Applications of physical chemistry in technology and material science

Thermodynamics and Its Applications in Material Development

The principles of thermodynamics are foundational to understanding how materials behave under various conditions, and they play a crucial role in the development of new materials. Thermodynamics encompasses the study of energy transfer and the driving forces behind chemical and physical processes, allowing scientists to predict and manipulate material behavior effectively. As physicist Max Planck stated,

"The science of today is the technology of tomorrow."

Several key aspects of thermodynamics are particularly relevant for material science:

• Energy Changes in Reactions: Thermodynamics helps in understanding the energy changes involved in chemical reactions, which is critical for designing processes that yield desired materials efficiently. The concept of enthalpy (ΔH) is central here, reflecting the heat content during a reaction. A favorable reaction typically occurs if the enthalpy change is negative, indicating an exothermic process.
• Spontaneity and Reaction Feasibility: The Gibbs free energy (ΔG) is a decisive factor in determining whether a reaction will proceed spontaneously. By applying the Gibbs free energy equation, scientists can assess the thermodynamic favorability of material synthesis, as described previously:

$\Delta G_{(reaction)}=\mathrm{\Delta H}-T·\mathrm{\Delta S}$

• Phase Relationships: The study of phase diagrams is a critical application of thermodynamics. These diagrams illustrate the stability of phases of a material at various temperatures and pressures. Understanding phase transitions is essential not only for alloy design but also for optimizing conditions during polymer formation and other material processes.
• Heat Capacity and Material Behavior: The capacity of a material to absorb heat (heat capacity) is another thermodynamic property that influences its performance in different applications. Materials with high heat capacities are often more desirable in applications where thermal stability is crucial, such as in aerospace engineering and electronic devices.

By leveraging the principles of thermodynamics, researchers can engineer materials with specific properties tailored for targeted applications. For instance, the manipulation of thermodynamic parameters can lead to the development of alloys with improved strength-to-weight ratios or polymers with enhanced durability.

To illustrate the practical implications of thermodynamics, consider the field of energy storage: batteries and fuel cells rely heavily on thermodynamic principles to optimize efficiency and performance. The ability to design materials that can effectively facilitate energy transfer and storage is revolutionizing energy technology.

In conclusion, thermodynamics serves as a vital compass guiding material scientists in their quest to innovate. With its ability to predict and optimize material behavior in diverse environments, it empowers the development of next-generation materials that can meet modern challenges head-on. As the renowned chemist Linus Pauling once remarked,

"To understand the world at a deeper level is important for avoiding errors when we try to change it."

Kinetics and Reaction Mechanisms in Technological Processes

The study of kinetics and reaction mechanisms is pivotal in understanding technological processes and material development. By examining the rates of chemical reactions and the pathways through which they occur, scientists can optimize processes that are essential for various technologies. Kinetics not only provides insight into how quickly a reaction happens but also offers a detailed view of the sequence of steps involved, known as the **reaction mechanism**. As the renowned chemist Michael Faraday famously stated,

"Nothing is too wonderful to be true, if it be consistent with the laws of nature."

Key aspects of kinetics and reaction mechanisms relevant to technology include:

• Rate Laws: These mathematical expressions relate the rate of a reaction to the concentration of its reactants. The general form of a rate law is:
  $\mathrm{Rate}=k\left[A\right]^m\left[B\right]^n$ where k is the rate constant, and [A] and [B] are the concentrations of reactants, with m and n being the respective orders of the reaction with respect to each reactant.
• Mechanistic Pathways: Understanding the various steps leading from reactants to products allows for the identification of rate-determining steps. This insight can unveil opportunities to enhance reaction efficiency, such as optimizing catalyst use or modifying reaction conditions.
• Temperature and its Effects: The effect of temperature on reaction rates is described by the **Arrhenius equation**, which states:
  $k=Ae-EA/\mathrm{RT}$ where EA is the activation energy, A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin. This relationship emphasizes the need for temperature control in industrial processes to maintain efficient reaction rates.
• Catalysis: Catalysts play a crucial role in many technological processes by lowering activation energy and increasing reaction rates. A well-designed catalyst can enhance production efficiency and selectivity, particularly in fields like pharmaceuticals, petrochemicals, and green chemistry.

By employing these kinetic principles, researchers can engineer processes that are not only faster but also more sustainable. For instance, optimizing the reaction conditions in the production of biodegradable plastics can significantly reduce energy consumption and environmental impact.

Moreover, the ability to predict and control reaction kinetics leads to innovations in device manufacturing. For example, in the development of lithium-ion batteries, understanding the kinetics of charge and discharge processes is vital for enhancing battery life and performance. As physicist Richard Feynman eloquently put it,

"The imagination of nature is far greater than the imagination of man."

In conclusion, kinetics and reaction mechanisms provide invaluable tools for advancing technology and improving material processes. As we continue to unravel the complexities of chemical reactions, the potential for innovation grows, paving the way for more efficient and sustainable technologies in our modern world.

Quantum Chemistry and Its Impact on Material Properties

Quantum chemistry plays a transformative role in understanding and manipulating material properties at an atomic and molecular level. By employing principles derived from quantum mechanics, researchers can delve into the electronic structure of materials, predicting how these electronic configurations influence properties such as conductivity, magnetism, and chemical reactivity. As physicist Niels Bohr profoundly stated,

"If you are not perplexed by quantum mechanics, you do not understand it."

Several core areas highlight the importance of quantum chemistry in material properties:

• Electronic Structure Theory: Quantum chemistry allows for the calculation of electronic structures through methods such as density functional theory (DFT) and Hartree-Fock approximations. These theories enable scientists to predict how electrons are distributed in a material, which directly affects its properties.
• Band Theory: Understanding the electronic band structure is crucial for identifying whether a material behaves as a conductor, semiconductor, or insulator. The positions of energy bands dictate the material's ability to conduct electricity. In semiconductors, the bandgap can be engineered through doping, enabling applications in electronics.
• Magnetic Properties: Quantum mechanics elucidates why certain materials exhibit magnetic properties. For instance, the alignment of unpaired electrons in atoms can lead to ferromagnetism or antiferromagnetism, which is pivotal in the development of magnetic materials used in data storage and spintronic devices.
• Reactivity and Catalysis: Quantum calculations can predict reaction pathways, providing insight into transition states and activation energies. This understanding is essential for designing more efficient catalysts that drive chemical reactions forward, minimizing energy consumption and enhancing yields.
• Nanomaterials: The unique properties of nanomaterials, often derived from quantum effects, are leveraged in various applications such as drug delivery systems, sensors, and photovoltaic cells. Quantum effects become pronounced at the nanoscale, where materials may exhibit unexpected behavior, leading to novel functionalities.

The impact of quantum chemistry extends beyond theoretical considerations. It has practical implications for technology and material science:

• Material Innovation: By recognizing how quantum properties influence macroscopic characteristics, researchers can design materials tailored for specific applications, such as high-efficiency solar panels or advanced battery systems.
• Drug Design: Quantum chemistry aids in pharmaceuticals by modeling interactions between drugs and biological molecules, leading to more effective drug candidates with fewer side effects.
• Computational Materials Science: The combination of quantum chemistry with computational techniques accelerates the discovery of new materials, allowing for simulations that can predict material behavior before synthesis.

As the renowned chemist Richard Feynman once noted,

"What I cannot create, I do not understand."

In conclusion, the integration of quantum chemistry into material science fosters advancements that hold promise for the future of technology. By unveiling the mysteries of atomic interactions and electronic properties, quantum chemistry paves the way for innovations that enhance everything from electronics to nanotechnology, demonstrating its invaluable relevance in the quest for cutting-edge materials.

Characterization Techniques in Physical Chemistry and Their Applications

Characterization techniques play a critical role in the field of physical chemistry, enabling scientists to elucidate the properties, structures, and behaviors of materials on both macroscopic and microscopic levels. These techniques not only offer insight into material composition but also guide researchers in tailoring materials for specific applications. As Nobel Prize-winning chemist Richard Smalley once noted,

"We need to be able to control the molecular level of materials to maximize their potential."

Among the most widely used characterization techniques in physical chemistry are:

• X-ray Diffraction (XRD): This technique is essential for determining the crystal structure of materials. By analyzing the pattern produced when X-rays are diffracted through a crystalline sample, scientists can identify the arrangement of atoms and the phase composition of materials.
• Scanning Electron Microscopy (SEM): SEM provides high-resolution images of a material's surface morphology. This technique allows for the observation of fine structural details, enabling insights into the physical effects of processing conditions on material properties.
• Transmission Electron Microscopy (TEM): TEM complements SEM by allowing for the analysis of internal structures at atomic resolution. Scientists can observe defects, dislocations, and phase boundaries, all of which can influence the performance of materials.
• Nuclear Magnetic Resonance (NMR) Spectroscopy: NMR can provide information about the local environment of atoms within a material, revealing details about molecular dynamics and interactions that are crucial for understanding reactivity and stability.
• Fourier Transform Infrared (FTIR) Spectroscopy: This technique enables the identification of functional groups and molecular vibrations within a material. FTIR is particularly useful for organic materials and polymers, playing a pivotal role in understanding reaction mechanisms and material properties.
• Thermogravimetric Analysis (TGA): TGA measures weight changes in a material as a function of temperature, allowing researchers to assess thermal stability, composition, and decomposition characteristics, which are essential for material durability.
• Differential Scanning Calorimetry (DSC): DSC provides information about thermal transitions in materials, such as melting and crystallization temperatures. Such data is crucial for assessing material stability under varying thermal conditions.

These techniques offer valuable data that inform material development and applications. For example, by utilizing XRD, researchers can optimize the crystallinity of semiconductors, essential for high-efficiency photovoltaic applications. Similarly, through SEM and TEM, scientists can investigate the microstructure of novel alloys, allowing for enhancements in mechanical properties tailored for aerospace applications.

Furthermore, the integration of these characterization methods with advanced computational tools results in a synergistic approach that accelerates materials discovery. The ability to correlate experimental data with theoretical models enhances our understanding of material behaviors, fostering innovations in fields ranging from nanotechnology to biochemistry. As physicist Albert Einstein aptly stated,

"Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand."

In conclusion, characterization techniques in physical chemistry are indispensable for advancing technology and material science. By providing critical insights into material structure and behavior, these techniques enable researchers to innovate and optimize materials for a wide array of applications, ultimately enhancing technological advancements.

Phase Diagrams and Their Importance in Material Design

Phase diagrams are crucial tools in material science, providing visual representations of the stability and interactions of different phases within a material under varying temperature and pressure conditions. By serving as maps of material behavior, phase diagrams enable scientists and engineers to understand phase transitions, mixtures, and the relationships between diverse material states. As stated by the noted materials scientist Professor John B. Goodenough,

"The path to success is paved with the knowledge of what is achievable."

Key aspects of phase diagrams and their significance include:

• Understanding Phase Stability: Phase diagrams delineate the temperature and pressure ranges at which different phases (solid, liquid, gas) coexist. For instance, the phase diagram of water is a classic example, illustrating how ice, liquid water, and water vapor behave at various conditions.
• Alloy Design: For metallic alloys, phase diagrams guide the selection of suitable compositions for desired mechanical properties. The iron-carbon phase diagram is essential for understanding the transformations between different types of steel and cast iron, influencing strength, ductility, and hardness.
• Polymer Processing: In the context of polymers, phase diagrams help manage thermal transitions, affecting the performance of materials. Recognizing the glass transition temperature (Tg) is vital for ensuring polymers maintain their intended mechanical properties throughout their use.
• Predicting Material Behavior: By consulting a phase diagram, researchers can anticipate how materials will respond to changes in environmental conditions, such as temperature fluctuations during processing or operational scenarios. This predictive capability is paramount in industries ranging from aerospace to electronics.
• Optimizing Material Performance: The ability to visualize phase relationships aids in tailoring materials for specific applications. For example, understanding the melting points and solubility ranges in a phase diagram can facilitate the development of alloys with enhanced corrosion resistance or thermal stability.

The integration of phase diagrams with other physical chemistry principles, such as thermodynamics and kinetics, further enriches material design strategies. For example, knowing the Gibbs phase rule, expressed as:

$F=C-P+2$

where F is the degrees of freedom, C is the number of components, and P is the number of phases, helps scientists understand the relationships between different variables. This knowledge is instrumental when attempting to synthesize new materials with desired properties.

Moreover, the utility of phase diagrams extends into innovative fields such as nanotechnology and biomaterials. Their ability to illustrate the stability of nanomaterials under various conditions is vital for developing advanced devices, while in biophysics, phase diagrams can elucidate the behavior of biomolecules in complex environments.

In conclusion, mastering the principles of phase diagrams allows material scientists to navigate the complexities of material design effectively. As the famous chemist Linus Pauling remarked,

"To understand the world at a deeper level is important for avoiding errors when we try to change it."

The Role of Intermolecular Forces in Material Properties and Applications

Intermolecular forces are fundamental interactions that significantly impact the physical and chemical properties of materials, playing a crucial role in their potential applications. These forces, though relatively weak compared to the covalent bonds within molecules, govern a wide array of phenomena observed in materials, influencing their structural integrity, phase behavior, and reactivity. As the eminent chemist Robert H. Grubbs stated,

"Real science is about the understanding and making of the real world, and that often entails the interactions between molecules."

Intermolecular forces can be classified into several key types:

• Van der Waals Forces: These include London dispersion forces, dipole-dipole interactions, and dipole-induced dipole forces. They are essential in defining the physical state of a material (solid, liquid, or gas) and are particularly significant in non-polar substances.
• Hydrogen Bonds: A specific and stronger type of dipole-dipole interaction, hydrogen bonds occur when hydrogen is covalently bonded to highly electronegative elements such as oxygen, nitrogen, or fluorine. This force is crucial in determining the unique properties of water, such as its high boiling point and solvent capabilities.
• Ionic Interactions: These forces arise between charged ions and are significant in ionic compounds, influencing their solubility, melting points, and other physical properties.

Understanding these intermolecular interactions is vital, as they directly determine various material characteristics:

• Boiling and Melting Points: Materials with strong intermolecular forces generally exhibit higher boiling and melting points. For instance, the high boiling point of water compared to methane can be attributed to hydrogen bonding, which requires considerably more energy to break.
• Solubility: The principle of "like dissolves like" illustrates how materials with similar intermolecular forces will mix well. For example, polar solvents such as water can dissolve ionic compounds or other polar molecules, while non-polar solvents are more effective for non-polar substances.
• Mechanical Properties: The strength of intermolecular forces can significantly affect the material's tensile strength and elasticity. This is critical in polymer science, where the arrangement of polymer chains and the associated intermolecular forces dictate the mechanical performance.
• Phase Behavior: Intermolecular forces govern phase transitions such as melting, freezing, and evaporation. By manipulating these forces, scientists can develop materials that exhibit specific phase behaviors under defined conditions, which is essential for applications such as thermoregulating fabrics.

By leveraging an understanding of intermolecular forces, researchers can innovate and improve material performance across various applications:

• Drug Formulation: In pharmaceutical science, hydrogen bonding interactions between drugs and their targets enhance effectiveness and selectivity.
• Material Coatings: The principles of intermolecular forces guide the development of coatings that enhance adhesion and hydrophobicity in various materials, leading to advances in corrosion resistance.
• Nanotechnology: At the nanoscale, intermolecular forces dictate aggregation, stability, and interactions among nanoparticles, influencing the development of new nanomaterials.

In conclusion, the role of intermolecular forces in determining material properties is foundational and far-reaching. As scientists continue to explore these interactions, the potential for creating innovative and functional materials expands. In the words of the physicist Albert Einstein,

"A new idea comes suddenly and in a quite different way than the conscious reasoning process."

Nanotechnology and Physical Chemistry: Advances and Applications

Nanotechnology represents a frontier in materials science, where advanced understanding at the nanoscale offers transformative applications across various sectors. By manipulating matter at atomic and molecular levels, researchers can design materials endowed with enhanced properties and functionalities that are impossible to achieve at larger scales. As physicist Richard Feynman aptly stated,

"There's plenty of room at the bottom."

The intersection of nanotechnology and physical chemistry yields numerous advances and applications, significantly impacting diverse fields:

• Enhanced Drug Delivery Systems: Nanoparticles can be engineered to deliver therapeutic agents directly to targeted cells, improving the efficacy of treatments while minimizing side effects. For instance, lipid nanoparticles have been pivotal in delivering mRNA vaccines, enabling rapid production and distribution of vaccines during health crises.
• Smart Sensors: Nanoscale materials exhibit unique electrical, optical, and magnetic properties, allowing for the development of highly sensitive sensors. These sensors can detect minute changes in environmental conditions, enabling applications in areas such as environmental monitoring, medical diagnostics, and food safety.
• Lightweight and Strong Materials: Nanocomposites, which combine nanoparticles with traditional materials, can exhibit remarkable strength-to-weight ratios. This innovation is particularly beneficial in aerospace and automotive industries, where reducing weight while maintaining structural integrity is crucial.
• Energy Storage and Conversion: Nanotechnology plays a critical role in the advancement of energy solutions, such as batteries and supercapacitors. Nanoscale materials can enhance the surface area, leading to improved charge storage capacity. For example, nanosilicon has demonstrated the potential to increase battery capacity significantly compared to traditional graphite.
• Nanotechnology in Agriculture: Nanoscale fertilizers and pesticides can enhance nutrient delivery and pest control, maximizing crop yield while minimizing environmental impact. This approach is essential in promoting sustainable agricultural practices.

The unique properties of nanomaterials arise from their high surface area to volume ratio and the dominance of quantum effects. These properties enable precise tuning of material behavior for specific applications. For instance, the quantum dots used in displays and LEDs exhibit size-dependent optical properties, allowing for vibrant colors and energy-efficient lighting.

It is worth noting that the integration of nanotechnology with physical chemistry also poses challenges, particularly concerning safety and environmental impact. Understanding the toxicological effects of nanoparticles and their behavior in biological systems is imperative for developing safe applications.

In conclusion, the advances in nanotechnology driven by physical chemistry have opened avenues for groundbreaking applications that address modern challenges. As we continue to innovate and explore this exciting field, the potential for improving technology and everyday life remains limitless. The words of chemist George Olah resonate in this context:

"It is the progress of science that will ultimately benefit society."

Corrosion Science and Physical Chemistry's Contributions to Material Durability

Corrosion science is a critical aspect of material durability that combines principles of physical chemistry with practical applications to enhance the longevity of materials. Corrosion, defined as the deterioration of materials due to chemical reactions with their environment, can lead to significant economic losses and safety hazards. As the leader in materials science, Dr. Robert E. U. W. Templin noted,

"Understanding the processes that underlie corrosion will allow us to develop materials that can withstand the test of time."

In corrosion science, several key factors influence the degradation of materials:

• Electrochemical Reactions: Corrosion generally occurs through electrochemical processes that involve oxidation and reduction reactions. For example, iron oxide formation during rusting can be represented as:

$\mathrm{4Fe}+4H++4O(aq)\to \mathrm{4Fe}(aq)+2H2O$

• Water and Oxygen Presence: The presence of moisture and oxygen significantly accelerates corrosion rates. In many environments, water acts as a medium for electrochemical reactions, while oxygen can facilitate the oxidation of metals.
• pH Levels: The acidity or basicity of the environment affects corrosion processes. For instance, acidic conditions can lead to increased metal ion solubility, speeding up the corrosion rate.
• Environmental Salts and Contaminants: Salts, particularly chlorides, can aggressively attack protective oxide layers on metals, greatly accelerating corrosion.

To mitigate corrosion and enhance material durability, physical chemistry employs various strategies:

• Coating Technologies: Protective coatings serve as barriers between the metal surface and the environment, limiting exposure to corrosive factors. Common coating materials include paints, galvanization with zinc, and more advanced polymer-based coatings.
• Corrosion Inhibitors: These substances, when added to an environment, can significantly reduce metal corrosion. Mechanisms include forming a protective film or affecting the electrochemical reactions at the metal surface.
• Material Selection: Choosing corrosion-resistant materials, such as stainless steel or high-performance alloys, is crucial for applications exposed to harsh environments.
• Corrosion Monitoring: Regular assessment of corrosion rates through techniques such as electrochemical impedance spectroscopy can inform maintenance and replacement strategies, ultimately enhancing material longevity.

The implications of corrosion science extend beyond individual structures to encompass broader societal and environmental impacts. By investing in research and development aimed at understanding corrosion mechanisms, industries can save costs associated with material failure and repair. As the late physicist Richard Feynman famously said,

"The principle of science is the following: It is not a matter of what you believe, but what you can prove."

In conclusion, combating corrosion through the principles of physical chemistry is essential for enhancing material durability and ensuring the sustainable use of resources. Continued advancements in corrosion science will lead to innovative materials and coatings that stand the test of time, bolstering safety and efficiency across various industries.

Polymer Chemistry: Physical Chemistry in the Development of New Materials

Polymer chemistry significantly leverages the principles of physical chemistry to develop innovative materials with tailored functionalities and enhanced performance. Polymers, large macromolecules composed of repeating structural units known as monomers, exhibit unique properties that arise from their molecular architecture, which makes them crucial in various applications ranging from packaging to advanced biomedical devices. As chemist Hermann Staudinger once remarked,

"The macromolecule is the king of all molecules."

Key areas in which physical chemistry informs polymer development include:

• Synthesis Techniques: Various polymerization techniques, such as addition polymerization and condensation polymerization, are used to create polymers with specific architectures. The control over reaction conditions allows chemists to dictate molecular weight, branching, and cross-linking, directly influencing the material's properties.
• Thermodynamic Considerations: The study of the thermodynamics of polymer solutions and melts is crucial for understanding phase behavior and phase transitions. The Flory-Huggins theory is a common model used to describe the mixing behavior of polymers and solvents, providing insights into solubility and compatibility, vital for applications like coatings and adhesives:
• Mechanical Properties: The mechanical performance of polymers, such as tensile strength and elasticity, is directly influenced by their molecular weight and chain arrangement. For instance, polymers like polyethylene exhibit varying mechanical properties depending on the degree of branching, transitioning from low-density (flexible) to high-density (rigid) variants. This relationship is pivotal in designing materials tailored for specific applications, including construction and automotive industries.
• Thermal Properties: The thermal behavior of polymers, including glass transition temperature (Tg), melting temperature (Tm), and decomposition temperature, is vital for thermal stability in applications. Understanding the heating and cooling cycles in processing allows for better optimization of materials for applications like electronics and packaging.
• Polymer Blends and Composites: The formulation of blends and composites combines different polymers or polymers with inorganic materials to produce enhanced characteristics, such as improved strength, flexibility, and heat resistance. This approach is particularly relevant in sectors like aerospace and automotive manufacturing, where performance and weight optimization are critical.

Advancements in polymer chemistry hold immense potential for future technological innovations. The incorporation of smart materials, which respond to external stimuli (e.g., temperature, light, moisture), exemplifies how polymers can evolve beyond traditional applications to create dynamic systems. As materials scientist M. Anne M. Lemaire stated,

"The beauty of a polymer lies in its adaptability."

In conclusion, the intersection of polymer chemistry and physical chemistry is a fertile ground for innovation. Through a deep understanding of polymer structures, synthesis techniques, and the principles of thermodynamics, researchers can develop materials that not only meet but exceed the demands of various applications. Thus, the future of materials enriched by polymer chemistry is limited only by our imagination and scientific inquiry.

Energy Solutions: Fuel Cells, Batteries, and Photovoltaics

Energy solutions, particularly in the form of fuel cells, batteries, and photovoltaics, underscore the pivotal role of physical chemistry in creating sustainable technologies that address global energy demands. As the renowned chemist Sir Humphry Davy once observed,

"The most important thing in science is not so much to obtain new facts as to discover new ways of thinking about them."

1. Fuel Cells: Fuel cells convert chemical energy directly into electrical energy through redox reactions, typically involving hydrogen and oxygen. The fundamental reaction in a hydrogen fuel cell can be represented as:

$\mathrm{2H}+O\to \mathrm{2H}₂O$

The efficiency and performance of fuel cells can be significantly enhanced by optimizing the reaction kinetics and reaction design. Key components include:

• Electrolytes: The choice of electrolyte affects the ion conductivity and overall efficiency; for instance, proton exchange membranes (PEMs) facilitate hydrogen ion movement while blocking electrons.
• Catalysts: Noble metals like platinum serve as effective catalysts in facilitating the oxygen reduction reaction, ensuring higher power output.
• Fuel Flexibility: Advanced fuel cells allow the use of different fuels, including natural gas and biofuels, expanding their applicability across various sectors.

2. Batteries: Batteries store chemical energy and convert it into electrical energy through electrochemical reactions. The most common example is the lithium-ion battery, widely used in consumer electronics and electric vehicles. The electrochemical reaction can be summarized as: