Optimizing the morphology of all-polymer solar cells for enhanced photovoltaic performance and thermal stability

Due to the complicated film formation kinetics, morphology control remains a major challenge for the development of efficient and stable all-polymer solar cells(all-PSCs). To overcome this obstacle, the sequential deposition method is used to fabricate the photoactive layers of all-PSCs comprising a polymer donor PTzBI-oF and a polymer acceptor PS1. The film morphology can be manipulated by incorporating amounts of a dibenzyl ether additive into the PS1 layer. Detailed morphology investigations by grazing incidence wide-angle X-ray scattering and a transmission electron microscope reveal that the combination merits of sequential deposition and DBE additive can render favorable crystalline properties as well as phase separation for PTzBI-oF:PS1 blends. Consequently, the optimized all-PSCs delivered an enhanced power conversion efficiency(PCE) of 15.21%along with improved carrier extraction and suppressed charge recombination. More importantly, the optimized all-PSCs remain over 90% of their initial PCEs under continuous thermal stress at 65 °C for over 500 h. This work validates that control over microstructure morphology via a sequential deposition process is a promising strategy for fabricating highly efficient and stable all-PSCs.

Design and analysis of an advanced thermal management system for the solar close observations and proximity experiments spacecraft

In this paper,the mission and the thermal environment of the Solar Close Observations and Proximity Experiments(SCOPE)spacecraft are analyzed,and an advanced thermal management system(ATMS)is designed for it.The relationship and functions of the integrated database,the intelligent thermal control system and the efficient liquid cooling system in the ATMS are elaborated upon.For the complex thermal field regulation system and extreme space thermal environment,a modular simulation and thermal field planning method are proposed,and the feasibility of the planning algorithm is verified by numerical simulation.A solar array liquid cooling system is developed,and the system simulation results indicate that the temperatures of the solar arrays meet the requirements as the spacecraft flies by perihelion and aphelion.The advanced thermal management study supports the development of the SCOPE program and provides a reference for the thermal management in other deep-space exploration programs.

Progress of semitransparent emerging photovoltaics for building integrated applications

With the rapid development of emerging photovoltaics technology in recent years,the application of building-integrated photovoltaics(BIPVs)has attracted the research interest of photovoltaic communities.To meet the practical application requirements of BIPVs,in addition to the evaluation indicator of power conversion efficiency(PCE),other key performance indicators such as heat-insulating ability,average visible light transmittance(AVT),color properties,and integrability are equally important.The traditional Si-based photovoltaic technology is typically limited by its opaque properties for application scenarios where transparency is required.The emerging PV technologies,such as organic and perovskite photovoltaics are promising candidates for BIPV applications,owing to their advantages such as high PCE,high AVT,and tunable properties.At present,the PCE of semitransparent perovskite solar cells(ST-PSCs)has attained 14%with AVT of 22–25%;for semitransparent organic solar cells(ST-OSCs),the PCE reached 13%with AVT of almost 40%.In this review article,we summarize recent advances in material selection,optical engineering,and device architecture design for high-performance semitransparent emerging PV devices,and discuss the application of optical modeling,as well as the challenges of commercializing these semitransparent solar cells for building-integrated applications.

Recent advances in two-dimensional photovoltaic devices

Two-dimensional(2D)materials have attracted tremendous interest in view of the outstanding optoelectronic properties,showing new possibilities for future photovoltaic devices toward high performance,high specific power and flexibility.In recent years,substantial works have focused on 2D photovoltaic devices,and great progress has been achieved.Here,we present the review of recent advances in 2D photovoltaic devices,focusing on 2D-material-based Schottky junctions,homojunctions,2D−2D heterojunctions,2D−3D heterojunctions,and bulk photovoltaic effect devices.Furthermore,advanced strategies for improving the photovoltaic performances are demonstrated in detail.Finally,conclusions and outlooks are delivered,providing a guideline for the further development of 2D photovoltaic devices.

