José Holguín-Veras

Diana G Ramírez-Ríos

Trilce Encarnación

Jesus Gonzalez-Feliu

Elise Caspersen

Carlos Rivera-González

Carlos A González-Calderón

Renato Da

Silva Lima

José Holguín-Veras

Diana G Ramírez-Ríos

Jesús González-Feliu

Metropolitan Economies and the Generation of Freight and Service Activity: An International Perspective

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Global urbanization has been growing rapidly in the past six decades. In the 1950s, less than one-third of the world's population lived in urban settlements. In 2014, this had scaled up to 54 percent of the population, and the trend is expected to continue. By 2050, the world is expected to be 34% rural and 66% urban, the opposite of what it was in the mid-twentieth century (United Nations, 2014b). With increasing urbanization, cities face numerous challenges, particularly in regard to the movement of goods in and out of city centres. These challenges will grow as cities do, and as the demand for goods and services are concentrated in urban areas, producing numerous externalities. Congestion, pollution, noise and safety are just some of the issues that cities must contend with on a daily basis in relation to trucks and other vehicles that carry freight. Service activity also contributes to daily vehicle trips in and out of urban centres. An example would be plumbing repair trucks that service both city offices and residents. All service-related vehicles add, in smaller proportions, to the commercial vehicle traffic present in city centres. Estimates from cities across the United States show that service trips represent only 10% of total freight trips generated (Holguín-Veras et al., 2018c); but in terms of parking needs, the effects may be larger. Studies show that service vehicles stay longer in parking spots, limiting curb space for freight vehicles [START_REF] Campbell | Freight and Service Parking Needs and the Role of Demand Management[END_REF].

Understanding urban economies and how these relate to urban freight and service activity is imperative to addressing the key challenges faced in city logistics. Policy makers will need, as a key indicator of this activity, accurate quantification of commercial vehicles that carry freight and services on a daily basis. Yet, data related to the count of trucks, semi-trailers and tractor-trailers may be limited, or unavailable at a city or metropolitan level. At this level, data on the number of trips taken by vans, sport utility vehicles (SUVs), crossovers, and small vehicles, which represents approximately 90 percent of all urban deliveries in some U.S. metropolitan areas [START_REF] Bronzini | Relationships Between Land Use and Freight and Commercial Truck Traffic in Metropolitan Areas[END_REF], is rarely available.

The main goal of this chapter is to put in the hands of the transportation community a cogent characterization of urban economies and the freight and service activity (FSA) they generate. Doing so will help transportation planners and decision-makers to understand the interconnections between the economy and FSA, and to gain an idea about the magnitude of the latter. In doing so, the chapter exploits a series of generation models of FSA which have been developed in multiple countries.

To pursue this goal, the authors selected a number of metropolitan areas of different sizes and from countries in different income ranges, analyzed key economic data and generated estimates for FSA at some of these urban centres. The models used correspond to New York and Albany, NY, United States (Holguín-Veras et al., 2017a), Oslo [START_REF] Caspersen | An Explorative Approach to Freight Trip Attraction in an Industrial Urban Area[END_REF] and Medellin [START_REF] Gonzalez-Calderon | Characterization and Analysis of Metropolitan freight patterns in Medellin, Colombia[END_REF]. Other cities where the models are available were included as well, as with Paris and Lyon (France), for which models have been built from a national rather than city-based database [START_REF] Gonzalez-Feliu | Aggregation Level, Variability and Linear Hypotheses for Urban Delivery Generation Models[END_REF]. The estimates provide a sense of the number of freight and service-related commercial vehicles moving daily in the areas considered, and result in FSA rates that can be transferred to other cities where no empirical estimates are available.

The chapter is divided as follows: The first couple of sections provide a brief overview of the selection of the metropolitan areas, and the data and models used to develop the analysis. The third section provides an initial analysis of the urban economies, followed by an in-depth analysis of those economies by industry sector. The subsequent sections provide the estimates of freight and service generation, and their relationship to urban economies for a subset of metropolitan areas, where FSA rates are provided and analyzed.

Metropolitan Areas Selected for the Analyses

For the analyses of urban and metropolitan economies and their implications regarding FSA, a selection of metropolitan areas around the world was developed. These urban areas belong to countries with different income ranges located on a number of continents. Based on the United Nations' 2015 ranking for urban agglomerations and metropolitan areas that exceed 300,000 in population (United Nations, 2014b), the selection was developed for three different classes: Class I, with populations between 6 to 22 million; Class II, with populations between 2 and 6 million; and Class III, with populations of less than 2 million. Each class size includes at least a metropolitan area from a high-income country and a middle-upper income country, as defined by United Nations (2014a). Table 1 shows the selected metropolitan areas and their classifications, followed by a brief description of each region represented. Note: Establishment refers to a place of business, which could be local or a branch location of a larger business.

Sao Paulo, Brazil

The metropolitan area of São Paulo (RMSP) is Brazil's largest, with 21 million inhabitants, distributed over 39 municipalities and 7,947 square kilometers (IBGE, 2017). It is the fourth largest urban agglomeration in the world, and concentrates nearly 18% of Brazil's total GDP in its important industrial and commercial complexes [START_REF] Brookings | Sao Paulo Metropolitan Area Profile[END_REF]. The latest statistics show that there were over 7 million jobs in nearly 450 thousand establishments in RMSP (Brazilian Ministry of Labour, 2016). The RMSP concentrates diversified and specialized services with special highlights in the areas of communications, culture, education, health, transportation and gastronomy. Additionally, it is an important centre for business tourism in Latin America, as well as for numerous multinational companies.

New York, NY, United States

The New York City metropolitan area is the largest in the United States, and includes the cities of Newark and Jersey, and neighboring counties located in the three states of New York, New Jersey and Pennsylvania, with 21 million inhabitants and extending 21,483 square kilometers. It reported a GDP per capita of USD $70,758 in 2016, a growth of 1.04% from the first statistic recorded in 2001 (U.S. Bureau of Economic Analysis, 2017). The latest statistics show that the number of non-agricultural jobs in the region is over 8 million (US Bureau of Labor Statistics, 2016). It is an important financial centre, and host to many national and international headquarters, particularly in the technology, real estate and insurance sectors. Also known as the "capital of the world," the city receives an estimated 59.7 million tourists each year [START_REF] Mcgeehan | Record Number of Tourists Visited New York City in 2015, and More Are Expected This Year[END_REF], with very active food and accommodation sectors.

Paris, France

The metropolis of Greater Paris-which refers to the administrative multi-town structure within the Île-de-France region-includes the city of Paris and the departments located in the "inner ring" of the region: Haut-de-Seine, Seine-Saint-Denis and Val-de-Marne. It has more than 7 million inhabitants, covers 762 square kilometers (Institut National de la Statistique et des Etudes Economiques-INSEE, 2018) and generates a GDP per capita of 97 thousand euros (Eurostat, 2018). It has total employment of 4 million and more than 600 thousand establishments in 2016 for the metropolis of Greater Paris (Institut National de la Statistique et des Etudes Economiques-INSEE, 2018). It is a smaller area within the most populated urban area in France, the Île-de-France region, with more than 12 million inhabitants (Île-de-France, 2018). The main economic activities are retailing and services-excluding public administration, but including transport and logistics (CCI Paris Île-de-France, 2017).

Phoenix, AZ, United States

Phoenix is the largest city of the state of Arizona and a major economic centre of the southwestern United States. The metropolitan area includes the city of Phoenix plus the cities of Mesa and Scottsdale, spans 37,725 square kilometers, and is home to 4.7 million inhabitants (US Bureau of Labor Statistics, 2016). The most recent GDP per capita measured for the Phoenix metro area (AZ) was USD $43,602 in 2016, slightly lower than the one reported in 2001 (U.S. Bureau of Economic Analysis, 2017). Employment, on the other hand, has grown faster than the national rate for the past five years, reporting over 1.6 million employees and nearly 95 thousand establishments (U.S. Census Bureau, 2016;[START_REF] Heraldo | Área Metropolitana, ¿Quiénes Somos?, ¿A Dónde vamos?[END_REF]. The city boasts a healthy job market with large aerospace and defense companies, as well as a growing market of technological companies, all attracted to Phoenix's lower cost of living compared with other metropolitan areas in the west.

Medellín (Valle de Aburrá), Colombia

Medellin is the second largest city in Colombia after its capital, Bogota. Its metropolitan area includes nine neighboring urban areas, known as the Valle de Aburrá metropolitan area. Its area extends to 1,157 kilometers, with a total of 3.8 million inhabitants. The data collected shows a total employment of more than 1.7 million (Área Metropolitana del Valle de Aburrá et al., 2012), and its metropolitan area makes the second highest contribution to the country's GDP, with nearly USD $8,500 per capita (Camara de Comercio de Medellín Para Antioquia, 2017). It is an important industrial urban area considering its manufacturing activity, and its international trade is also very active, with an international airport that handles a huge percentage of Colombia's imports and exports for different industry sectors, particularly the floriculture sector.

Puebla-Tlaxcala, Mexico

The metropolitan area of Puebla-Tlaxcala is the fourth largest in Mexico, with a total population of 2.9 million, according to the 2015 census (Instituto Nacional de Estadistica y Geografia -INEGI, 2018). The city of Puebla, its urban core, represents almost 50% of the population of the entire metropolis, and it reported a GDP per capita of USD $5,131 (Les Ateliers, 2012). The metropolitan area is composed of thirty-eight municipalities (Consejo Nacional de Planeacion, 2010). The metropolitan area reported an employment of 1 million, and 135 thousand establishments (Instituto Nacional de Estadistica y Geografia -INEGI, 2018). Puebla's economy was historically known for its industrial corridors, which have slowly been replaced by service sectors. This shift, so highly concentrated in its core city, has been accompanied by a reduction of economic activity (Puebla Online, 2018).

Barranquilla, Colombia

Barranquilla is the fourth largest city in Colombia, and the second largest in the Caribbean Basin after Miami FL. Its metropolitan area includes the city of Barranquilla and the municipalities of Puerto Colombia, Soledad, Malambo, and Galapa (US Commercial Service and Amcham Colombia, 2015). It has nearly 2 million inhabitants, and extends 520 square kilometers [START_REF] Heraldo | Área Metropolitana, ¿Quiénes Somos?, ¿A Dónde vamos?[END_REF]. In 2016, it reported over 900 thousand employees and a GDP per capita of USD $6,140 (Departamento Administrativo Nacional de Estadistica-DANE, 2018). It has been acknowledged as Colombia's Golden Gate Way due to its important maritime and river ports, which receive 60% of the metal and 40% of the steel consumed in Colombia (US Commercial Service and Amcham Colombia, 2015). Barranquilla is a dynamic industrial and commercial activity centre, with such important sectors as metalmechanics, logistics, energy and business services (PROCOLOMBIA, 2018).

Lyon, France

The Grand Lyon Metropolis is the second largest metropolitan area in France. It includes 59 municipalities, has a surface area of about 538 square kilometers, and counted 1.3 million inhabitants in 2014 (La Métropole de Lyon, 2018). It has a GDP per capita of 43,300 euros, occupying the thirteenth place among European cities (Le [START_REF] Progrès | C'est, en pourcentage, la part du Produit intérieur brut (PIB) de la nouvelle Région[END_REF]. The most recent data collected reported more than 600 thousand employees and 100 thousand establishments (Institut National de la Statistique et des Etudes Economiques-INSEE, 2018). The main industrial sectors are chemistry/environment and pharmaceutical production, digital and image industries and automotive manufacturing (Grand Lyon Economie, 2017).

Oslo (Greater Oslo region), Norway

Oslo is the capital of Norway, and the country's economic and governmental centre, as well as a traffic and cultural hub. The Greater Oslo region includes Oslo and another 45 surrounding municipalities that are both economically and socially connected to Oslo, covering an area of 8,894 square kilometers (Statistics Norway, 2018a). The region was home to 1.57 million people in 2015, which is approximately 30% of Norway's population (Statistics Norway, 2018b)and was one of Europe`s fastest growing in the last decade (Eurostat, 2017). Over 200 thousand establishments and nearly 900 thousand employees were registered in the region in 2015, of which approximately half were registered in the city of Oslo (Statistics Norway, 2018a).

Santiago, Dominican Republic

Santiago is the second largest city in the Dominican Republic, with a population of 577 thousand with an area of 524 square kilometers. Employment in Santiago has grown significantly in the past decade, as a result of the country's economic growth, with more than 450 thousand employees reported in 2016, and a GDP per capita of USD $12,626 (Banco Central de la República Dominicana, 2018). The city is located in a fertile region, the Cibao Valley, where cacao, coffee, tobacco, rice, and other agricultural export products are grown. The city's main economic activities are processing the region's agricultural products, as well as manufacturing tobacco products, pharmaceuticals, furniture and leather goods (Oficina Nacional de Estadistica-ONE, 2018).

Data and Models

Data Collected

This section describes the data collected to analyze the economies of the selected metropolitan areas. The data used for the analyses consists of the counts of establishments and employment per industry sector. The main source of these data are listed below, in Table 2. All datasets contain, for the entire metropolitan area, employment and establishment totals, and by industry sector. Given that the industry sectors were different among countries, a cross-referencing of these to the North American Industry Classification System (NAICS) had to be developed as part of the study. As Table 2 also highlights, some of the data is obtained from the census of establishments and business records in the respective Chambers of Commerce, while others were obtained from reports produced or estimates developed from secondary sources. The latter were used only if no primary data was available.

Freight and Service Generation Models

To assess the magnitude of FSA in cities, the authors applied state-of-the-art models to estimate daily freight and service vehicle trips in selected metropolitan areas. Freight Trip Generation (FTG) models were used for daily freight trips, which include daily freight trips produced and attracted to the establishment. Service Trip Generation (STA) models were used to estimate service trips. The limited data available from the service sector only captures Service Trip Attraction (STA), but not Service Trip Production.

The FTG models are available for the following geographical areas: New York and Albany, NY (United States), Paris and Lyon (France), Medellin (Colombia), and Oslo (Norway). The STA models are available for New York and Albany, NY (United States). These were linear and nonlinear Ordinary Least Square (OLS) models, as a function of industry type and employment, as shown in Equations 1 and 2, respectively. In the case where the values were reported per week, respective values per day were calculated, assuming that the firm operates for an average of 5.5 days per week.

Linear model:

E E f * ) (     (1) Non-linear model:   E E f * ) (  (2)
Where f stands for FTG or STA. The nonlinear model in Equation 2 is a result of natural log transformation of dependent and independent variables, as given below in Equation 3:

) ln( * ) ln( E A f    (3)
Also for the nonlinear model, the log transformation bias is corrected by considering Mean Squared Error (S 2 ) in the calculation of α, as given in Equation 4, where 'exp' represents exponential function [START_REF] Newman | Regression Analysis of Log-Transformed Data: Statistical Bias and its Correction[END_REF].

2 exp( ) 2 S A    (4)
Table 2 shows the summary of the models available. A brief description of the models used to estimate freight and service trips for the analysis is provided below.

FTG Models for the USA Freight Trip Generation (FTG) and Service Trip Attraction (STA) models were developed from survey data collected from establishments located in the New York City metropolitan area, and the New York State Capital District (i.e. Albany, NY and surrounding cities), as part of research funded by the National Cooperative Highway Research Program and the National Cooperative Freight Research Program (Holguín-Veras et al., 2017a). These establishment-level models are solely based on employment, and were developed by industry sector, based on the North American Industry Classification System (NAICS). Specifically, these are estimates for daily shipments sent, and deliveries received, at a two-digit level NAICS for the two US cities mentioned. FTG is the result of the total of daily shipments and deliveries, under the assumption that one freight shipment sent equals one freight trip produced, and one freight delivery received equals one freight trip attracted.

The models were implemented in the Freight and Service Activity Generation Software (Holguín-Veras et al., 2017b), where an aggregation procedure was developed to automatically generate the estimates for any city in the United States, using as input the Census Business Patterns (CBP) database. Through the software, models have been successfully applied to a number of large cities in the United States (Holguín-Veras et al., 2018c).

FTG Models for France

The FTG models for France are based on the work of Gonzalez-Feliu et al. ( 2016) and Sanchez-Diaz et al. ( 2016). Data collected from the French surveys on urban goods [START_REF] Ambrosini | Urban Freight Establishment and Tour Based Surveys for Policy Oriented Modelling[END_REF] were used to propose a set of models integrating a statistical analysis (mainly dispersion), and the FTG framework from Holguín-Veras et al.

FTG for Medellin

The FTG models for Medellin were estimated using survey data collected in 2011-2012. The surveys were conducted in 2947 establishments in the urban area [START_REF] Gonzalez-Calderon | Characterization and Analysis of Metropolitan freight patterns in Medellin, Colombia[END_REF]. The FTG models were estimated by industry sector. The estimates developed consist of daily shipments (production) and deliveries (attraction) at a two-digit level based on the International Standard Industrial Classification of All Economic Activities (ISIC). The estimates are for both FIS and SIS commercial establishments. Similar to the models for New York City and Albany, the estimates for FTG assume that one freight shipment sent equals one freight vehicle trip produced, and that one freight delivery received equals one freight vehicle trip attracted.

FTG Models for Oslo

The FTG models for Oslo were developed using survey data collected from establishments in Groruddalen, an urban area in the eastern part of Oslo, Norway. It covers four of Oslo's boroughs, and a wide spectrum of commercial and private activities. The survey was conducted in 2016, and inquired about the number of freight and service vehicles moving to and from the surveyed establishments during a typical week, as well as establishmentspecific characteristics [START_REF] Caspersen | An Explorative Approach to Freight Trip Attraction in an Industrial Urban Area[END_REF]. Resulting models were similar to the NCFRP 25 FTG models, except only non-linear models were estimated, as this relationship was the most suitable fit for the data, as explained in [START_REF] Caspersen | An Explorative Approach to Freight Trip Attraction in an Industrial Urban Area[END_REF].

Metropolitan Economies

To start the analyses of metropolitan economies, it is crucial to get a global picture of the economic activity in metropolitan areas. To develop the analysis, the authors observed key economic data (i.e. GDP, employment and establishments) from the selected metropolitan areas. This section highlights the relationship between population, economic indicators (i.e. GDP per capita) and the size of the economic activity (establishments and employment) at each metropolitan area.

To understand where these metropolitan areas stand in terms of population and economic activity, a ranking was developed for each of the cities, as shown in Table 4. The first three cities in the population ranking are some of the largest cities in the world. In the Americas, for instance, Sao Paulo is the second highest after Mexico City. New York follows as third highest, and is the largest metropolitan area in the United States. These same cities are the top three in the establishments and employment rankings, clearly corroborating what [START_REF] Kötter | Developing Urban Indicators for Managing Mega Cities[END_REF] mentioned about these cities being the centres and junctions of the global economy.

Based on population ranking, the metropolitan areas that follow are not as large, but fall in the category of cities where a significant proportion of the world's population live. In 2016, 1.7 billion people (23 percent of the planet's population) lived in a city with fewer than one million inhabitants (United Nations, 2016). Also, as shown in Table 4, some of these cities fall naturally in order of employment as well, which suggests that there is a correlation between employment and population size. In terms of establishment numbers, less populated cities such as Lyon have climbed up in ranking. A larger number of establishments is very common in the French context, where cities have a large proportion of small single-employee establishments. Santiago is the smallest of all the cities, but belongs to the category of cities that are expected to increase most rapidly in the next decade, according to the United Nations (2016) report. Also, as expected, it is the smallest in terms of establishments and employment.

In terms of income, GDP per capita clearly separates the cities belonging to high-income countries-i.e. France, Norway, and the United States-and the cities belonging to the middle-upper income countries-i.e. Brazil, Dominican Republic, Colombia and Mexico. There seems to be no clear connection between income and intensity of economic activity, as initially observed by the rankings of number of establishments and employment. Nevertheless, these GDP rankings were important to understand the level of investment that can be made in these cities, particularly in terms of business improvements and the revitalization of city centres. To understand the relationship of population and economic activity, as evidenced by the rankings of the metropolitan areas analyzed, plots for the logarithm of the population with the logarithm of number of establishments and employment were developed, as shown in Figure 1 and 2, respectively. The number of establishments per city has a linear relationship with population, regardless of the level of economic development of the city. As seen in Figure 1, all cities show that as population increases, the number of establishments also increases. In the middle-upper income cities, the number of establishments per person ranges from 0.01 to 0.04, while high income economies show a range of establishments per person of from 0.02 to 0.09. The lowest result for this ratio in high income economies is for Phoenix, in the United States, and the largest value reported is for Paris, France. The difference between these cases is due to the types of businesses located in these urban areas. Paris and Lyon have a large number of small micro-enterprises, which significantly increases the number of establishments per person, while a greater concentration of large businesses reduces this ratio. The relationship between population and employment shows less variability, and does not exhibit significant outliers, as shown in Figure 2. Here, the same correlation is shown between establishments and population. With a median number of jobs per inhabitant of 0.41, these employment numbers reflect the high levels of economic activity concentrated in the metropolitan areas.

Understanding that there exists a correlation in the size of the economic activity with the size of the city can provide city planners with tools to assess the challenges involved in the movement of goods and services to city centres. For instance, more populous cities will have higher demands for freight and services than a smaller city, thus face a more critical situation. Further sections will expand on these opportunities, where estimates for freight and service are compared among cities of different sizes and urban economies.

Freight and Service Intensive Sectors

To grasp the intensity of freight and service activity (FSA), it is essential to get a better understanding of those sectors that generate the most freight traffic, and those that generate the most service traffic. Industry sectors were classified as Freight-Intensive Sectors (FIS) or Service-Intensive Sectors (SIS). The FIS are those industry sectors for which the production and consumption of freight is an important component of their economic activities. The SIS are those sectors where the provision of services is the primary activity. Table 5 shows the resulting classification of the sectors, based on the North American Industry Classification System (NAICS). As shown, FIS do not just consist of warehouses and manufacturing facilities. Restaurants, hotels, and retail stores also consume freight on a daily basis. Moreover, the proportion of economic activity in the FIS accounts for half of all of the economic activity. Previous research done on the metropolitan and micropolitan areas of the United States has determined that 45% of all commercial establishments are accounted for in FIS, and 50% of employment is generated in FIS (Holguín-Veras et al., 2018a). This implies that efficiency or inefficiencies encountered in the movement of goods in these sectors will have a direct impact on half of the economy, and an indirect impact on the other half. It is also worth mentioning that these previous studies found that Transportation and Warehousing accounts for only 2.8% of commercial establishments, and 3.6% of employment in the US, while 30-35% of employment is concentrated in the Retail and Wholesale businesses. This suggests that city centres that most likely do not have warehouses or manufacturing facilities are still receiving a lot of freight traffic, given the daily deliveries produced and shipments received in restaurants, hotels and retail stores.

The SIS, on the other hand, consists of all businesses that offer as their primary activity a given service or range of services to their customers. Banks, insurance companies, healthcare facilities, computer service enterprises, attorney offices, management consulting firms, plumbing repair companies, and cable services are all examples of service-oriented businesses. Even though the intensity of freight is not as pronounced for these establishments as it is with FIS, service activity does have a significant impact on passenger and commercial vehicle traffic. On the passenger side, SIS includes the daily commuting of employees to these businesses, and on the commercial side, SIS involves vehicles that are required to get to establishments to perform a given service. The latter has important implications for urban logistics, particularly parking, as these vehicles typically spend extended periods of time at an establishment while performing a service. Thus, taking into account the number of service vehicles operating on a daily basis is essential for accurate city planning.

To understand the impact of FIS and SIS, total establishments and employment were obtained by industry sector for some of the metropolitan areas of analyses, as shown in Table 6 and7.

Freight Intensive Sectors

The first section of Table 6 shows that the percentage of establishments in FIS is significantly lower in metropolitan areas from high-income countries, where these represent typically half or below half of all establishments. In the middle-high income countries, FIS represents the majority of the establishments. This is the case of Sao Paulo (Brazil), Medellin (Colombia), and Puebla (Mexico), where FIS establishments represent 69, 70, and 70 percent of the total, respectively. With regards to FIS employment, the case is similar. For instance, Medellin shows 52 percent of employment in these sectors, and Puebla (Mexico) shows an employment of 81 percent of the total. Table shows another interesting pattern regarding the estimates in different geographical areas. In European cities, for instance, the average employment per establishment is significantly lower than it is in cities in the United States. This was discussed earlier, for in French cities, as the data shows, there is a higher proportion of smaller establishments, where the average employment per establishment is 5 to 6. This is also reflected in Oslo, which has an average of 8 employees per establishment. In the United States, the value varies between 12 and 20 employees per establishment. As population increases in the high-income countries, the number of establishments per resident increases. In the case of medium-high income cities, there is a consistent pattern of employment per resident. As population decreases, the number of employees per 1000 residents generally increases.

Table 6 also shows a breakdown by industry sector belonging to FIS, where some interesting patterns are observed. The percent of establishments for the consumer-oriented sectors, such as Retail Trade (NAICS 44-45), Wholesale Trade (NAICS 42), and Food and Accommodation Services (NAICS 72), represents a large proportion of the FIS, where the percent of establishments and employments ranges from 44 to 80%. Particularly in the highincome cities, the Construction (NAICS 23) sector is also highly represented, as it accounts for 20 to 30 percent of all establishments in FIS, and 12 to 20 percent of all employment in FIS. In the middle-high income cities there is a higher representation of the Manufacturing (NAICS 31-33) sector, and a lower representation of Construction (NAICS 23) establishments. In Medellin, for example, the Manufacturing sector is 16 percent of the total, while in Phoenix this sector is only 8 percent of total. In the Construction sector, the opposite holds true. In Medellin, Construction is only 6 percent, while in Phoenix it is 21 percent of the total establishments. 3,692,120 3,234,208 1,223,215 781,065 910,914 847,033 600,962 231,690 309,636 268,369 6,174,605 8,285,112 3,788,321 1,671,907 1,762,895 1,049,807 911,529 618,205 763,503

Service Intensive Sectors

When analyzing the breakdown by SIS, as observed in Table 7, there are additional patterns that are worth noting. The share of establishments generated by these sectors ranges from 40 to 66 percent in all metropolitan areas, with the exception of Puebla (Mexico), where the representation of establishments in SIS is much lower. The share of employment generated by SIS sectors ranges from 45 to 68 percent, with the exception of Puebla (Mexico) and Barranquilla (Colombia) with a share of 19 and 34 percent of all employment in SIS, respectively.

With respect to those sectors that generate a significant share of the jobs in urban areas in SIS, there is the Health Care and Social Assistance (NAICS 62) sector, which is very well represented in some countries but not as well represented in other countries. For cities in the US, in particular, this sector represents 30 percent of all employment registered in SIS. This is not the case for the cities in France, where the Health Care sector only accounts for 10 to 12% of the employment in SIS. In the Colombian cities, this percentage is much lower, as it represents only 7 to 8% of the employment in SIS.

Other industry sectors belonging to SIS are also well represented across metropolitan areas, particularly those that are related to technological services and sales. The Real Estate (NAICS 53) sector is particularly important in the French cities, as it represents almost half of all establishments in SIS. In terms of employment, the percentage is much lower, which suggests that most of these establishments are composed of single-person employees. The Professional and Technical (NAICS 54) sector is also very well represented in the majority of metropolitan areas, and represents 20 to 38 percent of all establishments, and 13 to 28 percent of all employment in SIS.

Freight and Service Activity

This section presents the estimates for freight and service trips in metropolitan areas in different parts of the world. To accomplish this, the authors selected metropolitan areas where FTG and/or STA models have been estimated, as explained in Section 2. The estimation of daily freight and service trips in the metropolitan areas of New York (United States), Paris (France), Medellin (Colombia), Lyon (France), and Oslo (Norway) were estimated directly from their models, as explained in previous sections. The metropolitan area of Phoenix (United States) used the New York and Albany (United States) models.

Table 8 shows the resulting estimates of FSA, together with the total population, number of establishments, and employment. In addition, the authors decided to include a series of rates that express either FTG or STA as unit rates of population, number of establishments, and employment. These rates provide a pragmatic and very useful mechanism to produce order-of-magnitude estimates of FSA for cities and metropolitan areas for which only approximate estimates are needed, or there are no trip generation models, or the input data are not available. An analyst would only need to decide which metropolitan area from Table 8 provides the best match for the area under study, and then apply the selected rates to the population, number of establishments, or employment. As observed, the magnitude of FSA is evidenced by how large the city is in regards to the population and employment indicators. A large city like New York, which reports over 500 thousand establishments and 8 million employees, generates approximately 2 million freight trips, and 150 thousand service trips daily. For a smaller city, such as Oslo, these numbers are reduced to 110 thousand daily freight trips generated, and 14 thousand daily service trips attracted.

The estimates also show that in some cities, the amount of freight and service generated is much higher when compared to another city of similar size. The city of Paris, with 7 million residents, shows 2.2 million freight trips generated, and approximately 130 service trips attracted; as compared to New York-a city double the size of Paris-which generates approximately 2 million freight trips and 150 service trips. This difference is due to the increased number of establishments obtained from Paris' database, which increases the number of freight and service trips substantially. Even so, both megacities coincide with an average of 3.3 daily trips per establishment. Another example is the city of Lyon, which shows 3.4 daily freight trips per establishment. This rate is much higher than the one obtained in Oslo, which generates nearly 1.5 daily freight trips per establishment.

Different freight rates are also observed among cities with varied income levels. The case of Medellin is an example of this, where FSA is under represented in lower income countries. Medellin shows the lowest freight trips per establishment, approximately 1.8, and 57 daily freight trips per 1000 residents. A city of similar size, Phoenix, shows a higher proportion of freight activity, with 3.5 freight trips per establishment, and 72 freight trips per 1000 residents.

Freight Activity for Freight Intensive Sectors

To illustrate the importance of freight in metropolitan areas, estimates of daily freight trips were analyzed at each FIS, as shown in Table 9.

As shown, in the largest metropolitan areas, total daily freight trips in FIS range from 1.9 to 2.2 million, which translates to approximately 80 to 110 daily trips per 1000 residents. If internet deliveries are included, using the ecommerce freight rates of 0.12 per resident estimated by the authors using the National Household Transportation Survey, this indicator could climb to 200 daily trips per 1000 residents. With respect to individual industry sectors, cities like Paris have a unique share of establishments, as they have a large share from intermediaries in the supply chain, as observed by the Wholesale Trade (NAICS 42), sectors. These sectors generate approximately 15 daily freight trips per establishment. New York City displays a slightly different pattern, as their larger share of freight trips comes from the local and consumer-oriented establishments, such as Retail Trade and Wholesale Trade (NAICS 42). Both sectors generate approximately 9 daily freight trips per establishment.

The medium to large cities, as observed from the estimates for Phoenix (USA) and Medellin (Colombia), show similar patterns to each other in terms of daily freight trips in their FIS. The total daily trips are approximately 45-50 per 1000 residents. They both have Retail Trade as the industry sector with the highest share of trips. They display some differences in their freight patterns in other industry sectors. In the case of Phoenix, the FIS sectors that generate the highest freight trips include other consumer-oriented sectors, such as the Wholesale Trade (NAICS 42) and Accommodation and Food Services (NAICS 72). Together, all three sectors generate approximately 10 trips per establishment. For Medellin, the second place is occupied by the Manufacturing (NAICS 31-33) sector, which is common in a city that hosts 20% of the largest companies in Colombia, particularly the largest textile manufacturers. Both Retail Trade (NAICS 44-45) and Manufacturing (NAICS 31-33) generate approximately 3.6 daily freight trips per establishment in Medellin. The smaller metropolitan areas also produce a significant amount of daily freight trips, approximately 110 to 350 thousand. Even though less populated, these cities display higher freight rates than the larger cities (i.e., Phoenix and Medellin), most likely due to the higher economic activity observed in these smaller cities. In both Lyon and Oslo the value ranges between 80 to 180 daily freight trips per 1000 residents. If internet deliveries are included, these values could surpass the 200 daily FTG per 1000 residents estimated for megacities. In terms of the top freight generators, both cities have Wholesale Trade (NAICS 42) and Modal Transportation and Warehousing (NAICS 48-49) at the top, with a cumulative share of 50% of all freight trips in the FIS, and a rate per establishment of 17 daily trips for Lyon, and 4 daily trips for Oslo.

Service Activity for Service Freight Intensive Sectors

To illustrate the importance of service in metropolitan areas, estimates of daily service trips were analyzed at each SIS, as shown in Table 10. The total estimates for daily service trips within SIS vary across metropolitan areas, as shown in Table 10. Larger metropolitan areas, such as New York and Paris, have much higher estimates for STA; typically more than 130,000 service trips on a daily basis. The smaller metropolitan areas show much lower estimates for STA, around 14,000 daily trips. For the majority of cities, service trips typically represent between 4 to 13% of all freight trips. Yet these numbers should not be underestimated, as these trips contribute significantly to the lack of parking in city centres, as service vehicles stay for prolonged periods of time, preventing other commercial vehicles (i.e. delivery trucks) from parking and/or unloading supplies (Holguín-Veras et al., 2018b).

Total daily service trip rates vary across countries. In the cities belonging to the United States, these were approximately 7 daily STA per 1000 residents. In the case of the Colombian city, Medellin, this number was much lower, approximately 4 daily STA per 1000 residents. In the capital of Norway, the rate is 9 daily STA per 1000 residents. In the case of France, this rate varies, as Paris shows 19 daily STA, while Lyon estimates 10 daily STA per 1000 residents. In the individual industry sectors that belong to SIS, it seems that the larger proportion of service trips belongs to the Health Care and Social Assistance (NAICS 62) sector. In the US cities, 40% of all service trips typically relate to this sector. In the European cities, approximately 20% of all service trips are within this sector. Yet, in the city of a lower income country (i.e. Medellin) the proportion is lower, as this sector accounts for 15% of the total STA. The only exception is Oslo, which has Professional and Technical Services (NAICS 54) as its largest generator of service trips, representing 44% of total STA.

Besides the Other Services (NAICS 81) sector-which occupies second place in most of the cities analyzed-the second most important sector varies across cities. In the medium-sized cities, Phoenix and Medellin, the Finance and Insurance (NAICS 52) sector accounts for approximately 20% of all service trips. New York also has this sector as the second most important, but it only represents 8% of all service activity in the city. For Lyon, the Real Estate (NAICS 53) sector is the second most important. In Oslo, the second most important is the Health Care and Social Assistance (NAICS 62) sector, followed by the Education Services (NAICS 61) sector.

Conclusions

This chapter provides an international comparison of metropolitan areas and the relationship of their economic activity to the freight and service generated in these areas. Metropolitan areas in a range of population size, income levels and economic development were selected among countries in Europe and the Americas. The general analyses developed show that growing urban areas are economic powerhouses, which contribute to a large share of the country's economic activity. The chapter also evaluated the contribution of establishments by industry sector to the urban economies, and their connection to FSA. Breaking down the analysis between FIS and SIS provides a better understanding of how urban economies are directly related to the generation of freight and service vehicle trips.

The bulk of the analysis focuses on how the size, income, and economic activity of the cities' FSA. Cities that are among the largest in the world, such as New York and Paris, are generating millions of daily freight trips, and hundreds of thousands of daily service trips. Smaller cities (e.g. Oslo, Norway) are also generating a huge amount of daily freight trips, but the magnitude is only a fraction of the total generated in larger cities. Further, lower income cities show less daily freight activity, but these numbers may merely be underestimates of the freight trips generated from all the informal jobs that are not reported in official databases. Service activity is less critical in smaller cities, but should not be ignored, as it has important implications for city planning for parking and parking facilities, as service trip vehicles occupy parking for longer periods of time.

The analyses reveal that a series of FSA rates provide a very consistent picture of freight and service activity in metropolitan areas: the freight trip generation per establishments (freight trips/ establishment-day) ranges between 1.53 (Oslo, Norway) and 3.55 (Phoenix, USA); the service trip attraction per establishment (service trips/ establishment-day) ranges from 0.16 (Medellin, Colombia) to 0.37 (Phoenix, USA); the freight trip generation per employment (freight trips/employee-day) ranges between 0.12 (Medellin, Colombia) and 0.23 (New York, USA); the service trip attraction per employment (service trips/employee-day) ranges from 0.01 (Medellin, Colombia) to 0.02 (Phoenix, USA); the freight trip generation per 1000 residents per day (freight trips/1000 residents-day) ranges between 56.68 (Medellin, Colombia) and 95.47 (New York, USA); while the service trip attraction per 1000 residents per day (service trips/1000 residents-day) ranges from 4.96 (Medellin, Colombia) to 9.14 (Oslo, Norway). Due to the overestimation of FSA in the French cities, the authors decided not to include them in these ranges.

These analyses are just the beginning of what should be a much deeper discussion about urban economies and FSA across the world. The results provide city planners and practitioners with international FSA rates that must be carefully applied as references for cities where no data on commercial vehicle traffic is available.

  (2011) and[START_REF] Holguín-Veras | Transferability of Freight Trip Generation Models[END_REF]. The authors examined different levels of aggregation and functional forms. The models are structured in 26 categories, where results from the most robust model were identified by[START_REF] Sanchez-Diaz | Assessing the Implications of Aggregating Data by Activity-Based Categories for Urban Freight Trip Generation Modeling[END_REF] in terms of both prediction capacity and heterogeneity caption.

Figure 1 :Figure 2 :

 12 Figure 1: Number of Establishments and Population per City

Table 1 : Metropolitan Areas Selected for the Analyses

 1

	Metropolitan Areas	Population	Area (in km2)	Density (Pop/km2)	Country's Income		GDP per capita (in USD)	Number of Establish-ments	Total Employment
	Class I: From 6 to 22M inhabitants
	Sau Paulo, Brazil	21,391,624	7,947	2,692	Upper-Middle	$	16,650.00	436,424	6,174,605
	New York, NY, USA	20,153,634 21,483	938	High	$	70,758.00	575,333	8,285,112
	Paris, France	7,020,210	762	9,213	High	$	96,845.28	676,090	3,788,321
	Class II: From 2 to 6M inhabitants
	Phoenix, AZ, United States 4,661,537	37,723	124	High	$	43,602.00	94,568	1,671,907
	Medellin, Colombia	3,777,099	1,157	3,263	Upper-Middle	$	8,489.00	117,514	1,762,895
	Puebla, Mexico	2,941,988	2,392	1,230	Upper-Middle	$	5,131.55	134,928	1,049,807
	Class III: Less than 2M inhabitants
	Barranquilla, Colombia	1,991,000	520	3,829	Upper-Middle	$	6,140.15	49,874	911,529
	Lyon, France	1,370,678	534	2,567	High	$	45,554.71	105,377	618,205
	Oslo, Norway	1,570,000	8,894	177	High	$	82,040.00	72,263	763,503
	Santiago, Dominican Rep.	577,000	524	1,101	Upper-Middle	$	12,626.00	9,541	485,037

Table 2 : Sources of Data for Selected Metropolitan Areas Metropolitan Area(s) Source

 2

	Sao Paulo, Brazil	Instituto Brasileiro de Geografia e Estatística (IGBE 2017)
	New York, NY, United States	US Bureau of Labor Statistics (2016)
	Paris, France	Institut national de la statistique et des études économiques (2013)
	Phoenix, AZ, United States	US Census Bureau (2016;2017)
	Medellin, Colombia	Area Metropolitana del valle de Aburra et al (2012)
	Puebla, Mexico	Instituto Nacional de Estadistica y Geografia -INEGI (2018)
	Barranquilla, Colombia	Dane (2015)
	Lyon, France	Grand Lyon Economique (2017)
	Oslo, Norway	Statistics Norway (2018)
	Santiago, Dominican Republic	Oficina Nacional de Estadistica-ONE (2018)

Table 3 : Functional Forms Available for Freight Activity in the Cities

 3

			Freight	Freight
	Metropolitan Area(s)	Functional Forms Available	Deliveries	Shipments	FTG	STA
			Received	Sent
	New York, USA	Linear Non-linear	x x	x x		x x
	Paris and Lyon, France	Linear			x
	Medellin, Colombia	Constant	x	x
	Oslo, Norway	Non-linear			x

Table 4 : Ranking of Metropolitan Areas

 4

	Rank	Population	GDP per capita (in USD)	Establishments	Employment
	1	Sao Paulo, Brazil	Paris, France	Paris, France	New York, NY, US
	2	New York, NY, US	Oslo, Norway	New York, NY, US	Sao Paulo, Brazil
	3	Paris, France	New York, NY, US	Sao Paulo, Brazil	Paris, France
	4	Phoenix, AZ, US	Lyon, France	Puebla, Mexico	Medellin, Colombia
	5	Medellin, Colombia	Phoenix, AZ, US	Medellin, Colombia	Phoenix, AZ, US
	6	Puebla, Mexico	Sao Paulo, Brazil	Lyon, France	Puebla, Mexico
	7	Barranquilla, Colombia	Santiago, Dominican Rep	Phoenix, AZ, US	Barranquilla, Colombia
	8	Oslo, Norway	Medellin, Colombia	Oslo, Norway	Oslo, Norway
	9	Lyon, France	Barranquilla, Colombia	Barranquilla, Colombia	Lyon, France
	10	Santiago, Dominican Rep	Puebla, Mexico	Santiago, Dominican Rep Santiago, Dominican Rep

Table 5 : Classification of Industry Sectors based on FSA

 5

	NAICS	Freight-Intensive Sectors (FIS)	NAICS	Service-Intensive-Sectors (SIS)
	11 Agriculture, Forestry, Fishing, Hunting	51 Information
	21 Mining, Quarrying, Oil / Gas…	52 Finance and Insurance
	22 Utilities	53 Real Estate and Rental and Leasing
	23 Construction	54 Professional,Scientific,Tech. Services
	31-33 Manufacturing	55 Management of Companies /
	42 Wholesale Trade	56 Administrative,Support,Waste Manag.
	44-45 Retail Trade	61 Educational Services
	48-49 Transportation and Warehousing	62 Health Care and Social Assistance
	72 Accommodation and Food Services	71 Arts, Entertainment, and Recreation
			81 Other Services
			92 Public Administration

Table 6 : Establishments and Employment by FIS NAICS Description

 6

	Sao Paulo,	Brazil	New York,	NY, US	Paris, France	Phoenix, AZ,	US	Medellin,	Colombia	Puebla,	Mexico	Barranquilla,	Colombia	Lyon, France	Oslo,	Norway	Santiago,	Dominican	Rep

Table 7 : Establishments and Employment by SIS

 7

	NAICS	Description		Sao Paulo,	Brazil	New York,	NY, US	Paris,	France	Phoenix,	AZ, US	Medellin,	Colombia	Puebla,	Mexico	Barranqui	lla,	Colombia	Lyon,	France	Oslo,	Norway	Santiago,	Dominican	Rep
							Establishments
	51	Information		5%	4%	5%	3%	7%	1%		5%		3%	5%		3%
	52	Finance and Insurance		7%	9%	8%	12%	13%	5%		9%		8%	3%		8%
	53	Real Estate		26%	11%	48%	12%	5%	6%		2%		50%	11%		8%
	54	Prof and Technical Services		34%	22%	2%	23%	27%	4%	23%		3%	38%	22%
	55	Management of Companies		0%	1%	0%	1%	2%	0%		1%		0%	0%		0%
	56	Administrative and Waste Mgmt		1%	9%	0%	10%	15%	9%	11%		1%	10%		7%
	61	Education Services		8%	3%	3%	3%	3%	7%		3%		3%	5%		6%
	62	Health Care and Social Assistance		16%	19%	2%	21%	7%	16%		7%		3%	12%	19%
	71	Entertainment		3%	4%	4%	2%	4%	2%		3%		1%	4%		5%
	81	Other Services		0%	19%	29%	13%	18%	50%	36%		28%	12%	22%
	Number of establishments (SIS)	135,097	325,124 448,096 57,352	34,847	35,154 20,327 69,805 33,214 4,262
	% SIS Establishments of Total		31%	57%	66%	61%	30%	26%	41%		66%	46%	45%
								Employment
	51	Information		6%	6%	9%	4%	5%	3%		9%		8%	7%		3%
	52	Finance and Insurance		10%	12%	12%	14%	9%	6%		5%		7%	5%		8%
	53	Real Estate		23%	4%	12%	4%	2%	4%		2%		9%	3%		8%
	54	Prof and Technical Services		29%	15%	3%	13%	13%	2%	22%		5%	28%	22%
	55	Management of Companies		0%	5%	0%	5%	1%	0%		1%		0%	0%		0%
	56	Administrative and Waste Mgmt		2%	9%	15%	16%	56%	13%	11%		20%	14%		7%
	61	Education Services		11%	7%	8%	5%	1%	25%		3%		13%	12%		6%
	62	Health Care and Social Assistance		16%	30%	10%	27%	8%	16%		7%		12%	22%	19%
	71	Entertainment		3%	4%	4%	4%	1%	2%		3%		1%	3%		5%
	81	Other Services		0%	8%	26%	7%	4%	30%	37%		25%	6%	22%
	Employment (SIS)	2,482,485 5,050,904 2,565,106 890,842 851,981 202,774 310,567 386,515 453,867 216,668
	%SIS Employment of Total		40%	61%	68%	53%	48%	19%	34%		63%	59%	45%
								Rates
	Establishments (SIS) per 1000 residents		6.32	16.13	63.83	12.30	9.23	12.88	10.21	50.93	21.16		7.39
	Employment (SIS) per 1000 residents		116.05	250.62	365.39	191.10	225.56	74.31	155.99 281.99 289.09 375.51
	Average Employment per Establishment (SIS)	18.38	15.54	5.72	15.53	24.45	5.77	15.28	5.54	13.66	50.84

Table 8 : Key Statistics per Metropolitan Areas

 8

	Description	New York, NY,	United States	Paris, France*	Phoenix, AZ,	United States	Medellin,	Colombia	Lyon, France*	Oslo, Norway
	FTG (FIS)	1,924,153	2,221,769	336,115	214,082	357,125	110,462
	Freight Shipments (FIS)	1,031,160	1,199,755	157,355	117,139	192,847	52,249
	Freight Deliveries (FIS)	892,993	1,022,014	178,760	96,943	164,277	58,214
	STA (SIS)	152,758	131,472	34,522	18,750	11,565	14,343
	Population	20,153,634	7,020,210	4,661,537	3,777,099	1,370,678	1,570,000
	Area (in km2)	21,482.85	762.00	37,723.28	1,157.39	534.00	8,894.00
	Density (pop per km2)	938.13	9,212.87	123.57	3,263.46	2,566.81	176.52
	GDP per capita (in USD)	70,758.00	96,845.28	43,602.00	8,489.00	45,554.71	82,040.00
	Establishments	575,333	676,090	94,568	117,514	105,377	72,263
	Employment	8,285,112	3,788,321	1,671,907	1,762,895	618,205	763,503
	FTG per establishment	3.344	3.286	3.554	1.822	3.389	1.529
	STA per establishment	0.266	0.194	0.365	0.160	0.110	0.198
	FTG per employment	0.232	0.586	0.201	0.121	0.578	0.145
	STA per employment	0.018	0.035	0.021	0.011	0.019	0.019
	FTG per 1000 residents	95.474	316.482	72.104	56.679	260.546	70.358
	STA per 1000 residents	7.580	18.728	7.406	4.964	8.437	9.135

Estimates of Freight and Service Activity (FSA) Key Socio-Economic Descriptors FSA Rates

  Data collected from these metropolitan areas include a significant number of small micro-enterprises, which increases the number of establishments per person and overestimates the values for FTG and STA.

*

Table 9 : FTG for Selected Metropolitan Areas in FIS

 9

	NAICS	Description	New York, NY,	United States	Paris, France	Phoenix, AZ,	United States	Medellin,	Colombia	Lyon, France	Oslo, Norway
			Freight Trip Generation
	23	Construction	8.8%	19.0%	10.5%	5.4%	18.7%	16.3%
	31-33 Manufacturing	7.9%	8.0%	10.7%	10.8%	11.7%	7.4%
	42	Wholesale Trade	20.3%	27.2%	15.9%	5.8%	26.2%	19.1%
	44-45 Retail Trade	35.5%	8.1%	40.4%	67.8%	9.7%	18.9%
	48-49 Transportation & Warehousing	14.2%	24.7%	6.1%	3.8%	22.2%	30.5%
	72	Accommodation and Food Services	13.3%	13.0%	16.5%	6.5%	11.5%	7.8%
	Total Freight Trip Generation (FIS)	1,924,153 2,221,769 336,115 214,082	357,125	110,462
			Internet Deliveries
	Population	20,153,634 7,020,210 4,661,537 3,777,099 1,370,678 1,570,000
	Internet Deliveries (Ratio=0.12)	2,418,436	842,425	559,384 453,252	164,481	188,400
	Total FTG Daily Trips (incl online deliveries)	4,342,589 3,064,194 895,499 667,334	521,606	298,862
			Freight Trip Rates
	Daily FTG per 1000 residents	95.474	316.482	72.104	56.679	260.546	70.358
	Daily FTG per 1000 residents (incl online deliveries) 215.474	436.482	192.104 176.679	380.546	190.358
	Daily FTG per Establishment	3.344	3.286	3.554	1.822	3.389	1.529
	Daily FTG per Employment	0.232	0.586	0.201	0.121	0.578	0.145

Table 10 : STA for Selected Metropolitan Areas

 10

	NAICS	Description	New York, USA	MSA	Paris, France	MSA	Phoenix AZ,	USA	Medellin,	Colombia MSA	Lyon, France	MSA	Oslo, Norway	MSA
		Service Trip Attraction
	51	Information	6.3%	13.0%	2.7%	7.6%	2.9%	2.8%
	52	Finance and Insurance	8.0%	11.4%	17.5%	20.5%	9.9%	3.1%
	53	Real Estate	0.1%	0.2%	0.1%	0.1%	20.4%	2.0%
	54	Professional and Technical Services	0.5%	0.1%	15.0%	19.8%	7.5%	44.3%
	55	Management of Companies	1.0%	0.0%	1.1%	1.5%	0.0%	0.1%
	56	Administrative and Waste Management	7.7%	0.7%	5.0%	8.3%	0.5%	4.5%
	61	Education Services	0.7%	0.4%	1.9%	2.5%	13.1%	14.3%
	62	Health Care and Social Assistance	45.9%	6.7%	41.9%	15.1%	9.1%	18.8%
	71	Entertainment	7.1%	11.9%	2.8%	5.7%	1.7%	2.9%
	81	Other Services (except Public Admin)	22.7%	55.6%	12.0%	18.9%	35.0%	7.3%
	Service Trip Attraction (SIS)	152,758	131,472	34,522	18,750	13,708	14,343
	Freight Trip Generation (FIS)	1,924,153 2,221,769 336,115 214,082 357,125 110,462
	% Service Trips of Freight Trips	8%	6%	10%	9%	4%	13%
		Service Trip Rates
	Daily STA (SIS) per 1000 residents	7.580	18.728	7.406	4.964	10.001	9.135
	Daily STA (SIS) per Establishment	0.266	0.194	0.365	0.160	0.110	0.198
	Daily STA (SIS) per Employment	0.018	0.035	0.021	0.011	0.019	0.019


Meng Liang

Anne Hébraud

Guy Schlatter
email: schlatter@unistra.fr

Modeling and on-line measurement of the surface potential of electrospun membranes for the control of the fiber diameter and the pore size

Keywords: electrospinning, modeling, fibrous morphology

Modeling and on-line measurement of the surface potential of electrospun membranes for the control of the fiber diameter and the pore size

Introduction

Electrospinning is a widespread technology enabling the fabrication of nanofibrous materials with most of the polymers available on the market and for a wide range of applications such as filtration [START_REF] Wang | Electret Polyvinylidene Fluoride Nanofibers Hybridized by Polytetrafluoroethylene Nanoparticles for High-Efficiency Air Filtration[END_REF], tissue engineering [START_REF] Nedjari | Electrostatic template-assisted deposition of microparticles on electrospun nanofibers: towards microstructured functional biochips for screening applications[END_REF], and biomedical applications [START_REF] Jang | Electrospun materials as potential platforms for bone tissue engineering[END_REF][START_REF] Chew | Sustained Release of Proteins from Electrospun Biodegradable Fibers[END_REF][START_REF] Thorvaldsson | Electrospinning of Highly Porous Scaffolds for Cartilage Regeneration[END_REF]. The principle of the process consists in subjecting a polymer solution droplet to a high electric field in the order of 1 kV/cm which induces the emission of a liquid jet toward a grounded counter-electrode, the socalled collector, located about 10-20 cm away from the jet emission. During its flight in the air, the electrified and charged jet is experiencing whipping movements allowing an efficient stretching and the solvent evaporation. A continuous fiber having a diameter in the range of 100-1000 nm is pseudo-randomly deposited in the form of a non-woven membrane. By playing with the material properties (polymer molar mass, concentration, nature of the solvents…) as well as the processing parameters (applied voltage, solution flow rate, jet emission-to-collector distance, collector geometry, air temperature and humidity…), membranes with various morphological and physical properties (fiber diameter, membrane pore size, polymer crystallinity, mechanical properties…) can be elaborated [START_REF] Xue | Electrospinning and Electrospun Nanofibers: Methods, Materials, and Applications[END_REF][START_REF] Zhu | Electrospun Nanofibers Membranes for Effective Air Filtration[END_REF][START_REF] Jiang | Electrospinning of polymer nanofibers for tissue regeneration[END_REF]. Because electrospinning is currently emerging in the industry, it is thus of prime importance to provide a robust online process monitoring.

Several articles deal with the effect of solution and processing parameters on the current reflecting the amount of charges carried by the electrospun jet [START_REF] Samatham | Electric current as a control variable in the electrospinning process[END_REF][START_REF] Yener | On the Measured Current in Needle-and Needleless Electrospinning[END_REF][START_REF] Shin | Experimental characterization of electrospinning: the electrically forced jet and instabilities[END_REF]. Current measurement is easy to implement. Indeed, by installing a resistor between the collector and the ground, the measurement of the difference of potential through the resistor allows calculating the electrospinning current thanks to the Ohm's law. Nevertheless, the current is mainly related to the processing conditions, such as the imposed electric field and solution flow rate and its conductivity. It doesn't give any information neither on the amount of charges remaining in the membrane during and after electrospinning nor on the internal structure of the fibrous membrane. The online measurement of the surface potential resulting from the residual charges accumulating in the membrane during its fabrication may be an efficient way to get complementary information on the membrane during its fabrication. Such online control could help (i) to fine tune the processing conditions which can fluctuate during the time of production and (ii) to have an immediate action on the process when these fluctuations occur. Researchers highlighted that residual charges remaining on the deposited fiber may represent an important amount of the total charges carried by the fiber just before its landing on the collector [START_REF] Choi | Residual Charges during Electrospinning Assist in Formation of Piezoelectricity in Poly(Vinylidene Fluoride-co-Trifluoroethylene) Nanofibers[END_REF]. In electrospinning, charges are present due to dipole orientation, space charge separation and direct injection of charges into the fibers [START_REF] Lowell | Absorption and conduction currents in polymers: a unified model[END_REF][START_REF] Catalani | Evidence for Molecular Orientation and Residual Charge in the Electrospinning of Poly(butylene terephthalate) Nanofibers[END_REF][START_REF] Ignatova | Study of charge storage in the nanofibrous poly(ethylene terephthalate) electrets prepared by electrospinning or by corona discharge method[END_REF][START_REF] Gao | Electret mechanisms and kinetics of electrospun nanofiber membranes and lifetime in filtration applications in comparison with corona-charged membranes[END_REF]. Understanding, how charges accumulate on the membrane during its fabrication and how charges dissipate through its thickness is also necessary for applications dealing with electret filters for air cleaning [START_REF] Wang | Electret Polyvinylidene Fluoride Nanofibers Hybridized by Polytetrafluoroethylene Nanoparticles for High-Efficiency Air Filtration[END_REF]. Indeed, in addition to the well-known specific properties of nanofibrous membranes (i.e. small diameter, high specific surface area and tortuous porous structures) adapted for filtration applications, electrostatic forces may also play an important role on the air filtration performance thanks to the presence of charged fibers enhancing the efficiency to adsorb or repel the dust [START_REF] Wang | Electret Polyvinylidene Fluoride Nanofibers Hybridized by Polytetrafluoroethylene Nanoparticles for High-Efficiency Air Filtration[END_REF][START_REF] Choi | Residual Charges during Electrospinning Assist in Formation of Piezoelectricity in Poly(Vinylidene Fluoride-co-Trifluoroethylene) Nanofibers[END_REF][START_REF] Gao | Electret mechanisms and kinetics of electrospun nanofiber membranes and lifetime in filtration applications in comparison with corona-charged membranes[END_REF][START_REF] Amin | Effects of porosity gradient of multilayered electrospun nanofibre mats on air filtration efficiency[END_REF][START_REF] Tabti | Factors that influence the corona charging of fibrous dielectric materials[END_REF][START_REF] Cho | Residual charge and filtration efficiency of polycarbonate fibrous membranes prepared by electrospinning[END_REF]. For biomedical applications, such electrets may also be interesting as they improve cell spreading and proliferation [START_REF] Tong | Enhancing the biological performance of osteoconductive nanocomposite scaffolds through negative voltage electrospinning[END_REF]. Moreover, it was reported that charge transfer and accumulation through the membrane, as well as charge dissipation, occurring in the process of electrospinning may impact the morphology of fibers and the inner structure of the membrane [START_REF] Yalcinkaya | Measurement and analysis of jet current and jet life in roller electrospinning of polyurethane[END_REF][START_REF] Li | Effects of reversed arrangement of electrodes on electrospun nanofibers[END_REF][START_REF] Yan | Self-Assembly of Electrospun Polymer Nanofibers: A General Phenomenon Generating Honeycomb-Patterned Nanofibrous Structures[END_REF][START_REF] Yao | Self-assembly of electrospun nanofibers into gradient honeycomb structures[END_REF][START_REF] Tong | A new nanofiber fabrication technique based on coaxial electrospinning[END_REF][START_REF] Kim | Effect of ionic salts on the processing of poly(2-acrylamido-2methyl-1-propane sulfonic acid) nanofibers[END_REF]. Indeed, it was shown that residual charges carried by the fibers may form an electrostatic template [START_REF] Nedjari | Electrostatic template-assisted deposition of microparticles on electrospun nanofibers: towards microstructured functional biochips for screening applications[END_REF] driving the deposition of the incoming electrospun jet allowing the fabrication of membranes with various morphologies through self-assembling processes [START_REF] Ahirwal | From self-assembly of electrospun nanofibers to 3D cm thick hierarchical foams[END_REF][START_REF] Lavielle | Controlled formation of poly(ε-caprolactone) ultrathin electrospun nanofibers in a hydrolytic degradation-assisted process[END_REF] or with the help of patterned collectors [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF][START_REF] Nedjari | Thick electrospun honeycomb scaffolds with controlled pore size[END_REF].

In this article, the evolution of the surface potential during in-situ charging by electrospinning and after stopping electrospinning is studied as a function of various processing parameters (applied voltage on the emitter, polymer concentration in the solution and ambient relative humidity). An original model of the in-situ charging is proposed and shows the correlation between the characteristic features of the surface potential variation with the porous morphology of the fabricated membrane. The study of the surface potential decay measured after stopping electrospinning is also discussed with the help of a double exponential model.

Finally, the experimental results, supported by the model, demonstrate that the online measurement of the surface potential could be an efficient way to monitor the process of electrospinning regarding the final morphology of the nanofibrous membrane and its building during processing.

Materials and methods

Materials and solution preparation

PLA (Mw=180kDa, Natureworks) was used as received, Dichloromethane (DCM), N, N-Dimethylformamide (DMF), benzyltriethylammonium chloride (TEBAC salt) were purchased from Sigma-Aldrich. PLA/DCM/DMF solution was prepared by dissolving PLA in DMF/DCM (50:50 v/v) with stirring 24h prior to electrospinning. The PLA electrospinning parameters are shown in Table 1.

The addition of TEBAC salt (0.5% w/w) in PLA solution was studied for monitoring purposes.

PLA and TEBAC were added in DMF/DCM in a glass bottle with magnetical stirring overnight at room temperature. The conditions of electrospinning PLAsalt-S2 were identical to those of PLA-S2 (see Table 1).

Electrospinning process

Fig. 1 presents the sketch of the experimental setup of electrospinning. The polymer solutions were fed by a syringe pump (Fischer scientific) at 1 mL/h with a stainless steel needle having an inner diameter of 0.5 mm. The needle was electrically connected to a DC power supply (Spellman SL10). The needle-to-collector distance was fixed at 15 cm. The cylindrical collector (diameter = 110 mm and width = 30 mm) was mounted around the rotor connected to the ground, an insulating Teflon ring was fixed between the collector and the rotor to avoid any charge transfer directly from the collector to the rotor. The collector was electrically connected to a metallic ring at a distance of 20 cm from the collector to avoid any fibers deposition on this ring. The metallic ring was mechanically linked to the rotor by a thick insulating ring of Teflon.

A resistor of 500 MΩ was installed between the ring and the rotor connected to the ground allowing the calculation of the electrospinning current from the measurement of the potential of the metallic ring, thanks to the Ohm's law. The velocity of rotation of the rotor was set at 120 rpm.

To measure the surface potential at the top surface of the membrane, a non-contacting

electrostatic

SEM measurements

The morphology of fibers and particles was studied by scanning electron microscopy (SEM) (Vega-3, Tescan). The samples were gold coated (sputter Quorum Q 150 RS, Quorum Technologies) for 2 min before SEM characterization. Fiber diameters are given in Table 1.

Results

Fig. 2a shows the potential at the bottom of the fibers mat and the surface potential 𝑉 over the membrane recorded during 𝑡 𝑠𝑝𝑖𝑛 = 300 s of electrospinning PLA in the case of PLA-S2 conditions (see Table 1) and after stopping electrospinning (for 𝑡 > 𝑡 𝑠𝑝𝑖𝑛 ). The measurement of the potential of the collector (Probe 2, see Fig. SEM pictures obtained after b) t spin = 5 𝑠, c) t spin = 30 𝑠 and t spin = 300 𝑠 under PLA-S2 conditions.

In-situ charging under different parameters during electrospinning

Evolution of the membrane surface potential during electrospinning: a model

Electrospinning can be seen as a process allowing the layer by layer building of a porous membrane. The electric behavior is depicted in Fig. 3. At time 𝑡, when the jet, having a linear charge density λ, enters in contact with the top surface of the membrane, it starts to release its charges towards the ground along the electrical circuit formed by the interconnected fibers. At the same time, the freshly deposited fiber starts to build the layer of pores located at the top surface of the membrane. The elementary domain of this interconnected circuit is the pore which is a small volume of air surrounded by charged fiber segments. Consequently, one pore may be modeled by a parallel resistor-capacitor circuit (Fig. 3) having a characteristic time 𝜏 = 𝑅 𝑝 𝐶 𝑝 . The capacitance 𝐶 𝑝 may be linked with the pore size, the capacitor being made of a dielectric, the air, surrounded by the charged electrodes, the fiber strands. The resistance 𝑅 𝑝 of the elementary circuit may be linked with the intrinsic resistivity of the fiber, the quality of the fiber-fiber contact points and the number of contact points per unit volume of membrane.

During the deposition process, the electrospun jet brings a constant amount of charges per unit time, thus the elementary current 𝑖 𝑝 flowing through the 𝑅 𝑝 𝐶 𝑝 circuit is constant during time 𝑡. If the 𝑅 𝑝 𝐶 𝑝 circuit is formed at time 𝑡′, it is thus subjected to the following difference of potential 𝑑𝑢 (𝑡) :

𝑑𝑢 (𝑡) = (1 -𝑒 -(𝑡-𝑡 ′ ) 𝜏 ⁄ )𝑖 𝑝 𝑅 𝑝 (1)
Assuming that the membrane has an electrical resistance 𝑅 𝑚 and a surface 𝑆 𝑚 , an average of 𝑃 = 𝑆 𝑚 𝐷 𝑝 2 ⁄ pores of diameter 𝐷 𝑝 forms an elementary porous layer of membrane made of 𝑃 𝑅 𝑝 𝐶 𝑝 circuits in parallel (depicted in red in Fig. 3). The equivalent resistance of such elementary porous layer is thus 𝑑𝑅 𝑚 = 𝑅 𝑝 /𝑃 and the equivalent capacitance is 𝑑𝐶 𝑚 = 𝑃𝐶 𝑝 .

Consequently, the elementary layer of pores has the same difference of potential 𝑑𝑢 (𝑡) as a single pore as well as the same characteristic time 𝜏 = 𝑑𝑅 𝑚 𝑑𝐶 𝑚 = 𝑅 𝑝 𝐶 𝑝 . Furthermore, the current flowing through the elementary layer of pores corresponds to the total electrospinning current i. Thus, a porous layer of thickness 𝑑𝑦 at position 𝑦 and formed at time 𝑡 ′ , is subjected

to the following difference of potential at time 𝑡:

𝑑𝑢 (𝑡) = (1 -𝑒 -(𝑡-𝑡 ′ ) 𝜏 ⁄ )𝑖𝑑𝑅 𝑚 (2)
The surface potential at time 𝑡 of the membrane having a thickness ℎ(𝑡) is the sum of the potential 𝑑𝑢 (𝑡) of all elementary layers plus the difference of potential through the resistor 𝑅 used for the measurement of the current:

𝑉(𝑡) = 𝑅𝑖 + ∫ 𝑑𝑢 (𝑡) ℎ(𝑡) 0 = 𝑅𝑖 + ∫ (1 -𝑒 -(𝑡-𝑡 ′ ) 𝜏 ⁄ )𝑖 𝑑𝑅 𝑚 𝑑𝑡 ′ 𝑑𝑡 ′ 𝑡 0 (3)
It is assumed that the rate of resistance 𝑅 ̇𝑚 = 𝑑𝑅 𝑚 𝑑𝑡 ′ and the characteristic time 𝜏 are constant.

Thus, after integration of equation ( 3), the surface potential can be expressed as:

𝑉(𝑡) = 𝑅𝑖 + [𝑡 -𝜏(1 -𝑒 -𝑡 𝜏 ⁄ )]𝑖𝑅 ̇𝑚 (4)
Fig. 4 shows the trend of 𝑉 as a function of 𝑡 and how the parameters 𝑖, 𝜏 and 𝑅 ̇𝑚 can be graphically obtained. It is seen that:

𝑉(𝑡 ≪ 𝜏) ~ 𝑉(𝑦 = 0) = 𝑉 0 = 𝑅𝑖 (5)
𝑉 0 corresponds to the potential at the collector-membrane interface (i.e. at the position y = 0)

and can be easily measured in order to get the current 𝑖.

When 𝑡 ≪ 𝜏, the surface potential is almost constant. Indeed, the characteristic time is the time it takes to completely charge a layer of characteristic thickness ℎ 𝜏 . When 𝑡 ≫ 𝜏, all the layers located below the upper layer of fibers of characteristic thickness ℎ 𝜏 are completely charged and are equivalent to a resistive layer of interconnected fibers having a thickness of ℎ(𝑡) -ℎ 𝜏 .

Under this condition, the surface potential evolves linearly with time:

𝑉(𝑡 ≫ 𝜏) ~ 𝑅𝑖 + [𝑡 -𝜏]𝑖𝑅 ̇𝑚 (6)

Effect of applied voltage during electrospinning

Experimental curves of the surface potential as a function of time for various applied voltages are given in Fig. S1b of Supp. Data. Fig. 5a shows that the current, corresponding to the amount of charges brought by the jet per unit time, increases obviously with the applied voltage. The final slope of the surface potential, corresponding to 𝑑𝑉 𝑑𝑡 = 𝑖𝑅 ̇𝑚, is almost constant from 15 kV to 25 kV (Fig. 5b). An increase of 𝑖𝑅 ̇𝑚 is observed for the highest voltage, i.e. at 30 kV, meaning that for this condition the resistance of the membrane increases faster than in the other cases. It was observed by SEM that when the voltage increases continuously, a more intense electrostatic force acts on the jet resulting in thinner fibers and more efficient solvent evaporation (see Table 1 and Fig. S1a of Supp. data). Indeed, for the lowest applied voltage, fusion among fibers at their contact points is observed resulting in an overall lower membrane electrical resistance. From Fig. 5b, it is also shown that the characteristic time 𝜏 decreases gradually with the increase of the voltage, with a value changing from 79s to 21s when increasing the applied voltage at the emitter from 15kV to 30kV. Furthermore, it is shown that the fiber diameter decreases with the applied voltage (Fig. 5a and5c) resulting thus to a decrease of the average pore size of the fibrous mesh. [START_REF] Ma | Ultra-fine cellulose nanofibers: new nano-scale materials for water purification[END_REF] As shown in the previous section, the characteristic time relies on the average pore size having each a capacitance directly correlated with their size. Thus, a decrease in the fiber diameter results in the production of membranes with smaller pores and consequently a decrease of the capacitance 𝐶 𝑝 and the characteristic time 𝜏.

Effect of Polymer concentration during electrospinning

As shown in Fig. 6a, the polymer concentration in the solution does not impact significantly the current, the values varying from 0.09 µA to 0.13 µA when changing the concentration from 7% to 13%. Actually, the current is the consequence of complex mechanisms. Indeed, regarding the polymer alone, at constant solution feeding rate (i.e. 1 mL/h), an increase of the polymer concentration results in the increase of the fiber flow rate increasing thus the rate of charges landing on the collector and consequently the current. Concurrently, increasing the concentration induces the enlargement of the solution viscosity decreasing thus the efficient production of fiber and consequently, the current. In our case, these two phenomena being in competition resulted in a current which is almost constant with the concentration. However, as shown in Fig. 6b and Fig. S2b of Supp. Data, τ increases gradually and significantly from 8 s to 200 s when the concentration increases from 7% to 13% whereas the slope 𝑖𝑅 ̇𝑚 is almost constant with, however, a small increase observed for the highest studied concentration. Once again, the characteristic time seems to be in good correlation with the size of the pores being proportional with the fiber diameter (Fig. 6c). Thus, as shown in Fig. 6a, increasing the polymer concentration induces the enlargement of the fiber diameter due to high solution viscosities and thus leads to remarkable increase of 𝜏 but with a low effect on the slope

Effect of Ambient relative humidity during electrospinning

No significant effect of the ambient relative humidity (RH) on the current was observed (Fig. 7a). The current being influenced by many parameters, it is complex to draw any conclusion. In contrary, the two main parameters, 𝜏 and 𝑖𝑅 ̇𝑚, describing the surface potential model evolve significantly with RH (see Fig. 7b and Fig. S3b of Supp. Data). First, a gradual increase of τ was observed. Once more, it can be noticed that 𝜏 increases with the pore size of the membrane.

Indeed, as measured by SEM, the fiber diameter increases sharply with RH (Table 1, Fig. 7a and 7c) resulting in the formation of larger pores [START_REF] Ma | Ultra-fine cellulose nanofibers: new nano-scale materials for water purification[END_REF]. It was also observed an effect of RH on the slope 𝑖𝑅 ̇𝑚 of the curves representing the surface potential as a function of time. A significant decrease of 𝑖𝑅 ̇𝑚 is firstly observed when RH increases from 28% to 48%. Then, the slope 𝑑𝑉 𝑑𝑡 = 𝑖𝑅 ̇𝑚 is rising sharply when increasing RH from 48% to 58%. These results show that RH mainly affects the electrical resistance rate of the membrane 𝑅 ̇𝑚 instead of 𝑖𝑅 ̇𝑚, the current being indeed almost constant with RH . The membrane resistance 𝑅 𝑚 is linked with the resistivity of the polymer, here PLA, the quality of the fiber-fiber contact points and the number of contact points per unit volume of membrane. As shown in Fig. S3a of Supp. Data, all these features seem to change as a function of RH explaining thus the complex trend of 𝑖𝑅 ̇𝑚.

Decay of the surface potential of the membrane after stopping the fiber productionmechanism of residual charges dissipation

Surface potential decay: a model

In this section, the stored charges release mechanism is studied over after stopping electrospinning. When the power supply connected to the emitter is switched-off, the jet is no more produced, the current is thus equal to zero and no more charges are deposited. Since the current is null, no charges are released to the ground. However, a decrease of the surface potential over time is observed as shown in Fig. 8. Several mechanisms of charge release can explain the surface potential decay. First, charges located at the topmost surface of the membrane are subjected to ion neutralization with air. This charge release phenomenon may occur at short times, characterized by a time denoted 𝜏 𝑠 . Second, charges mostly located at the surface of the fibers, but inside the porosity of the membrane, should release their charges within each pore having already participated to the kinetic of in-situ charging by electrospinning. It is thus expected that this second characteristic time of decay, denoted 𝜏 𝑚 , is in the same order than the characteristic time τ measured during in-situ charging. This medium characteristic time 𝜏 𝑚 is expected to be higher than 𝜏 𝑠 . Third, in-situ electrospinning may lead the production of charges efficiently trapped in the bulk of the fibers. Indeed, although electrospinning of PLA leads to the fabrication of fibers with low crystallinity [START_REF] Nedjari | Electrospun Honeycomb as Nests for Controlled Osteoblast Spatial Organization[END_REF], charges may be trapped inside the fibers between amorphous and crystalline domains. This charge release phenomenon may occur at long times characterized by a time denoted 𝜏 𝑙 . Thus, although a double exponential fitting was proposed in the literature for fibrous membranes charged by corona effect [START_REF] Thakur | Study of charge decay in corona-charged fibrous electrets[END_REF], it is expected that the surface potential decay may be modeled by the sum of three exponential functions as follows:

𝑉(𝑡) = 𝐴 𝑠 𝑒
Fig. 8. Surface potential decay after stopping electrospinning carried out under the conditions of PLA-S2 (see Table 1). Experimental data (grey line), model with two characteristic times only (short dashed blue line), model with 2 characteristic times and one asymptote (dashed green line), model with three characteristic times only (dashed-point red line).

Fig. 8 shows the surface potential decay obtained after stopping electrospinning carried out under the conditions of PLA-S2 with a long time of acquisition of 2000 s. The model described by Eqn. 7 fits perfectly the experimental data. After fitting by a least square method, the obtained times were respectively 𝜏 𝑠 =11 s, 𝜏 𝑚 =104 s and 𝜏 𝑙 =2183 s. A double exponential model was tested in order to compare the fitting quality:

𝑉(𝑡) = 𝐴 1 𝑒 -( 𝑡-𝑡 𝑠𝑝𝑖𝑛 𝜏 1 ) + 𝐴 2 𝑒 -( 𝑡-𝑡 𝑠𝑝𝑖𝑛 𝜏 2 ) (8)
Using Eqn. 8, one characteristic time is obviously lost, leading to bad fitting as shown in Fig. 8. In this case, the obtained characteristic times were 𝜏 1 =51 s and 𝜏 2 =1187 s. Another model can be proposed, using also two characteristic times but introducing an asymptote 𝑉 ∞ instead of the long time as introduced in the model described by Eqn. 7. The model is the following:

𝑉(𝑡) = 𝑉 ∞ + 𝐴 𝑠 𝑒 -( 𝑡-𝑡 𝑠𝑝𝑖𝑛 𝜏 𝑠 ) + 𝐴 𝑚 𝑒 -( 𝑡-𝑡 𝑠𝑝𝑖𝑛 𝜏 𝑚 ) (9)
Eqn. 9 also allows a good fitting of the experimental data as 𝑉 ∞ can also be linked to the behavior at long times whereas 𝜏 𝑠 and 𝜏 𝑚 play the same role as in the model using three characteristic times. Using Eqn. 9, the least square method gave the corresponding characteristic times: 𝜏 𝑠 =17 s and 𝜏 𝑚 =166 s. Because in the next part, all measurements of the surface potential decay were carried out during a time of 150 s, the three exponential model didn't allow a good estimation of the long time 𝜏 𝑙 . Thus, the model using two characteristic times with an asymptote 𝑉 ∞ (Eqn. 9) was chosen to fit the experimental data and only the behavior at short and medium times was studied. Furthermore, the following normalized weight factors were also studied as a function of the processing conditions:

𝐴 𝑠 % = 100 𝐴 𝑠 𝑉 ∞ +𝐴 𝑠 +𝐴 𝑚 (10)
𝐴 𝑚 % = 100 𝐴 𝑚 𝑉 ∞ +𝐴 𝑠 +𝐴 𝑚 (11) 𝑉 ∞ % = 100 𝑉 ∞ 𝑉 ∞ +𝐴 𝑠 +𝐴 𝑚 (12)
Effect of Applied voltage on the surface potential decay after stopping electrospinning Fig. 9 presents both 𝜏 𝑠 and 𝜏 𝑚 obtained from Eqn. 9 to fit the surface potential decay measured after applying various voltages on the emitter. The curves giving the surface potential decay as a function of time for various applied voltage are given in Fig. S4 of Supp. Data. It should be mentioned that the two exponentials are needed to fit adequately all experimental data. The normalized weight factors are not influenced by the applied voltage whereas the medium decay process is preponderant compared to the short one. The discharged of the top surface, characterized by the short time 𝜏 𝑠 being in the order of 10 s, is a little bit faster for the membranes produced for the highest voltage. Indeed, the highest applied voltage led to the production of membranes with the thinnest fibers and consequently having the largest surface area offered to the ions of the air for a quick decay. It is also shown that the short time decay is around ten times faster than the medium one. A slow decrease of the medium time with applied voltage is observed. Moreover, 𝜏 𝑚 is of the same order of magnitude than the characteristic time 𝜏 determined from the modeling of the surface potential during in-situ charging by electrospinning. These features seem to show that 𝜏 𝑚 and 𝜏 rely on the same physical mechanisms originating from the effect of the pores of the membrane on the kinetic of the surface potential. However, the effect of applied voltage on 𝜏 𝑚 is weaker than what was observed for τ during electrospinning. Although efficient charge injection is expected in the bulk of the fibers produced for the highest applied voltage, it is observed that 𝑉 ∞ % , characterizing the amount of bulk charges, is surprisingly constant with applied voltage. However, such result must be taken with caution because the measurements were carried out along short period, i.e.150 s, that don't allow a precise description of the kinetic at long times. observed for 𝜏 , 𝜏 𝑚 increases with RH , 𝜏 𝑚 being in the same order of magnitude than 𝜏 .

Effect of Ambient relative humidity on the surface potential decay

Furthermore, it is worth noting that the fact that RH influences almost only the charges located on the surface of the fibers confirms that the mechanism leading to the surface potential decay at medium time 𝜏 𝑚 is due to the release of surface charges and not to bulk charges inside the fibers. Finally, a significant increase of 𝑉 ∞ % is observed for the highest RH showing that a high amount of bulk charges, having the longest characteristic times, are stored in the matrix of the fibers. Indeed, because PLA is a hydrophobic polymer, diffusion of water into the electrospun jet results in the rapid precipitation of PLA [START_REF] Thammawong | Electrospinning of poly(l-lactide-co-dl-lactide) copolymers: Effect of chemical structures and spinning conditions[END_REF]. Such rapid precipitation may lead to a high amount of defects in the polymer matrix explaining thus the high amount of charges which are usually trapped in the defects [START_REF] Gao | Electret mechanisms and kinetics of electrospun nanofiber membranes and lifetime in filtration applications in comparison with corona-charged membranes[END_REF]. medium times but with a much higher accuracy. Indeed, the medium time 𝜏 𝑚 , obtained from the fitting of the surface potential decay measured after stopping electrospinning, is of the same order of magnitude than the time 𝜏 measured during electrospinning. Both 𝜏 𝑚 and 𝜏 follow the same behavior as a function of the studied processing parameters: a decrease with increasing voltage and the opposite when increasing either the polymer concentration or the ambient relative humidity. However, the characteristic time 𝜏 revealed to be much more sensitive than 𝜏 𝑚 . Such difference can be explained by the fact that the surface potential measured during electrospinning takes into account a continuously fresh deposited top surface which immediately starts to release its charges. Thus, 𝜏 may be more related to the combination of the release at short times ( 10 s) of charges located on the top surface and the release at medium times ( 100 s) of the charges located in the pores just below the top surface under construction.

In fact, in the proposed model of in-situ charging by electrospinning (Eqn. 4), the 𝜏 value can be related to the electrical characteristics at the different length scales: (i) the pore, (ii) the elementary layer having the surface of the membrane and the thickness of one pore and (iii) the whole membrane under building. Each of them is related to the pore structure of the membrane:

𝜏 = 𝑑𝑅 𝑚 𝑑𝐶 𝑚 = 𝑅 𝑝 𝐶 𝑝 = 𝑅 𝑚 𝐶 𝑚 (13)
Assuming that the membrane electrical resistance 𝑅 𝑚 evolves linearly with time:

𝑅 𝑚 = 𝑅 ̇𝑚𝑡 (14)
And using equations 13 and 14, it is possible to give an estimation of the membrane capacitance 𝐶 𝑚 :

𝐶 𝑚 = 𝜏 𝑅 ̇𝑚𝑡 (15)
Because the number of elementary layers in the thickness of the membrane is proportional to the time of deposition and that the current is constant during time, 𝑑𝑅 𝑚 and 𝑑𝐶 𝑚 scale as:

𝑑𝑅 𝑚 ∝ 𝑅 ̇𝑚 ∝ 𝑑𝑉/𝑑𝑡 (16)
𝑑𝐶 𝑚 ∝ 𝜏 𝑅 ̇𝑚 ∝ 𝜏 𝑑𝑉/𝑑𝑡 [START_REF] Amin | Effects of porosity gradient of multilayered electrospun nanofibre mats on air filtration efficiency[END_REF] Thus, knowing that the average number of pores 𝑃 for one elementary layer of membrane of surface 𝑆 𝑚 is 𝑃 = 𝑆 𝑚 𝐷 𝑝 2 ⁄

and that the characteristic size of a pore 𝐷 𝑝 is proportional to the fiber diameter 𝐷 𝑝 ~𝜙𝑓 , [START_REF] Ma | Ultra-fine cellulose nanofibers: new nano-scale materials for water purification[END_REF] the resistance and the capacitance of a pore scale respectively as: In order to verify the proposed scaling law, all data points obtained in the various operating conditions (applied voltage, polymer concentration and ambient relative humidity) were represented in graphs. The first one, gives

𝑅 𝑝 ∝ 𝑑𝑉/𝑑𝑡 𝜙 𝑓 2 (18) 𝐶 𝑝 ∝ 𝜙 𝑓 2 𝜏 𝑑𝑉/𝑑𝑡 (19)
𝜙 𝑓 2 𝜏 𝑑𝑉/𝑑𝑡
as a function of the measured fiber diameter 𝜙 𝑓 (Fig. 12a). Because of Eqn. 19, this graph is proportional to the graph of the pore capacitance 𝐶 𝑝 versus 𝜙 𝑓 . It is shown that whatever the processing condition (highlighted by the different symbols in the graph), 𝐶 𝑝 is well correlated with the fiber diameter (Fig. 12a). The following scaling law can thus be obtained for electrospinning of PLA on a flat collector:

𝐶 𝑝 ∝ 𝜙 𝑓 4.87 (20)
Consequently, the fiber diameter can also be plotted as a function of

𝜏 𝑑𝑉/𝑑𝑡
and a good correlation is obtained (Fig. 12b) giving thus 𝜙 𝑓 as a function of only the physical quantities obtained from the measurement of the surface potential:

𝜙 𝑓 ∝ [ 𝜏 𝑑𝑉/𝑑𝑡 ] 0.21 (21)
It is thus shown for the first time that the measurement of the surface potential, thanks to the use of an electrostatic voltmeter, is a simple method giving accurate information at the local scale of the nanofiber diameter of an electrospun membrane. Moreover, such a method should allow the detection of variations in the porous morphology and/or membrane's quality during its fabrication. In order to illustrate such feature, 0.5wt% of TEBAC salt was added in the PLA solution and electrospun under the conditions PLAsalt-S2 (see Table 1) which are equivalent to the PLA-S2 standard conditions without salt. The addition of the salt brings a high amount of charges in the electrospun jet which explains the significant increase of the current (0.74 µA for PLAsalt-S2 calculated from 𝑉 at 𝑡 = 0 𝑠 compared to 0.1 µA for PLA-S2). Moreover, as opposed to the pure PLA system (see Fig. 2a), the addition of TEBAC perturbs significantly the evolution of the surface potential 𝑉. Indeed, Fig. 13a shows that the surface potential does not increase linearly with time as it was observed in the case of PLA-S2 as well as for all other studied pure PLA systems. The accumulation rate of charges in the membrane, characterized by the slope 𝑑𝑉/𝑑𝑡, is thus not constant during electrospinning. Fig. 13b shows indeed that the salt is not homogeneously distributed which could explain that the charges are not regularly brought by the jet explaining the observed instabilities. The on-line measurement of the surface potential seems to be an efficient way for the monitoring of the electrospinning stability and quality of the produced membrane.

Conclusion

Here, we showed that the measurement of the surface potential of the membrane can be easily carried out online during the process of electrospinning using an electrostatic voltmeter.

A model was proposed to follow the kinetics of the surface potential during in-situ charging by electrospinning for various operating conditions. The model is characterized by a characteristic time 𝜏, linked to the formation of an elementary porous layer of the membrane and by the slope 𝑑𝑉/𝑑𝑡 , measured at steady state, and related to the electrical resistance of the membrane induced by the fiber resistivity and the quality and the density of fiber-fiber contact points. The kinetic of the surface potential decay after stopping electrospinning was also studied. Three characteristic times can be identified during scaffold discharge. A short time 𝜏 𝑠 , having a value in the range of ten seconds, can be correlated to the rapid charge release occurring on the topmost surface of the membrane. A medium time 𝜏 𝑚 , having a value of several tens of seconds up to more than one hundred of seconds, relies on the charge release inside each pore of the membrane. The times 𝜏 𝑚 and 𝜏, having the same physical origin, they are in the same order of magnitude. However, 𝜏 obtained from in-situ charging during electrospinning, is more sensitive to the processing conditions. Finally, the long time 𝜏 𝑙 , being at least one order of magnitude higher than the medium time, characterizes the release of the charges trapped in the bulk of the fibers.

The measurement of the surface potential allows thus the detection of variations in the porous morphology of the membrane during its fabrication. Furthermore, in combination with the measurement of the current, it is an efficient and complementary method to get more insight into the overall process of electrospinning for a robust online monitoring. Last but not least, the method also gives immediate information on the residual charges stored in the fibrous membrane which is an important feature for the elaboration, by electrospinning in-situ charging, of electrets for filtering applications.

Fig. 1 .

 1 Fig. 1. Sketch of the experimental setup allowing the measurement of the membrane surface

Fig. 2 .

 2 Fig. 2. Electrospinning in the case of PLA-S2 conditions. a) Evolution of the surface potential

Fig. 3 .

 3 Fig. 3. Charge accumulation during electrospinning. The fibers form an interconnected

Fig. 4 .

 4 Fig. 4. Theoretical evolution of the membrane surface potential as a function of the time and the characteristic parameters 𝑉 0 , 𝑖, 𝜏 and 𝑅 ̇𝑚 of the curve.

Fig. 5 .

 5 Fig. 5. a) Evolution of the current (red triangles) and the fiber diameter (blue discus) as a

Fig. 6 .

 6 Fig. 6. a) Evolution of the current (red triangles) and the fiber diameter (blue discus) as a

Fig. 7 .

 7 Fig. 7. a) Evolution of the current (red triangles) and the fiber diameter (blue discus) as a

Fig. 9 .Fig. 10 .

 910 Fig. 9. a) Short 𝜏 𝑠 (blue discus) and medium 𝜏 𝑚 (red triangles) times and b) normalized weight factors (𝐴 𝑠 : blue discus, 𝐴 𝑚 : red triangles, 𝑉 ∞ : green squares) as a function of applied voltage

Fig. 11 shows

 11 Fig.11shows 𝜏 𝑠 and 𝜏 𝑚 obtained to fit the surface potential decay measured for various

Fig. 11 .

 11 Fig. 11. a) Short 𝜏 𝑠 (blue discus) and medium 𝜏 𝑚 (red triangles) times and b) normalized weight factors (𝐴 𝑠 : blue discus, 𝐴 𝑚 : red triangles, 𝑉 ∞ : green squares) as a function of relative

Fig. 12 .

 12 Fig. 12. a) Correlation between 𝐶 𝑝 and the fiber diameter 𝜙 𝑓 . b) Correlation between the fiber

Fig. 13 .

 13 Fig. 13. Effect of the addition of a salt in the solution on the stability of the surface potential

  ). a) Evolution of the surface potential. b) SEM picture of PLA fibers with TEBAC salt. The two rings highlight fiber domains having no salt particles on their surface.

Table 1

 1 Preparation parameters of PLA fibers and resulting fiber diameter

		Concentration (w/w)	Voltage	Relative humidity	Average fiber diameter (nm)
	PLA-S1	7%	25kV	38%±2%	323 ± 169
	PLA-S2	9%	25kV	38%±2%	445 ± 97
	PLA-S3	11%	25kV	38%±2%	546 ± 127
	PLA-S4	13%	25kV	38%±2%	659 ± 77
	PLA-S5	9%	15kV	38%±2%	572 ± 229
	PLA-S6	9%	20kV	38%±2%	571 ± 154
	PLA-S7	9%	30kV	38%±2%	407 ± 67
	PLA-S8	9%	25kV	28%±2%	271 ± 99
	PLA-S9	9%	25kV	48%±2%	515 ± 81
	PLA-S10	9%	25kV	58%±2%	730 ± 133
	PLAsalt-S2	9%	25kV	38%±2%	182 ± 40

Acknowledgements

The authors are grateful to the French National Research Agency for the financial support of this work (Project MimHeart ANR-15-CE08-0010-02). We thank China Scholarship Council (CSC) for the financial support of the PhD student. We also thank Christophe Sutter, Christophe Mélart, Michel Wolf and Thierry Djekriff for their help in the electrospinning set up.

Supplementary Data. Curves of surface potential and complementary SEM pictures related to this article can be found online free of charge at https://doi.org/10.1016/j.polymer.XXXXXXXXXXXXX