Key Insights
The European plastic bottles and containers market is poised for steady expansion, with a projected market size of 35.18 million units and an estimated CAGR of 3.87% during the 2019-2033 study period. This growth is fueled by escalating demand across diverse end-use industries, including food and beverages, pharmaceuticals, and personal care. The ubiquitous nature of plastic packaging in daily life, coupled with its cost-effectiveness, durability, and versatility, underpins this sustained market trajectory. Key resins like Polyethylene (PE), Polyethylene Terephthalate (PET), and Polypropylene (PP) continue to dominate the material landscape, offering a wide range of properties suitable for various product categories such as bottles, jars, canisters, and tubs. The convenience and portability offered by plastic packaging are particularly instrumental in driving consumption within the burgeoning bottled water and beverage sectors. Furthermore, advancements in plastic manufacturing technologies and the development of specialized packaging solutions for sensitive products like pharmaceuticals are contributing to the market's upward momentum.

Europe Plastic Bottles & Containers Market Market Size (In Million)

Despite the overall positive outlook, the market encounters certain restraints, including increasing regulatory scrutiny and growing consumer preference for sustainable packaging alternatives. The European Union's commitment to reducing plastic waste and promoting a circular economy presents both challenges and opportunities for market players. Companies are increasingly investing in research and development to innovate with recycled plastics and bio-based materials, aiming to align with environmental mandates and consumer expectations. The competitive landscape is characterized by the presence of established global players like Amcor Group GmbH, Berry Global Inc., and ALPLA Group, alongside specialized regional manufacturers. Strategic collaborations, mergers, and acquisitions are likely to shape the market dynamics as companies strive to enhance their product portfolios, expand their geographical reach, and secure a stronger foothold in this evolving sector. The focus on lightweighting, enhanced barrier properties, and smart packaging solutions will continue to be critical for sustained competitive advantage.

