften hos Fmax. Ett högt hårdhetsvärde är önskvärt eftersom det kopplas direkt positivt till pellets hållbarhet. Alla lövträslag som testades var hårdare än referensmaterialet. Ask förkortar pelletskaminens livslängd avsevärt, därför är det önskvärt att producera så lite aska som möjligt. Umsafwa och Unwenge har den lägsta mängden metaller som anger den minsta mängd aska som bildas vid förbränning av pellets. Umsafwa med MC på 12% och Umwenge med MC på 10% är den bästa mixen baserat på denna studie.

The subject of this project is to study spun cellulose fibers made by Spinnova Oy inFinland. The fibers are spun using an environmentally friendly spinning process withoutuse of harsh chemicals.The spun filaments and the yarn based on these filaments were characterized and usedas reinforcement in polylactic acid biopolymer (PLA) and in biobased epoxy resin. Acomprehensive mechanical and morphological characterization of the single filamentsand their yarn was conducted. It was found that the single filaments are flat with a largewidth/thickness ratio, they are porous especially on one side and some cellulosemicrofibril orientation is observed on the filament surface. The single filaments are stiffand strong if compared to commercial regenerated cellulose filaments but are difficultto handle as they are very small and extremely light. The yarn showed to have lowermechanical properties but is easier to handle during the process of compositemanufacturing. Unidirectional fiber-reinforced composites were made using theSpinnova-yarn and PLA polymer applying film-stacking processing method. Thecomposite mechanical properties were studied and the results showed that themechanical performance of the PLA was significantly improved. The strength improvedfrom 54 MPa of the neat PLA to 95 MPa and the stiffness from 3.4 to 8.6 GPa withaddition of 22 wt% Spinnova-yarn.The main challenge of the project was handling the single filaments and their yarn todevelop a suitable manufacturing process which allows to exploit the potential of themto obtain a homogeneous fiber “preform” and to achieve good impregnation with the PLA matrix.