Solution‑Processed Thin Film Transparent Photovoltaics:Present Challenges and Future Development

Electrical energy is essential for modern society to sustain economic growths.The soaring demand for the electrical energy,together with an awareness of the environmental impact of fossil fuels,has been driving a shift towards the utilization of solar energy.However,traditional solar energy solutions often require extensive spaces for a panel installation,limiting their practicality in a dense urban environment.To overcome the spatial constraint,researchers have developed transparent photovoltaics(TPV),enabling windows and facades in vehicles and buildings to generate electric energy.Current TPV advancements are focused on improving both transparency and power output to rival commercially available silicon solar panels.In this review,we first briefly introduce wavelength-and non-wavelengthselective strategies to achieve transparency.Figures of merit and theoretical limits of TPVs are discussed to comprehensively understand the status of current TPV technology.Then we highlight recent progress in different types of TPVs,with a particular focus on solution-processed thin-film photovoltaics(PVs),including colloidal quantum dot PVs,metal halide perovskite PVs and organic PVs.The applications of TPVs are also reviewed,with emphasis on agrivoltaics,smart windows and facades.Finally,current challenges and future opportunities in TPV research are pointed out.

Polymer Fiber Rigid Network with High Glass Transition Temperature Reinforces Stability of Organic Photovoltaics

Organic photovoltaics(OPVs)need to overcome limitations such as insufficient thermal stability to be commercialized.The reported approaches to improve stability either rely on the development of new materials or on tailoring the donor/acceptor morphology,however,exhibiting limited applicability.Therefore,it is timely to develop an easy method to enhance thermal stability without having to develop new donor/acceptor materials or donor–acceptor compatibilizers,or by introducing another third component.Herein,a unique approach is presented,based on constructing a polymer fiber rigid network with a high glass transition temperature(T_(g))to impede the movement of acceptor and donor molecules,to immobilize the active layer morphology,and thereby to improve thermal stability.A high-T_(g) one-dimensional aramid nanofiber(ANF)is utilized for network construction.Inverted OPVs with ANF network yield superior thermal stability compared to the ANF-free counterpart.The ANF network-incorporated active layer demonstrates significantly more stable morphology than the ANF-free counterpart,thereby leaving fundamental processes such as charge separation,transport,and collection,determining the device efficiency,largely unaltered.This strategy is also successfully applied to other photovoltaic systems.The strategy of incorporating a polymer fiber rigid network with high T_(g) offers a distinct perspective addressing the challenge of thermal instability with simplicity and universality.

Bio-PCM Panels Composed of Renewable Materials Interact with Solar Heating Systems for Building Thermal Insulation

This article aims to present the feasibility of storing thermal energy in buildings for solar water heating while maintaining the comfort environment for residential buildings.Our contribution is the creation of insulating composite panels made of bio-based phase change materials(bio-PCM is all from coconut oil),cement and renewable materials(treated wood fiber and organic clay).The inclusion of wood fibers improved the thermal properties;a simple 2%increase of wood fiber decreased the heat conductivity by approximately 23.42%.The issues of bio-PCM leakage in the cement mortar and a roughly 56.5%reduction in thermal conductivity with bio-PCM stability in composite panels can be resolved by treating wood fibers with an adjuvant by impregnating them in bio-PCM in the presence of the treated clay generated.Clay and wood fiber were treated with adjuvants that are both biological and environmentally acceptable,as confirmed by FTIR spectroscopy.The heat transfer bench(DIDATEK)showed a decrease in thermal conductivity.By using differential scanning calorimetric(DSC)analysis,the investigation of thermal stability and enthalpy during two heating cycles of pure bio-PCM and composite bio-PCM was validated.The novel renewable material was used to create composite panels for the trial prototype,which took the shape of a component attached to the solar heating system,33.57%less heat was lost,according to the heat transfer research.The outcomes demonstrated the possibility of replacing traditional electric water heating in residential buildings with solar water heating systems.

Thermal Stability and Degeneration Behavior of Solar Selective Absorber Based on WTi-Al_(2)O_(3)Cermet

A WTi-Al_(2)O_(3)cermet-based solar selective absorber was prepared to investigate the atomic diffusion induced spectral selectivity degeneration.The as-deposited coating exhibits superior absorptance(0.934)and low thermal emittance(0.098),as well as excellent thermal stability with a selectivity of 0.900/0.07 even after annealing at 923 K for 400 h in Ar ambient.However,the multilayer coating failed after being subjected to annealing at 923 K for 400 h in an air environment,as indicated by a decrease in solar absorptance to 0.912 and an increase in thermal emittance to 0.634.The microstructure characterizations reveal that the annealed coating exhibits a columnar morphology along the vertical direction of the substrate.The presence of abundant grain boundaries in the multilayer coating promotes the outward diffusion of Cr and Mn atoms in the stainless-steel substrate.The Mn atoms,in particular,possess the capability to migrate towards the surface of the coating and undergo an oxidation reaction with oxygen,facilitating the formation of a thick Mn_(2)O_(3)layer.The roughness of the coating surface was significantly increased in this case,adversely affecting solar absorptance due to amplified sunlight reflection.In addition,the rocketing of thermal emittance is attributed to the destabilization of W infrared reflective layer during the annealing.These findings highlight the importance of considering the outward diffusion of Mn and Cr elements in the stainless-steel substrate when optimizing solar selective absorbers.

Leakage Proof,Flame-Retardant,and Electromagnetic Shield Wood Morphology Genetic Composite Phase Change Materials for Solar Thermal Energy Harvesting

Phase change materials(PCMs)offer a promising solution to address the challenges posed by intermittency and fluctuations in solar thermal utilization.However,for organic solid-liquid PCMs,issues such as leakage,low thermal conductivity,lack of efficient solar-thermal media,and flamma-bility have constrained their broad applications.Herein,we present an innova-tive class of versatile composite phase change materials(CPCMs)developed through a facile and environmentally friendly synthesis approach,leveraging the inherent anisotropy and unidirectional porosity of wood aerogel(nanowood)to support polyethylene glycol(PEG).The wood modification process involves the incorporation of phytic acid(PA)and MXene hybrid structure through an evaporation-induced assembly method,which could impart non-leaking PEG filling while concurrently facilitating thermal conduction,light absorption,and flame-retardant.Consequently,the as-prepared wood-based CPCMs showcase enhanced thermal conductivity(0.82 W m^(-1)K^(-1),about 4.6 times than PEG)as well as high latent heat of 135.5 kJ kg^(-1)(91.5%encapsula-tion)with thermal durability and stability throughout at least 200 heating and cooling cycles,featuring dramatic solar-thermal conversion efficiency up to 98.58%.In addition,with the synergistic effect of phytic acid and MXene,the flame-retardant performance of the CPCMs has been significantly enhanced,showing a self-extinguishing behavior.Moreover,the excellent electromagnetic shielding of 44.45 dB was endowed to the CPCMs,relieving contemporary health hazards associated with electromagnetic waves.Overall,we capitalize on the exquisite wood cell structure with unidirectional transport inherent in the development of multifunctional CPCMs,showcasing the operational principle through a proof-of-concept prototype system.

Forestvoltaics,Floatovoltaics and Building Applied Photovoltaics(BAPV)Potential for a University Campus

The United Nations’Sustainable Development Goals(SDGs)highlight the importance of affordable and clean energy sources.Solar energy is a perfect example,being both renewable and abundant.Its popularity shows no signs of slowing down,with solar photovoltaic(PV)panels being the primary technology for converting sunlight into electricity.Advancements are continuously being made to ensure cost-effectiveness,high-performing cells,extended lifespans,and minimal maintenance requirements.This study focuses on identifying suitable locations for implementing solar PVsystems at theUniversityMalaysia PahangAl SultanAbdullah(UMPSA),Pekan campus including buildings,water bodies,and forest areas.A combined technical and economic analysis is conducted using Helioscope for simulations and the Photovoltaic Geographic Information System(PVGIS)for economic considerations.Helioscope simulation examine case studies for PV installations in forested areas,lakes,and buildings.This approach provides comprehensive estimations of solar photovoltaic potential,annual cost savings,electricity costs,and greenhouse gas emission reductions.Based on land coverage percentages,Floatovoltaics have a large solar PV capacity of 32.3 Megawatts(MW);forest-based photovoltaics(Forestvoltaics)achieve maximum yearly savings of RM 37,268,550;and Building Applied Photovoltaics(BAPV)have the lowest CO2 emissions and net carbon dioxide reduction compared to other plant sizes.It also clarifies the purpose of using both software tools to achieve a comprehensive understanding of both technical and economic aspects.

Resist Thermal Shock Through Viscoelastic Interface Encapsulation in Perovskite Solar Cells

Enhancing the lifetime of perovskite solar cells(PSCs)is one of the essential challenges for their industrialization.Although the external encapsulation protects the perovskite device from the erosion of moisture and oxygen under various harsh conditions.However,the perovskite devices still undergo static and dynamic thermal stress during thermal and thermal cycling aging,respectively,resulting in irreversible damage to the morphology,component,and phase of stacked materials.Herein,the viscoelastic polymer polyvinyl butyral(PVB)material is designed onto the surface of perovskite films to form flexible interface encapsulation.After PVB interface encapsulation,the surface modulus of perovskite films decreases by nearly 50%,and the interface stress range under the dynamic temperature field(−40 to 85°C)drops from−42.5 to 64.8 MPa to−14.8 to 5.0 MPa.Besides,PVB forms chemical interactions with FA+cations and Pb^(2+),and the macroscopic residual stress is regulated and defects are reduced of the PVB encapsulated perovskite film.As a result,the optimized device's efficiency increases from 22.21%to 23.11%.Additionally,after 1500 h of thermal treatment(85°C),1000 h of damp heat test(85°C&85%RH),and 250 cycles of thermal cycling test(−40 to 85°C),the devices maintain 92.6%,85.8%,and 96.1%of their initial efficiencies,respectively.

Vertically aligned montmorillonite aerogel-encapsulated polyethylene glycol with directional heat transfer paths for efficient solar thermal energy harvesting and storage

The conversion and storage of photothermal energy using phase change materials(PCMs)represent an optimal approach for harnessing clean and sustainable solar energy.Herein,we encapsulated polyethylene glycol(PEG)in montmorillonite aerogels(3D-Mt)through vacuum impregnation to prepare 3D-Mt/PEG composite PCMs.When used as a support matrix,3D-Mt can effectively prevent PEG leakage and act as a flame-retardant barrier to reduce the flammability of PEG.Simultaneously,3D-Mt/PEG demonstrates outstanding shape retention,increased thermal energy storage density,and commendable thermal and chemical stability.The phase transition enthalpy of 3D-Mt/PEG can reach 167.53 J/g and remains stable even after 50 heating-cooling cycles.Furthermore,the vertical sheet-like structure of 3D-Mt establishes directional heat transport channels,facilitating efficient phonon transfer.This configuration results in highly anisotropic thermal conductivities that ensure swift thermal responses and efficient heat conduction.This study addresses the shortcomings of PCMs,including the issues of leakage and inadequate flame retardancy.It achieves the development and design of 3D-Mt/PEG with ultrahigh strength,superior flame retardancy,and directional heat transfer.Therefore,this work offers a design strategy for the preparation of high-performance composite PCMs.The 3D-Mt/PEG with vertically aligned and well-ordered array structure developed in this research shows great potential for thermal management and photothermal conversion applications.

Electro-Optical Model of Soiling Effects on Photovoltaic Panels and Performance Implications

In this paper,a detailed model of a photovoltaic(PV)panel is used to study the accumulation of dust on solar panels.The presence of dust diminishes the incident light intensity penetrating the panel’s cover glass,as it increases the reflection of light by particles.This phenomenon,commonly known as the“soiling effect”,presents a significant challenge to PV systems on a global scale.Two basic models of the equivalent circuits of a solar cell can be found,namely the single-diode model and the two-diode models.The limitation of efficiency data in manufacturers’datasheets has encouraged us to develop an equivalent electrical model that is efficient under dust conditions,integrated with optical transmittance considerations to investigate the soiling effect.The proposed approach is based on the use of experimental current-voltage(I-V)characteristics with simulated data using MATLAB/Simulink.Our research outcomes underscores the feasibility of accurately quantifying the reduction in energy production resulting from soiling by assessing the optical transmittance of accumulated dust on the surface of PV glass.

Analysis for Effects of Temperature Rise of PV Modules upon Driving Distance of Vehicle Integrated Photovoltaic Electric Vehicles

The development of vehicle integrated photovoltaics-powered electric vehicles (VIPV-EV) significantly reduces CO2 emissions from the transport sector to realize a decarbonized society. Although long-distance driving of VIPV-EV without electricity charging is expected in sunny regions, driving distance of VIPV-EV is affected by climate conditions such as solar irradiation and temperature rise of PV modules. In this paper, detailed analytical results for effects of climate conditions such as solar irradiation and temperature rise of PV modules upon driving distance of the VIPV-EV were presented by using test data for Toyota Prius and Nissan Van demonstration cars installed with high-efficiency InGaP/GaAs/InGaAs 3-junction solar cell modules with a module efficiency of more than 30%. The temperature rise of some PV modules studied in this study was shown to be expressed by some coefficients related to solar irradiation, wind speed and radiative cooling. The potential of VIPV-EV to be deployed in 10 major cities was also analyzed. Although sunshine cities such as Phoenix show the high reduction ratio of driving range with 17% due to temperature rise of VIPV modules, populous cities such as Tokyo show low reduction ratio of 9%. It was also shown in this paper that the difference between the driving distance of VIPV-EV driving in the morning and the afternoon is due to PV modules’ radiative cooling. In addition, the importance of heat dissipation of PV modules and the development of high-efficiency PV modules with better temperature coefficients was suggested in order to expand driving range of VIPV-EV. The effects of air-conditioner usage and partial shading in addition to the effects of temperature rise of VIPV modules were suggested as the other power losses of VIPV-EV.

Comprehensive Examination of Solar Panel Design: A Focus on Thermal Dynamics

In the 21st century, the deployment of ground-based Solar Photovoltaic (PV) Modules has seen exponential growth, driven by increasing demands for green, clean, and renewable energy sources. However, their usage is constrained by certain limitations. Notably, the efficiency of solar PV modules on the ground peaks at a maximum of 25%, and there are concerns regarding their long-term reliability, with an expected lifespan of approximately 25 years without failures. This study focuses on analyzing the thermal efficiency of PV Modules. We have investigated the temperature profile of PV Modules under varying environmental conditions, such as air velocity and ambient temperature, utilizing Computational Fluid Dynamics (CFD). This analysis is crucial as the efficiency of PV Modules is significantly impacted by changes in the temperature differential relative to the environment. Furthermore, the study highlights the effect of airflow over solar panels on their temperature. It is found that a decrease in the temperature of the PV Module increases Open Circuit Voltage, underlining the importance of thermal management in optimizing solar panel performance.

Experimental Investigation of the Stability of the Performance Characteristics of a Photovoltaic Module in the Face of Environmental and Meteorological Factors

The explosive technological improvement of photovoltaic systems as well as the necessity of populations to come to less expensive energy sources, that have led to an implosion at the level of solar panel manufacturers. This causes a large flow of these equipments to developing countries where the need is high, without any quality control. That conducted an experimental investigation on the performance characteristics of a 250 wp monocrystalline silicon photovoltaic module in other to check the verification and quality control. Most of these PV panels which often have missing informations are manufactured and tested in places that are inadequate for our environmental and meteorological conditions. Also, their influences on the stability of internal parameters were evaluated in order to optimize their performance. The results obtained at maximum illumination (1000 w/m2) confirmed those produced by the manufacturer. The analysis of these characteristics showed that the illumination and the temperature (meteorological factors) influenced at most the stability of the internal characteristics of the module in the sense that the maximum power increased very rapidly beyond 750 w/m2 but a degradation of performance was accentuated for a temperature of the solar cells exceeding 50°C. The degradation coefficients were evaluated at -0.0864 V/°C for the voltage and at -1.6248 w/°C for the power. The 10° inclination angle of the solar panel proved to be ideal for optimizing overall efficiency in practical situations.

Solar Photovoltaics Development in Nigeria: Drivers, Barriers, and Policies

Energy access is vital to a nation’s economic growth and its populace’s social well-being. Still, there is a lack of adequate energy in Nigeria, negatively affecting the country’s socio-economic development. Due to the inadequate energy supply, some manufacturing companies shut their operations, and most Nigerians now use backup generators (BUGs) with their attendant health hazards, environmental pollution, and global warming. The need for energy access and a sustainable energy supply through renewable energy (RE) resources necessitates adopting solar photovoltaics (PV) in Nigeria. Studies on Nigeria’s energy accessibility and sustainability are generally on RE development and a few on solar PV applications. This research covers the need for an in-depth analysis of the growth of solar PV in Nigeria, and the research question is: What factors promote or limit the adoption of solar photovoltaics in Nigeria? A method of Systematic Literature Review (SLR) and Thematic Analysis (TA) is employed for the analysis. The research findings are divided into drivers, barriers, and policies. Some identified factors promoting the adoption of solar PV are energy poverty and the urgency to improve electricity supply, the ease of its operation and maintenance, and the Nigerian government’s commitment to clean electricity supply with policy initiatives and increased awareness of solar PV applications. Conversely, some noticed factors mitigating the growth of solar PV are poor tariff systems, dual subsidies of electricity and petroleum, and lack of finance and economic incentives.

Smart Monitoring of Solar Photovoltaic Panels by the Approach of Machine Learning

The exploitation of renewable energy has become a pressing task due to climate change and the recent energy crisis caused by regional conflicts.This has further accelerated the rapid development of the global photovoltaic(PV)market,thereby making the management and maintenance of solar photovoltaic(SPV)panels a new area of business as neglecting it may lead to significant financial losses and failure to combat climate change and the energy crisis.SPV panels face many risks that may degrade their power generation performance,damage their structures,or even cause the complete loss of their power generation capacity during their long service life.It is hoped that these problems can be identified and resolved as soon as possible.However,this is a challenging task as a solar power plant(SPP)may contain hundreds even thousands of SPV panels.To provide a potential solution for this issue,a smart drone-based SPV panel condition monitoring(CM)technique has been studied in this paper.In the study,the U-Net neural network(UNNN),which is ideal for undertaking image segmentation tasks and good at handling small sample size problem,is adopted to automatically create mask images from the collected true color thermal infrared images.The support vector machine(SVM),which performs very well in highdimensional feature spaces and is therefore good at image recognition,is employed to classifying the mask images generated by the UNNN.The research result has shown that with the aid of the UNNN and SVM,the thermal infrared images that are remotely collected by drones from SPPs can be automatically and effectively processed,analyzed,and classified with reasonable accuracy(over 80%).Particularly,the mask images produced by the trained UNNN,which contain less interference items than true color thermal infrared images,significantly benefit the assessing accuracy of the health state of SPV panels.It is anticipated that the technical approach presented in this paper will serve as an inspiration for the exploration of more advanced and dependable smart asset management techniques within the solar power industry.

Thin Film Photovoltaic/Thermal Solar Panels

A solar panel is described,in which thin films of semiconductor are deposited onto a metal substrate.The semiconductor-metal combination forms a thin film photovoltaic cell,and also acts as a reflector-absorber tandem,which acts as a solar selective surface,thus enhancing the solar thermal performance of the collector plate.The use of thin films reduces the distance heat is required to flow from the absorbing surface to the metal plate and heat exchange conduits.Computer modelling demonstrated that,by suitable choice of materials,photovoltaic efficiency can be maintained,with thermal performance slightly reduced,compared to that for thermal-only panels.By grading the absorber layer-to reduce the band gap in the lower region-the thermal performance can be improved,approaching that for a thermal-only solar panel.

Contrastive Observation of Solar Thermal and Photovoltaic Resource

Solar thermal and photovoltaic applications are the most w idely used and the most successful w ay of commercial development in solar energy applications. Observation and assessment of solar thermal and photovoltaic resources are the basis and key of their large-scale development and utilization. Using the observational data carried out from Beijing southern suburbs observation station of China M eteorological Administration in summer of 2009,preliminary solar thermal and photovoltaic resources characteristics for different w eather conditions,different angle and different directions are analyzed. The results show that:(1) In sunny,cloudy or rainy w eather conditions,both of solar thermal and photovoltaic sensors daily irradiance have consistent change in trend. Solar thermal irradiance is larger than photovoltaic. Under sunny conditions,solar thermal global radiation has about 2.7%higher than the photovoltaic global radiation. Under cloudy w eather conditions,solar thermal global radiation has about 3. 9%higher than the photovoltaic. Under rainy w eather conditions,solar thermal global radiation has about 20% higher than the photovoltaic.(2) For different inclined plane daily global radiation,southern latitude-15 °incline is the maximum and southern vertical surface is the minimum. The order from large to small is southern latitude-15 ° incline,southern latitude incline,southern latitude+15 °incline,horizontal surface and southern vertical surface. Southern latitude-15 °incline global radiation has about 41% higher than the southern vertical surface.(3) For different orientation vertical surface daily global radiation,southern vertical surface is the maximum and w estern vertical surface is the minimum,w hich eastern vertical surface is in the middle. Southern vertical surface global radiation has about 20% higher than the w estern vertical surface.