Europe Plastic Bottles & Containers Market Company Market Share

Dive deep into the dynamic Europe Plastic Bottles & Containers Market with our comprehensive report. This in-depth analysis provides unparalleled insights into market structure, growth drivers, segmentation, and future trends. Essential for industry leaders, strategists, and investors navigating the evolving landscape of plastic packaging in Europe. Discover key opportunities and challenges shaping the market from 2019 to 2033, with a detailed focus on the base and forecast years of 2025-2033.
Europe Plastic Bottles & Containers Market Market Structure & Innovation Trends
The Europe Plastic Bottles & Containers Market exhibits a moderate to high market concentration, with a blend of large multinational corporations and specialized regional players. Innovation is a critical differentiator, driven by the increasing demand for sustainable packaging solutions and enhanced product functionality. Regulatory frameworks, particularly those focused on plastic waste reduction and circular economy initiatives, are profoundly influencing market dynamics and encouraging the adoption of novel materials and designs. Product substitutes, such as glass and metal containers, present a competitive challenge, although plastic's cost-effectiveness, versatility, and lightweight properties continue to secure its dominance in many applications. End-user demographics are shifting towards environmentally conscious consumers and evolving lifestyle habits, further pushing innovation. Mergers and acquisitions (M&A) activities are strategic maneuvers aimed at expanding market reach, acquiring new technologies, and consolidating market share. Notable M&A deals are projected to contribute significantly to the market's overall value, estimated to reach xx Million in value during the forecast period.
Europe Plastic Bottles & Containers Market Market Dynamics & Trends
The Europe Plastic Bottles & Containers Market is poised for robust growth, driven by a confluence of expanding end-use industries and a sustained consumer preference for convenient and affordable packaging solutions. The Compound Annual Growth Rate (CAGR) is projected to be approximately xx% from 2025 to 2033. A key growth driver is the burgeoning food and beverage sector, which continuously requires a vast array of bottles and containers for products ranging from bottled water and carbonated soft drinks to milk and other beverages. The pharmaceutical and personal care industries are also significant contributors, demanding high-quality, safe, and tamper-evident plastic packaging for medications, cosmetics, and toiletries. Technological disruptions are revolutionizing the market, with advancements in materials science leading to the development of lighter, stronger, and more sustainable plastics, including those with higher recycled content. The increasing adoption of reusable and refillable packaging models, spurred by legislative mandates and growing consumer awareness regarding environmental impact, is another transformative trend. This shift is not only influencing product design but also the entire supply chain, from manufacturing to collection and recycling. Consumer preferences are increasingly aligned with sustainability, leading to a higher demand for packaging that is perceived as eco-friendly, recyclable, or made from recycled materials. This evolving consumer mindset is compelling manufacturers to invest in innovative solutions that minimize environmental footprint without compromising on functionality or aesthetics. The competitive dynamics are intensifying, with companies focusing on differentiation through product innovation, supply chain optimization, and strategic partnerships. Market penetration for advanced plastic packaging solutions is expected to rise, driven by stringent environmental regulations and a growing corporate commitment to sustainability goals. The overall market value is anticipated to reach xx Million by the end of the forecast period, reflecting its sustained expansion and importance within the European economy.
Dominant Regions & Segments in Europe Plastic Bottles & Containers Market
The Germany stands out as a dominant region within the Europe Plastic Bottles & Containers Market, propelled by its strong industrial base, advanced manufacturing capabilities, and stringent environmental regulations that foster innovation in sustainable packaging. The Polyethylene Terephthalate (PET) segment, specifically for Bottles, demonstrates exceptional dominance across multiple end-use industries.
Resin Dominance:
- Polyethylene Terephthalate (PET): Continues to be the preferred resin for beverage bottles due to its excellent clarity, barrier properties, and recyclability. Its widespread use in bottled water and soft drinks solidifies its leading position.
- Polyethylene (PE): Holds significant sway in the packaging of household chemicals, industrial goods, and some food products, particularly in its High-Density (HDPE) and Low-Density (LDPE) forms, owing to its chemical resistance and flexibility.
- Polypropylene (PP): Gains traction in applications requiring higher heat resistance and rigidity, such as tubs and certain types of containers for food and personal care products.
Product Dominance:
- Bottles: Represent the largest product segment by volume and value, catering to the immense demand from the beverage, pharmaceutical, and personal care sectors.
- Jars & Canisters: Exhibit strong growth, driven by their application in food preservation, cosmetics, and household chemicals.
End-use Industry Dominance:
- Beverage: This sector is the paramount driver of the plastic bottles and containers market, with Bottled Water and Carbonated Soft Drinks accounting for a substantial share. The increasing demand for convenient and portable beverage options, coupled with ongoing product innovations, sustains this segment's leading position.
- Food: A critical end-user, the food industry relies heavily on plastic containers for preserving freshness, ensuring safety, and facilitating convenient consumption across a wide range of products.
- Personal Care & Toiletries: This segment's continuous demand for aesthetically pleasing, functional, and safe packaging solidifies its importance.
Key drivers for this regional and segmental dominance include:
- Economic Policies: Favorable economic conditions and supportive government policies encouraging domestic manufacturing and innovation.
- Infrastructure: Well-developed logistics and supply chain networks facilitate efficient distribution of plastic bottles and containers across Europe.
- Consumer Demand: A strong and consistent consumer base for packaged goods, particularly beverages and food, underpins the market's growth.
- Regulatory Landscape: Stringent regulations promoting recycling and circular economy principles incentivize the use of recyclable materials like PET and drive innovation in product design.
Europe Plastic Bottles & Containers Market Product Innovations
Product innovations in the Europe Plastic Bottles & Containers Market are heavily skewed towards enhancing sustainability and functionality. The development of lightweight PET bottles made from a higher percentage of post-consumer recycled (PCR) material is a significant trend, reducing both the environmental impact and the overall cost of packaging. Companies are also exploring mono-material solutions to improve recyclability and bio-based plastics as alternatives to conventional fossil fuel-derived polymers. Innovations in barrier technologies are extending product shelf-life, particularly for sensitive food and beverage products. Furthermore, the introduction of smart packaging features, such as track-and-trace capabilities and temperature indicators, is gaining traction, especially within the pharmaceutical and high-value food segments. These innovations provide competitive advantages by meeting evolving consumer demands for eco-friendly products and offering enhanced performance.
Report Scope & Segmentation Analysis
This report meticulously analyzes the Europe Plastic Bottles & Containers Market, segmented across key parameters. The Resin segmentation includes Polyethylene (PE), Polyethylene Terephthalate (PET), Polypropylene (PP), and Other Resins, each with distinct applications and market shares projected to grow at varying rates. The Product segmentation covers Bottles, Jars, Canisters, Boxes, Gallons, Tubs, and Other Products, with Bottles expected to maintain its leading position due to widespread demand. The End-use Industries are thoroughly examined, including Food, Beverage (Bottled Water, Carbonated Soft Drinks, Milk, Other Beverages), Pharmaceuticals, Personal Care & Toiletries, Industrial, Household Chemicals, Paints & Coatings, and Other End-use Industries. The Beverage sector, particularly Bottled Water and Carbonated Soft Drinks, is anticipated to exhibit robust growth, while Pharmaceuticals and Personal Care & Toiletries will showcase steady expansion driven by increasing consumer spending and health awareness.
Key Drivers of Europe Plastic Bottles & Containers Market Growth
The Europe Plastic Bottles & Containers Market's growth is propelled by several critical factors. The increasing demand for convenient and portable packaging solutions across diverse end-use industries, particularly food and beverages, remains a primary driver. Technological advancements in polymer science are enabling the development of lighter, stronger, and more sustainable plastic materials, including those with enhanced recyclability and higher recycled content. Furthermore, evolving consumer preferences leaning towards eco-friendly and sustainable packaging options are compelling manufacturers to innovate and adopt circular economy principles. Supportive regulatory frameworks in Europe, focusing on waste reduction and plastic recycling, are also fostering market expansion by encouraging investment in new technologies and business models.
Challenges in the Europe Plastic Bottles & Containers Market Sector
Despite the positive growth trajectory, the Europe Plastic Bottles & Containers Market faces significant challenges. Stringent environmental regulations and increasing public scrutiny regarding plastic waste can lead to higher operational costs and necessitate substantial investments in recycling infrastructure and sustainable material development. Volatility in raw material prices, primarily linked to crude oil, can impact profit margins and influence pricing strategies. The limited availability of high-quality recycled plastic feedstock presents a hurdle to achieving ambitious circularity targets. Moreover, fierce competition from alternative packaging materials like glass and metal, coupled with the continuous need for innovation to meet evolving consumer and regulatory demands, adds to the market's complexity.
Emerging Opportunities in Europe Plastic Bottles & Containers Market
Emerging opportunities in the Europe Plastic Bottles & Containers Market are predominantly centered around sustainability and innovation. The growing demand for refillable and reusable packaging systems presents a significant growth avenue, requiring investment in new designs and infrastructure. The development and adoption of advanced recycling technologies, such as chemical recycling, offer solutions for hard-to-recycle plastics and can unlock new sources of high-quality recycled materials. There is also a rising opportunity in bio-based and biodegradable plastics, catering to niche markets and specific product requirements where performance and environmental impact are paramount. Furthermore, the expansion of e-commerce is driving the demand for specialized, durable, and lightweight plastic packaging solutions for shipping and delivery.
Leading Players in the Europe Plastic Bottles & Containers Market Market
- Plastipak Holdings Inc
- Alpha Packaging Inc
- Comar LLC
- Graham Packaging
- Amcor Group GmbH
- Greiner Packaging International GmbH
- Berry Global Inc
- Resilux NV
- Gerresheimer AG
- ALPLA Group
Key Developments in Europe Plastic Bottles & Containers Market Industry
- January 2024: Petainer and Oonly launched the first refillable PET bottles for mineral water in Hungary to promote circularity in the beverage sector in view of the new deposit return scheme in the country.
- October 2023: ALPLA and TÖNISSTEINER revealed a reusable and recyclable PET bottle for mineral water, made entirely from post-consumer recycled material and designed to reduce both weight and carbon consumption.
Future Outlook for Europe Plastic Bottles & Containers Market Market
The future outlook for the Europe Plastic Bottles & Containers Market is overwhelmingly positive, driven by sustained demand from key end-use industries and a strong commitment to circular economy principles. The market is expected to witness accelerated growth fueled by continuous innovation in sustainable materials, lightweight designs, and advanced recycling technologies. Strategic investments in expanding production capacity for recycled plastics and developing innovative refillable/reusable systems will be crucial. The market's trajectory will be significantly shaped by the effectiveness of regulatory frameworks in driving the transition towards a more sustainable and circular plastic packaging ecosystem, presenting substantial opportunities for companies that can adapt and lead in this evolving landscape.
Europe Plastic Bottles & Containers Market Segmentation
-
1. Resin
- 1.1. Polyethylene (PE)
- 1.2. Polyethylene Terephthalate (PET)
- 1.3. Polypropylene (PP)
- 1.4. Other Re
-
2. Product
- 2.1. Bottles
- 2.2. Jars
- 2.3. Canisters
- 2.4. Boxes
- 2.5. Gallons
- 2.6. Tubs
- 2.7. Other Products
-
3. End-use Industries
- 3.1. Food
-
3.2. Beverage
- 3.2.1. Bottled Water
- 3.2.2. Carbonated Soft Drinks
- 3.2.3. Milk
- 3.2.4. Other Beverages
- 3.3. Pharmaceuticals
- 3.4. Personal Care & Toiletries
- 3.5. Industrial
- 3.6. Household Chemicals
- 3.7. Paints & Coatings
- 3.8. Other End-use Industries
Europe Plastic Bottles & Containers Market Segmentation By Geography
-
1. Europe
- 1.1. United Kingdom
- 1.2. Germany
- 1.3. France
- 1.4. Italy
- 1.5. Spain
- 1.6. Netherlands
- 1.7. Belgium
- 1.8. Sweden
- 1.9. Norway
- 1.10. Poland
- 1.11. Denmark

Europe Plastic Bottles & Containers Market Regional Market Share

Geographic Coverage of Europe Plastic Bottles & Containers Market
Europe Plastic Bottles & Containers Market REPORT HIGHLIGHTS
| Aspects | Details |
|---|---|
| Study Period | 2020-2034 |
| Base Year | 2025 |
| Estimated Year | 2026 |
| Forecast Period | 2026-2034 |
| Historical Period | 2020-2025 |
| Growth Rate | CAGR of 3.87% from 2020-2034 |
| Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1. Increasing Adoption of Lightweight Packaging Methods; Changing Demographic and Lifestyle Factors
- 3.3. Market Restrains
- 3.3.1. Growing Environmental Concerns Over the Use of Plastics
- 3.4. Market Trends
- 3.4.1. The Beverages Segment is Expected to Hold a Significant Market Share
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Europe Plastic Bottles & Containers Market Analysis, Insights and Forecast, 2020-2032
- 5.1. Market Analysis, Insights and Forecast - by Resin
- 5.1.1. Polyethylene (PE)
- 5.1.2. Polyethylene Terephthalate (PET)
- 5.1.3. Polypropylene (PP)
- 5.1.4. Other Re
- 5.2. Market Analysis, Insights and Forecast - by Product
- 5.2.1. Bottles
- 5.2.2. Jars
- 5.2.3. Canisters
- 5.2.4. Boxes
- 5.2.5. Gallons
- 5.2.6. Tubs
- 5.2.7. Other Products
- 5.3. Market Analysis, Insights and Forecast - by End-use Industries
- 5.3.1. Food
- 5.3.2. Beverage
- 5.3.2.1. Bottled Water
- 5.3.2.2. Carbonated Soft Drinks
- 5.3.2.3. Milk
- 5.3.2.4. Other Beverages
- 5.3.3. Pharmaceuticals
- 5.3.4. Personal Care & Toiletries
- 5.3.5. Industrial
- 5.3.6. Household Chemicals
- 5.3.7. Paints & Coatings
- 5.3.8. Other End-use Industries
- 5.4. Market Analysis, Insights and Forecast - by Region
- 5.4.1. Europe
- 5.1. Market Analysis, Insights and Forecast - by Resin
- 6. Competitive Analysis
- 6.1. Market Share Analysis 2025
- 6.2. Company Profiles
- 6.2.1 Plastipak Holdings Inc
- 6.2.1.1. Overview
- 6.2.1.2. Products
- 6.2.1.3. SWOT Analysis
- 6.2.1.4. Recent Developments
- 6.2.1.5. Financials (Based on Availability)
- 6.2.2 Alpha Packaging Inc
- 6.2.2.1. Overview
- 6.2.2.2. Products
- 6.2.2.3. SWOT Analysis
- 6.2.2.4. Recent Developments
- 6.2.2.5. Financials (Based on Availability)
- 6.2.3 Comar LLC*List Not Exhaustive
- 6.2.3.1. Overview
- 6.2.3.2. Products
- 6.2.3.3. SWOT Analysis
- 6.2.3.4. Recent Developments
- 6.2.3.5. Financials (Based on Availability)
- 6.2.4 Graham Packaging
- 6.2.4.1. Overview
- 6.2.4.2. Products
- 6.2.4.3. SWOT Analysis
- 6.2.4.4. Recent Developments
- 6.2.4.5. Financials (Based on Availability)
- 6.2.5 Amcor Group GmbH
- 6.2.5.1. Overview
- 6.2.5.2. Products
- 6.2.5.3. SWOT Analysis
- 6.2.5.4. Recent Developments
- 6.2.5.5. Financials (Based on Availability)
- 6.2.6 Greiner Packaging International GmbH
- 6.2.6.1. Overview
- 6.2.6.2. Products
- 6.2.6.3. SWOT Analysis
- 6.2.6.4. Recent Developments
- 6.2.6.5. Financials (Based on Availability)
- 6.2.7 Berry Global Inc
- 6.2.7.1. Overview
- 6.2.7.2. Products
- 6.2.7.3. SWOT Analysis
- 6.2.7.4. Recent Developments
- 6.2.7.5. Financials (Based on Availability)
- 6.2.8 Resilux NV
- 6.2.8.1. Overview
- 6.2.8.2. Products
- 6.2.8.3. SWOT Analysis
- 6.2.8.4. Recent Developments
- 6.2.8.5. Financials (Based on Availability)
- 6.2.9 Gerresheimer AG
- 6.2.9.1. Overview
- 6.2.9.2. Products
- 6.2.9.3. SWOT Analysis
- 6.2.9.4. Recent Developments
- 6.2.9.5. Financials (Based on Availability)
- 6.2.10 ALPLA Group
- 6.2.10.1. Overview
- 6.2.10.2. Products
- 6.2.10.3. SWOT Analysis
- 6.2.10.4. Recent Developments
- 6.2.10.5. Financials (Based on Availability)
- 6.2.1 Plastipak Holdings Inc
List of Figures
- Figure 1: Europe Plastic Bottles & Containers Market Revenue Breakdown (Million, %) by Product 2025 & 2033
- Figure 2: Europe Plastic Bottles & Containers Market Share (%) by Company 2025
List of Tables
- Table 1: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Resin 2020 & 2033
- Table 2: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Product 2020 & 2033
- Table 3: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by End-use Industries 2020 & 2033
- Table 4: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Region 2020 & 2033
- Table 5: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Resin 2020 & 2033
- Table 6: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Product 2020 & 2033
- Table 7: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by End-use Industries 2020 & 2033
- Table 8: Europe Plastic Bottles & Containers Market Revenue Million Forecast, by Country 2020 & 2033
- Table 9: United Kingdom Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 10: Germany Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 11: France Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 12: Italy Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 13: Spain Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 14: Netherlands Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 15: Belgium Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 16: Sweden Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 17: Norway Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 18: Poland Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
- Table 19: Denmark Europe Plastic Bottles & Containers Market Revenue (Million) Forecast, by Application 2020 & 2033
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Europe Plastic Bottles & Containers Market?
The projected CAGR is approximately 3.87%.
2. Which companies are prominent players in the Europe Plastic Bottles & Containers Market?
Key companies in the market include Plastipak Holdings Inc, Alpha Packaging Inc, Comar LLC*List Not Exhaustive, Graham Packaging, Amcor Group GmbH, Greiner Packaging International GmbH, Berry Global Inc, Resilux NV, Gerresheimer AG, ALPLA Group.
3. What are the main segments of the Europe Plastic Bottles & Containers Market?
The market segments include Resin, Product, End-use Industries.
4. Can you provide details about the market size?
The market size is estimated to be USD 35.18 Million as of 2022.
5. What are some drivers contributing to market growth?
Increasing Adoption of Lightweight Packaging Methods; Changing Demographic and Lifestyle Factors.
6. What are the notable trends driving market growth?
The Beverages Segment is Expected to Hold a Significant Market Share.
7. Are there any restraints impacting market growth?
Growing Environmental Concerns Over the Use of Plastics.
8. Can you provide examples of recent developments in the market?
January 2024: Petainer and Oonly launched the first refillable PET bottles for mineral water in Hungary to promote circularity in the beverage sector in view of the new deposit return scheme in the country.
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4750, USD 4950, and USD 6800 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in Million.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Europe Plastic Bottles & Containers Market," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Europe Plastic Bottles & Containers Market report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the Europe Plastic Bottles & Containers Market?
To stay informed about further developments, trends, and reports in the Europe Plastic Bottles & Containers Market, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database



Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)

Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations

Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence


