What's up everybody I'm TheMangoos, you are awesome and today I'm talking about Hood, Outlaws and Legends. This is a new game by Focus Home Interactive. Hood is an interesting mix of third person player vs player and player vs environment. The game does have cross play matchmaking, but you currently can't send invites cross platforms so you will play against other consoles, but you can't make a group with someone on PlayStation if you're playing on PC. I've been busy as hell with work and appointments lately, but what time I've had to myself has been spent playing this game, I am absolutely hooked. Hood provides opportunities for a variety of gamer types to excel. Are you a twitch reflex no scope aim god? Take Robin or Mirian and dominate fights. Are you an old washed up has been like me that lost those skills a long time ago, but you still have a mind for strategy? Then hop on John or Took and call the shots for your team while staying focused on objectives. Today I'm going to go over the basics of the game, give you my thoughts and then show you a full match so you can decide for yourself if this is something that you're interested in. For now the main game mode is 4v4. You pick from four different legends based on characters from Robin Hood. Little John is my personal favorite. Each legend brings a unique skill set to the group and a well balanced team is your best path to success. The two teams load into one of five maps populated by NPC guards. Your goal is to silently make your way across the map, assassinating any guards in your way and eventually find the sheriff. Once he's located you need to pickpocket his key. After you have the key you locate the fault, open that up and grab a chest of gold. Then you take the gold to one of the very six extraction points on the map. Once the gold is loaded you need to winch it up notch by notch until you eventually have the chest. That all sounds easy, but remember there's another team of four players attempting to do the same thing with the same objectives. While there are two teams there's only one sheriff, one key and one chest of gold so you can kill the enemy team members and take the objective for yourself. For example maybe they get to the sheriff first, but you can still kill whoever has the key, take it and unlock the vault for your own team. Sounds pretty simple, but there's much more depth to the game which is something many people playing it don't seem to understand. When making your way through the map you can simply fight the various guards and kill them, just straight up 1v1 carnage, however it's much more efficient to assassinate them from behind. When you fight the guards or otherwise alert them they of course call in more guards, all the gates in the area drop and worst of all the enemy team is alerted to your position. There are various types of guards as well, you got simple soldiers, crossbowmen and knights. Soldiers and crossbowmen are pretty easy kills for the two melee heroes but the knights can be a bit of a pain, especially if you have to fight a large group of them. The sheriff is also a constant threat. He continues to roam around the map after you pick pocket him and he really zeroes in on you when you have the chest of gold.  You can take him down for a short period of time with gas, smoke or explosives. The vault's general location is shown to your team when you pick pocket the key, but the key holder is the only one that knows the exact location. If you're in comms make sure to let your team know where it is. After you get the vault open it's time to carry the chest. The two melee legends, Toc and John, carry the chest much faster than Mirian or Robin so you always want to have at least one melee on your team. You have multiple extraction points to choose from and most teams will attempt to just get to the closest one, but we found that taking the chest all the way to the point closest to your home spawn is the best strategy. There are spawn points located around the map that can be captured, but your initial point will always stay the same. It's especially important not to alert the guards when your team has the chest since that will tell the enemy team right where you are. Try having one of your bruisers carry the chest while one person watches his back and your range and stealthier teammates take out any guards in your way. The final step is to winch the gold out and this is where the game usually turns into a clusterfuck. The two melee legends can winch the gold out faster but it still takes some time and the enemy team can swoop in while you're cranking your last notch, team wipe you and win.  You do get gold for each step you complete and each notch you winch so it's not a complete loss but man it hurts when that happens. The winch portion of the game is usually where you have the most team fights. The sheriff always makes his way to the area so you have him trembling around taking you by surprise and the guards respond so unless your team is super alert you will get spotted and the enemy team will know where you are. This is my only complaint with the game.  The main goal is to get the gold and even if you lose the match you can still get a pretty good sum if you performed well. You choose how much gold to give to yourself and to the people. Gold is used in the hideout to buy perks, outfits and weapons skins. You have three slots for your perks that are unlocked as you progress and the perks can greatly increase your effectiveness but often come with some kind of downside.  You also have an ultimate meter that fills up as you play. Getting kills, assassinations or carrying the chest fills that meter faster. Each legend has a passive ability, different gear they can pick up around the map and an ultimate ability. Robin is a sniper that excels at taking out guards from range, one-shotting enemy players with headshots and providing cover while you winch. He does have limited amount of arrows so you will need to find resupply points around the map. He can melee with his bow and he can perform a leaping punch with from the sprint but it's not very effective against, say, a jawn. He has a dodge for his defensive option and that is pretty nice. His trait allows him to tag targets for longer and his gear is a flashbang that blinds enemies and man is it bright on your screen when you get blinded. I'm betting they're going to get some complaints about that and they might change that around to just darkening your screen or something. His ultimate is an explosive arrow that's great for taking the sheriff down, blasting high health enemies and interrupting the winch.  She's quick and can assassinate from any angle.  She has a rolling attack if she may lays from sprint. And she also has a wrist mounted crossbow that gives her some range options with single fire or three round burst, three bolt burst I guess you should say. She does need to replenish her bolts just like Robin. Her gear is a smoke grenade and that obscures vision and gives you a great way to get stealth kills. Marianne's ultimate is that she goes invisible until she takes an action. You can still see a shimmer of her outline if you're paying close attention, but when you're in the middle of a fight it's pretty common to suddenly get off by Marianne. She also has a dodge for her defensive and it's a little quicker and takes a little less stamina than Robin's does. Took is the healer of the group. He regen stamina faster than the others and uses a flail with both a light and heavy attack. Think what they actually call it is a sensor like the incense spreading things that they used to use but anyway it's a flail. He can also perform a heavy attack from sprint. The heavy attack is medium range, stuns and it's very effective. He can also block and parry attacks. His gear is a gas grenade that prevents people in the area from regaining stamina. His ultimate is an AoE heal that also reveals any enemies in the area. John is the melee specialist. He can open up gates to allow his team to pass through blocked areas, but just be careful if you drop it on them they will die. He wields a hammer with light and heavy attacks and can also perform a leaping hammer attack from sprint. He can also block and parry. John's gear is an explosive grenade that can be used on the sheriff or to interrupt winching. His ultimate gives him crazy health and stamina. My biggest complaint for him is that when he walks it looks like he's touching cotton and desperately trying to find a bathroom. As you can probably tell I've been really impressed with this game. It's a refreshing mix of PvP and PvE that encourages teamwork and strategy. There are of course a few things that I don't like, the winch finish being one, but the positives massively outweigh the negatives here. If you've had your eye out for something new and different, then I highly suggest giving it a try. It's available on Steam, I don't think I've mentioned that yet. I'm going to go ahead and show you guys a full match, so stick around if you want to see that, but if not, you guys have a good one. Fair enough, fair enough. God, here. That's why you always listen to your priests. Celtic priests, I'll get them. Will you tag them? I figured I'd get the, you know. Well, no, killing gets me all faster. Oh, that too, yeah. Robin can't help but be accurate. Did you see that? Get the, get the knight, you know. I don't know if that works. Shit, did you see that?  Yeah, okay, assassin, anyone gets any, anyone's old faster. I know, mine's more useful. I agree with that. Crossbowman here. Fair. God, here. Actually, yeah, shoot the guard because...  Oh my god.  God damn it, man.  Yo, okay, it's standing my way. I'm laughing because I want to assassinate.  I was wondering how that...  What was that?  He was talking to me. No, he fucking, he's like, yo, shoot the guard. Right there.  Oh, man, I'm crying.  Don't make me talk to my friends, please. King, I'm telling you, man, we're number one in friendship for a reason. Okay. And welcome to the, to the discord.  I'm with... We're... Are we just... Stay out of the way. I don't...  Unknown, alerted. Uh, yeah, get him and I'll rush. There you go. One crossbow down. I love that. That is one of my favorites. Someone's got to go back and clip that. I got him. I got him. I got him. I got him. Yeah, it's still one of my favorites. There he is. Uh, looks like there's a... You got him. Okay. You had me worried for a split second there. Yeah, I'll get this guy. Oh, I thought about vaulting over the wall instead, but... Oh, that portacus almost just killed me. Yeah, it did. Now I must have watched it. Oh, he's facing destruction. He's definitely looking at us. Yes. I'm like, man, the ball's on this dude. Uh, that's the church. Of course it's in the church. Okay. Oh, the other side of the map we go. All right, I'm going to bring my new boyfriend. Okay.  Yeah, I'm going to bring him with me. You guys should go on the bridge to the portacus. I'll... I want to watch this. Are you kidding me? This is fun. Oh, they're right there. All right. He's almost dead. Robbing down. Sheriff? Oh, no. Yes, it wasn't me that died to the sheriff for once. I thought we had a connection. All right. There's a robin alive over there. Careful. Where? It was on the other side of the bridge. Like where I'm in. Nicely. Oh, yeah. I'm dead. I don't know where you are. Yeah. Yeah. Yeah, where you're at. He's coming up on you. He's coming up on you. He's not dead. He's not dead. Yeah, it's going to be. I got B if you guys want to continue into the church. There's...  Oh, I did not know you were behind me raving. That's what I just said. Yo, let's go get B. We still have the key. What's going on here? Yeah, I got it. Nice shot.  Oh, I see them, man. We avenged you. Nice swing. I did it through supervision. The teamwork. Is that the way you told me to swing my hammer? Man, I don't know if I could have done it without you. Are you guys still all right over there? What's going on? I don't know what you're talking about. I'm by the church. Wait, I hear a boat. The guard on my way. Yeah, I just heard it too. He's right here.  He's just right here. He could have assassinated us and he didn't. Hey, behind us, behind us, behind us. Oh, what? You got the guard? No, just a two right there. Can you see him? What room in the church are we going to? Is that where? No, I see the robin. Honestly, that's three.  I'm just robbing right behind you. I got you. There's a Joan creeping up. There he is. There he is. Impact ultimate arrow. Oh, damn. I was trying to pop it.  Let's go say I'll fucking. What? Parried him. No, I'm in the middle of the game. I'm eating it. I missed. Hey, Duke. He really wants me for some reason. Okay. I'm sorry. Where did we determine that?  Yes, I did. It didn't kill him. I got. I got. Oh, they're whole team right here. Actually. Oh, sorry. I know it's going to build. You're fine. You got him. I need arrows anyway. You said the vestibule vestry. What floor? Zero. So it's right here. I'm sorry. Yeah. I was just hung. Oh, found him. Is it help out there? This is awkward. I got him. I got him. All right. I love that between the arrow pull and your between the arrow pull back. Oh, you want to see? Oh, these rag dolls, man. I can't. They're so funny. I have to show. Dude, I have to.  Oh, I saw it. She skyrocketed like she took off into space. All right, wetlands.  We're going all the way across the map. As soon as my alt's built, I'm dropping this. Okay. Got me. Unfortunately, they keep spawning back at A. Okay. Can you? Is that a Marianne just saw? Okay. My goose is with me. Cool. I'm right here with you. Yeah. Door door. They're in here with us. That's what I thought. Right? Let's go down here. Go down here. Bottle and that get downstairs. Robin's dead. Alt's ready. I'm dropping here. John right behind me, but keep going. Robin and two or outside running in now. Come down here. Come down here. I'm not here. We're good. There's a grenade coming down. No, no. Say, say, say you're good. Comment down. All right. John's like half health. I scared him off for now. I don't think this is the way to the wetlands. Well, it's not, but we're here. Um, we go out this way. No. This is this door open? No. All right. Yeah. Oh, okay. Come here. I know. I know where we're going. Come here. There's this door. Follow ping. It's right here. This is an accident. I'm watching behind you. I'm watching behind you. Thank you. This is an accident. I got an alt ready. Oh, Raven, have you seen how to opens the door? No. He uses a key in unlocks it. Hey, you want to go bridge or savage? Actually, let's go right here on the side of the bridge. Oh, service tunnel, service road. Well, this one, yeah. He opens it like a savage. With a key? Yeah, with a key. Oh, he just opens it like a. That's what the behind us behind us. Behind us, King. Keep going. Keep walking. I got your man. You watching it? I got. Yeah, I'm dealing with people on a. Watch out. They're trying to drags at us from up top. Yeah. Rub it into both down. The left. Sweet. No. Left, left, left. Sure, sure. It's all distracted. He moves slower than you do, even with chest. You're fine. No, no, no, no.  No, go, go, go, go. I'm going to wetland. I'm dead. There's another guy right there. Watch out. He just ran past you. Oh, no. All right. Drop it and then crouch here. We'll try to ambush them. Unless you're marked by Cheryl. Yeah, I'm revealed by Cheryl. Oh, I'm dead. There you are.  Thank you on my level. You're welcome. Oh, yeah. Are you still revealed? Yeah, I'm just going to walk. Yeah, keep going. I'm hiding in the flowers, I guess. I think we're far enough away that they can take A, and it doesn't really matter anymore. Yep. Dude, that was funny. His character model tackled you, and I literally hit him with the R, too.  Wait, I can't shoot through this. Oh, my God. This game is what I was robbing on day. That's a hitbox, huh?  Yeah, they're literally made for me to poke out of it. It's like, all right, robbing down. I'm going to go back for B. All right. Why? Just in case it cuts off their spawning. Okay. Keeps them a little bit further away. No, I think you're too good to be that far from us. Two of them are just spawning right in front of me. Woo. Yeah, that's what I mean. I got this, dude. Don't worry. Okay.  All right. There's three of them on me. There we go. Let me go. Oh, there's a dog right there. I got him. I got him. I got him. All right. There's two robins and a half. I do not have him. He's got me. I got him. Or not. No. No. This guy's unexecutable. There we go. Hey, they're trying to grab you right now. Threat me. Threat me. Threat me. That guy's about to have a bad day. Get hammered. You just flail him right in the nuts. Yeah. There are John's coming right there. Coming down. I have three of them on me. So just whatever you're doing, keep doing it. I'm going to heal here in a second. Just to. Where did John go? He's right up here. Both robins are on me right now. Yeah. He's on the bridge here. I'll deal with that.  You just keep. All right. They got there. Where's he at? I don't see him up here anyway. Yeah. I don't see him up here anyway. Right there. There he is. Nope. Right there. He's on us. He's on us. He's on us. I'm alive.  I'm going to stick your grenade on him. Nice. I'm dead. Hell yeah. Nice. We got one more. I got a robin. I got killed by let me go crazy. 96.  Are you guys okay over there? Or is there still one up? I got sniped somewhere. Did I kill one? No, I found him. Yeah. King's on. And there goes his head. Oh, wait, that's real. I was totally about to try to walk. Let's push it. Let's push it. Push. I'll keep an eye out on the up top. Or do they have C? They do have C. Yeah. That's how they're getting back so fast. Yep. Up there up top. Up top. Up top. Both of them. Just killed him. Nice. I'm bolting down. I missed a John. John's on me. All right. I'm coming to help. I'm just going to keep cranking. Just keep cranking, dude. Crank away. I got one robin. I'm busy right now. Oh god, I'm getting hit. Up top, up top, up top. I'm keeping one robin distracted. Got him. I'm adjusting position. I got killed by dark exodus. I got killed. I got a kill while I was flashbang. That was kind of nice. The robin's almost dead. Do you want me to get me? Sure, got me. There's Crank. Crank, Crank, you and me mangers. Let's go. You got it. Oh, I got this. Yeah, you got it. GGs. Flashbang me. This has got to be your guy. Last win. Nicely done. And then go.


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Okay, now, hello everyone. Welcome to tonight's stream. Well, tonight for me, it might be morning or afternoon for you wherever you are, but I am Robin Shaw and I am teaching live from South Korea, but I am a Canadian teacher. Welcome to the students. I'm just gonna give a quick check to the top students who are here and who have commented, commented, commented. Maybe I need a little tea to get my voice energized. All right, Layla's here, how's it going? I feel this week was longer. You know, I feel the same as you, Layla. This week seemed longer than usual. Slip walker still here, okay. I'm happy to see you, Slip walker. You're still around. That means there's still hope for the world. This is listening.  I always wear a black hat. Kavino, hello, Kavino. Kavino likes to ask travel questions. So, Kavino, this is the best place to ask me travel questions. And I know you have a lot of travel questions, Kavino. So, ask away here. Lolly Lolly, Lolly Lolly's here, but Lolly Lolly is shy. She doesn't wanna speak to me as a friend. All right, let's get started. I forget why we're here though. Start asking some English questions. It's been a couple weeks since I answered some English questions, so hopefully you've been studying English in that time and you have come across some strange, interesting English that you're not sure how to use and maybe you wanna ask now. And if you don't have any English questions, you're free to ask life questions or talk about some other topic. Let's get it started. Kavino asks the comments here. Wouldn't you have any idea to travel to other countries? Well, I'm gonna fix your question because your question is not correct. Let's go to the whiteboard here and I'm putting Kavino's comment here and I'm gonna fix the grammar for you because that's why we're here. I'll make it bigger. Wouldn't you, well, we need a question mark. For any question, make sure you have a question mark. So, wouldn't you have any idea to travel other countries? Now, Kavino, this question is awkward in English but we're gonna fix it up. Maybe we're not gonna start with, wouldn't you? Do you have any idea? Okay, that's a good start. Do you have any idea? And I'm gonna use a which countries you might travel to next. That might be a, it's a very difficult question to ask. This might be a better way to phrase it. Do you have any idea which countries you might travel to next? That's a possible way to ask that. So, do you have any idea which countries you might travel to next or which country? But for me, it's countries because you could use country. But for me, yeah, I've probably traveled to multiple countries. And Layla asks, oh, why is it? I wanna keep it big here. Is black your favorite color Robin? No, I wear a lot of black or dark, dark black, black or dark blue on the live stream because I can't wear my other shirts. If a shirt has stripes or checks pattern, it doesn't really look good on YouTube. So I usually wear, we say a solid color, just one color, no pattern. So I like to wear solid colors just because it's YouTube. So yeah, you'll see a lot of black, a lot of blue. I don't wear, I don't have clothes or a solid red or purple or pink. And Covino, you didn't learn, I taught you, if you're gonna ask a question, I don't know if it's a question because I don't see a question mark. So how about the weather condition in your country? We always need that question mark. This is critical for a question. How's the weather condition in your country? You could just say how's the, how is, I'm gonna make this more of a speaking phrase. How's the weather in your country, condition in your country? You don't need to say condition, you can say. How's the weather there? That's an easy way to ask that question. How's the weather there? And I could say the weather's cool in Korea. And Sleepwalkers asking, is the expression bah humbug, so this is the expression and I don't think it's capitalized. Old fashion, as I understand it means nonsense. Well, this is a famous expression from, I believe, Scrooge. The Christmas story about Scrooge. Scrooge is a very stingy person. He doesn't like to spend money or give money. He's not generous. And he often, in the book, who wrote Scrooge? Scrooge, I already, books, I'm forgetting. Everything I learned in university. Charles Dickens, oops. Okay, so in his book, Christmas Carol, Scrooge always says bah humbug. So it's all in English. Nobody's gonna say that. Nobody's gonna say that these days. Nobody. Zero percent. And bah humbug just means, yeah, it could mean nonsense or I don't like that. But it's only gonna be in Scrooge. Or Charles Dickens, Christmas Carol. Bah humbug is what Scrooge says. No, nobody in modern times is gonna say that. And sound, okay, Layla's got two weeks of questions here. The sound of construction behind my house is quite noisy. That is totally annoying me. Well, yeah, that's right. But as I read this, this is okay, this is okay, this is okay, this is okay, this is okay, this is okay, but I'm using totally and it's right. But it seems a little awkward to me. I would just use, this is really annoying me. I know you wanna try to use bigger vocabulary or more interesting vocabulary, but sometimes we just use simple vocabulary. It's, you know, and if we're speaking, we're probably gonna use contraction. That's really annoying. And that, yeah, it's really an annoying me or it's really annoying. That's really annoying. I would even say the sound of construction behind my house is quite noisy. It's really, that would be a period, new sentence. I would say it's really annoying. Jose Gonzalez, I like to wear solid colors too. Also, I don't like to wear brand name. So some of my other clothes might have Nike or Adidas and I don't wanna wear any brand name on the live stream. So the clothing rule is solid color and no logo or brand name. So my clothing options are limited. All right, Cavino, if I get a chance to travel to another country, to another, okay, I'm gonna fix up your English here, Cavino. If I get a chance to travel to another, if we're gonna use another, we're talking about one. So you can say, I definitely will come visit you. That's correct, that's good. But when we're using other and another, here let me, another is usually another one and other ones like that. So one, another country, other countries. So if I get a chance to travel to other countries, I will definitely come to visit you. If I get a chance to travel to another country, I will definitely come to visit you. So singular, we're gonna use another, plural, we're gonna use other. Doesn't seem to be many people here today. If you're watching, say hello, let me know you're watching. Robin, do you leave your comfort zone very often and begin something different in life?  Yeah, I don't think I have a comfort zone. Every, I'm pretty brave and I'm, it's very easy for me to disrupt my comfort zone. Yes is the answer, always I'm leaving my comfort zone. Leila, I just saw these two words, abstain and refrain and that they are similar or synonyms. But I guess they're not. They seem like synonyms. Why do you say they're not? Then went to the dictionary and made the following sentence. It's okay, so let's keep these up here. We have abstain and refrain. They seem like synonyms to me, but let's see what you got. I want to lose some weight, weight will be uncomfortable. I must refrain from fast food. All right, refrain from, we might say eating. Well, before I get to the next sentence, can we say abstain here? Yeah, sure, I think you can. There's synonyms. I'm just gonna check out the dictionary because I am not a walking dictionary. So refrain, so refrain means to stop yourself from doing something. So if I must stop myself from eating fast food, okay, so refrain works, abstain means decide not to do it. Cause it's bad for your health, something like that. So it seems like very close synonyms here. I will abstain from talking, interact.  Yeah, I think those work, those are fine. I don't think there's a problem there. They seem like synonyms to me. So don't worry about that, Leila, those sentences look fine. Oh, who's this? Lolly Lolly, she's planning on cooking and she's planning to move. Why do we use on in the first sentence? Okay, I know why. I know exactly why we use on, but can I explain it? Probably not, I get it. All right, so I think you gotta focus on the ING here. So if you wanted, you can say, you can make the same sentence with moving. So she's planning on. So I think the connection here, she's planning on, if we're gonna use planning on, then your next sentence is gonna be verb ING. All right, she's planning to move. Well, you're not using the ING, you're using the infinitive. So similar, you could say she is planning to cook. So it depends on the grammar you want to use for the sentence and let's just, so you could say she is planning on cooking tonight. Let's make a full sentence. She is planning on moving tomorrow. She is planning to move tomorrow. She is planning to cook tonight. Yeah, that's it. So planning on cooking, planning to move. That's how we use it. I mean the same thing. The crying of baby, the crying baby. Okay, I recommend just say the crying baby, but you're saying the crying of the baby is really annoying. Yeah, Leila, I don't think you have a problem with annoying. You're using it fine, no problem with annoying. That's correct. Ramadan. Oh, how do you wish, please teach us. How do you wish, this is a question? You're asking a question? What is your question? I don't know, is this an English question? I do not celebrate Ramadan, so I really cannot teach about that. So it starts, so how do you wish someone a happy Ramadan? So this is Ramadan. 2020 begins in the evening of Friday, April 1st, and ends in the evening of Sunday, May 1st. Dates may vary. How to express Ramadan greetings. Okay, so I just went to the internet, which is a better teacher than me. So Ramadan Mubarak and Ramadan Karim, these are Arabic sayings that translate to blessed Ramadan and generous Ramadan. So I think that answers your question. You could say to people blessed Ramadan, or generous Ramadan, in English. But I don't know, I'm sorry, I don't celebrate Ramadan. Robin, among foreign teachers, your coworkers, do many of them have YouTube channels? No, none of them. None of them have YouTube channels? No, none of my coworkers have YouTube channels. Lalli Lalli, just rechecking the Ramadan, blessed Ramadan. Okay, who's asked this, sorry, Lalli Lalli, there's no end to learning English. Why verb ING after two? There's no end to learning English. Well, this is your gerund, I don't have time to teach gerunds, I think I've done that in other videos. So this is the verb, how do you express, I cannot think today, the verb. All right, and now in the form of a verb with ING. So, I don't know the technical rule. This is all I can find, and it looks, it's too technical for me. That's not the rule, that's, oh, how come it's not copying? I want to copy from the internet. It's important to recognize that the word to is a preposition in these cases because it must be followed by a gerund. This is your gerund. It is not part of the infinitive form of the verb. So you have to consider that there's no end to, and then that's not an infinitive verb. That's the technical, I don't know a quick answer, I don't know a quick rule to that, just very often with gerunds, before the gerund you're gonna have two, what's another one? I look forward to eating dinner, how about that? So, this is the connected expression. I look forward to eating dinner, something like that. You cannot say I look forward to eat dinner. This doesn't work, no. And you cannot say there's no end to learn English, no, because you can't use the infinitive, you gotta use the gerund. So, think of this two connected to forward, don't think of this two as connected to the verb. Hope that helps, lolly lolly, that's a little more technical for me to properly teach that without a lot of preparation. Do native speakers use lunch as a verb commonly? For example, I am going to lunch with you. Well, here it is not a verb, this is a kind of a location. I guess it could be a verb because you could say, I'm going to Canada with you. So, in this case, Canada is not, this is not the verb of the sentence. So, this is kind of the location where we're saying, I'm going to lunch with you, I'm going to the place we eat lunch. So, this going to, again, you're thinking of the two as a verb to lunch. Now, it is possible that this is a verb in this sentence. I'm going to lunch with you, but using lunch as a verb, but I don't think we think of it that way. We think of it more as a location. I'm going to the lunch place with you, but we don't say place. Sure, now I'm going to lunch with you, but it could be a verb too. You could look at it two ways. You could look at it, I think more commonly is the place, but it could also, I'm going to lunch, then it would be a verb to eat lunch with you. That is possible too, but I don't think it's as common. Indeed, Mubashir. Teacher Robin, can you fix this, these is one sentence or many sentences for us if something type incorrectly. We perform, don't offer, prayer. Why are you saying sell out?  You could just make one verb, pray, we pray five times a day. Perform prayer seems like too many verbs there. I'm trying to, because I got to educate myself on Arabic, Muslim, or Islam, prayer rituals. These are expressions I do not know how to use. Salat, I see a lot of salah. Would that be right too? We pray salah five times a day. Sorry I can't help you with that, M.D. Mubashir. To distinguish between used to, be used to, get used to. I made some sentences, I don't see them. Yeah, Lee, Lucina, hello. Hi, I saw this in the book, Vocabulary News, some examples with go, ng, and I didn't understand when I will put ing with go, verbay, main verb, or both. I don't understand immediately also. Do you have example sentences? I like, I gotta think, I like to, to go jogging like that. So this is your jaren, I like to go jogging. So what's the root, you're looking for a rule? I don't know all the rules at the top of my head. But yeah, in English, I think I cannot, I cannot teach, your face is in the way. Let's move my face. I cannot teach jaren's in detail today. That's not an easy thing to teach in two minutes. So if you wanna study more and to understand, I would suggest called YouTube and check out a video on jaren's. This will help you better than me right now because this is something I would need to prepare more examples to teach right now.  Let's look at your examples.  Yeah, these are jaren's in the morning and Bob is going fishing. Yeah, those are all common expressions in English. They all make sense, jaren's. There's not a lot of jaren expressions so you can probably learn them and memorize them within a day how we use jaren's. But sorry, Kelly, I cannot do a full lesson on jaren's right now. That's a little more difficult and I cannot give a quick answer. I have to move on. Clarification about Robin, I don't know. Ines, hello, Arturo, hello from Honduras. Funny story in Honduras, when I was in Honduras, I traveled through Central America and I crossed the border, I think it's from El Salvador, right, El Salvador to Honduras. It was nighttime and I walked across the border and I missed the bus to the city. So I had the hitchhike in Honduras.   He drove me about one hour in Honduras to the hotel and I gave him $20 for a thank you. And he didn't speak any English so then I don't speak any Spanish. So he picked me up and I'm like, body language, 100%. Pointy, pointy. Yes, no. Oh, that's my memory, my good memory of Honduras. Okay, I understand, Covino. And this is from Unes teacher. Please, can you explain when exactly we use go to and will and what's the difference between them? Uh, I'm going to, I don't think it's go to. So example, you're talking about future tense. Is that your question or future tense? I will go to Canada tomorrow. I'm going to go to Canada tomorrow. Are you asking about that? So it's will and going to future tense. There is a technical rules when we use will. There's technical rules when we use am going to, but I think in the modern English day, most native speakers are not following these rules. We're using will and am going to interchangeably in the same to express the future. I'm not sure if that's your question. What else could it be go to and will? You could just have present simple tense. I go to Canada tomorrow. I will go to Canada tomorrow. Now this is possible, where you're not. Yes, Google wants to change it to the future tense, but sometimes we express in speaking. Don't do this in writing, but in speaking, a native speaker will often express a future event using present tense, like I go to. This is not future tense. This is present tense. So sometimes, yes, we use present tense to express a future action, usually a near action. Tomorrow is near. So if you said I go to Canada in 10 years, that's a little too far. So I go to Canada tomorrow. A native speaker might say that for future tense, only speaking if you're writing, I'm going to Canada tomorrow. All right, let's check out Layla's used to. I used to visit many concerts. She is used to saying the truth. Okay, you're using used to and used to correctly. But the verbs are awkward. I used concerts, we don't visit concert. We go to a concert. I used to go to many concerts. We go to concerts. We don't visit concerts. And she is used to saying the truth. This is okay, but a native speaker is probably going to say telling the truth. Usually we use the verb tell for truth. Tell the truth or tell a lie. Tell the truth or tell a lie. We use the verb tell, not saying. But the used to is fine. She gets used to the hot weather. What do you think about them? Oh, the sentences, okay. She or you, why did I say she? Anyway, you probably confused me with the gets because you does not put an S on the verb. You get used to, you, this should be past tense. You got used to the hot weather as something that passed or you will future get used to the hot weather. Present continuous. You are getting used to the hot weather. All right, so this is one of these ways is how we're going to use the grammar. You past tense, future tense, or present continuous tense. But the get used to is fine. Robin, who's saying this sleepwalker? Robin, sometimes I see that native speakers use did instead of past form of the verbs. Okay, let's see. For example, I did write. Is it correct? It did write it. Yeah, what do you mean by inversion? Not inversion. Yeah, for speaking, it's hard to teach speaking sometimes because, you know, students are learning the rules and then they hear these native speakers saying weird stuff with English. Yeah, you know, there's weird things like this. I do write books. So ideally you should say I wrote it and I do write books. You should say I write books. So these kinds of sentences, yeah, they're going to make the little grammar adjustments. I don't know if there's a technical rule, but these are used more for emphasis. So it's speaking, you know, in speaking, we often use thing words for more emphasis and these would be emphasis words. But if you're writing an essay, just write the normal way. Hello, hello. We have a special guest. Hello, Joe. How's it going? That person who picked you up and drove for about one hour, who's writing this, Leila? Was unique. Didn't care about the way to connect with you as a foreigner. What's the question? What's the question, Leila?  Okay, now I understand. I thought you were asking a question. So this is real. That person who picked you up and drove for about one hour was unique. Yes. Well, no, I think wherever I travel in the world, people always help. So I don't think he's unique. I think he was normal. It's normal for humans to help each other. He didn't care about the way to connect. He was just a human helping a human. And I think that's normal, not special. All right. Eunice, thank you. And Leila, why did you not get home early? Why didn't you get home early? What's the difference between them? And which one is more natural? Well, right away, this one's more natural because it's a contraction and contractions are better. This is possible. This sounds like someone's angry and they might say this. This is a spoken English. So you're gonna see this in spoken English. It means the same thing. Why did you not get home early? I think the emphasis on this, the grammar is structured to put more emphasis on the not. So that's possible. This is natural. They're both natural. Depends what you're trying to express. What's the difference between them? Nothing. Which one is more natural? I'd say this one's better. You're gonna hear this one. It's not wrong. Is it possible to use visit cities? Yes. Why can't you use visit to country? Yes, you can. I visit Canada. I visit Toronto. That's perfectly okay. Let's use a past tense because Google wants me to put past tense. That's fine. You can visit cities. You can visit countries. I visited Disneyland. Something like that. Making my tea. I was asking questions in the chat. I'm all caught up in the chat. I don't think I missed any questions. All right, I will end the live stream in a few minutes. Get any last questions or comments in. I was filming some videos today with teacher Fiona. If you know my YouTube channel, there's a teacher called Fiona. I was teaching, or I was filming videos with her today. Videos about tongue twisters. Hello. Oh, Stella's here. Hello, Stella. Hello, Mrs. Robin. It's time to take them to the next level. Thank you, teacher. Hello. How do I take them to the next level? Hussain. Hussain Ahmed from Sri Lanka. We have a lot of students from Sri Lanka. I went to Sri Lanka 2016. Beautiful country, beautiful. I love Sri Lanka. I wish I had, I spent more time there. I hope to go back to Sri Lanka. All right, Layla's sticking in a question. Yeah, Hyunwoo is in America. Let's have some coffee. Could we have coffee? When do native speakers use one and two and the first? I'm more concerned with this error right here. First is more friendly. Let's have some coffee. Could we have coffee? Well, this is what you're gonna say to your friend.  Could we have coffee is something you say to the waiter or waitress? This is more of an order. So this is what you're gonna say to your friend. This is what you're gonna say to the waiter. Could we have and probably gonna use some coffee. We have some coffee. Let's make it more polite, please. But if you're talking to your friend, let's have some coffee or let's have some coffee. You can also say let's get some coffee and this is an order. You wouldn't say to your friend, could we have some coffee? Robin, what was the strangest and hardest questions? What were the strangest and hardest questions you were asked today? Probably strange. I don't think there was a strange question. The hardest would be anything with grammar that people come in with the grammar questions and a lot of the times I don't know the technical rules because there's so many situations. But I do my best. No strange questions today. But I must say the most difficult questions usually come from Alyssa. So if Alyssa is still listening, I doubt she is. But if she's still around, she usually asks the difficult, really difficult questions to me. Stuff I really have never thought about. Layla, you ask a lot of normal questions, Layla. Your questions are good. They're all normal. Sleepwalker probably has really interesting questions too. Yeah, Alyssa's are difficult. Sleepwalkers are interesting and Layla is normal questions. So which ones do I like teaching? I like the normal questions. They're easy. Sometimes sleepwalker has really interesting stuff like the Baham bug today. No one's ever asked me about Baham bug. So sleepwalker, keep them coming. But Alyssa, when I get Alyssa's questions, I'm sweating. Uh-oh, what's this? I don't know. I think we're gonna end the stream now. Thank you everyone for watching and please spend your time every day, sometime every day studying English. I will see you again soon. Until then, have a good week. So take care and...


To understand how this long chain forms let's limit ourselves to just looking at the phi and the psi bonds. Actually I'll make things even easier. Remember that from a Shandlen diagram that there were just two or three regions that was happy. So let's take a this amino acid and say it can kind of be in an A state or a B state and I'll forget everything. This is trivial right? It's two states here multiplied by two states here, multiplied by two states here, multiplied by two there, two to the power of eight or something that's piece of cake. The problem is that you have more than eight amino acids in a protein and this comes back to that what I mentioned that the exponential function grows faster than you think. In this case it's a power function but it's similar. So if I have two states per residue and then I have n residues, well that means if I have 100 residues remember those were among the smallest proteins I had in that table. That's going to be two to the power of 100 different combinations and that's roughly 10 to the power of 30 which is around the largest number you can represent in a single position. Let's assume that nature is super fast at testing things out here that I can test one new conformation per picoseconds. There is no way it's that fast but let's just assume that. If I test one per 10 to the minus 12 seconds that would mean that this would take 10 to the power of 18 seconds to test every single conformation. Well that's not much, just seconds right? It's 30 billion years. The world is only 4.3 billion years old. So there is no there is no theoretical way for this chain to test every single possible conformation and yet it does. The person who first realized this this paradox is Osiris Leventhal who did those movies I showed you in lecture two and it's even called Leventhal's paradox. So what Leventhal's paradox says is that we know that this change finds the thermodynamic minimum. Christian Anfess improved that and yet there is absolutely no way for the chain to test every single possible conformation. So how does it even find that conformation? We don't know. One way or another it does but it can't be brute force searching. Brian Robson did a fun cartoon of this many years ago. The great protein making this jump that we have no idea about. And for almost 20 or 30 years this had remained a gigantic challenge. So we do know that the proteins do take the form but how does the process happen? This is going to be super important if we want to engineer proteins and there's been remarkable progress in this I would say the last 10 years. This recently as 2020 we're now finally able to predict protein structures accurately. This is not going to be a trivial problem to solve. It will depend on free energy. It will depend on things happening in a certain sequence and of course at the end we are not necessarily going to do brute force searching. But to understand this hierarchy we will have to go to the next step in studying the so-called secondary structure elements of proteins.


is a very exciting announcement. My name is Sheena Wright, I'm the first Deputy Mayor, and we are, as Anna told me to say, Buenos dias! But as you know, I had the honor of serving as the Deputy Mayor for Strategic Initiatives at the beginning of this administration. I will tell you, the position is demanding, but incredibly rewarding. And what makes rewarding is it's a unique role in this administration that has the huge opportunity to make a significant impact in the difference in lives of everyday New Yorkers. Whether it's working with the next generation of change makers and in managing the Department of Youth and Community Development, the great work that it will continue to do with summer rising, summer youth employment, working with CUNY, or the Mayor's Office of Child Care and Early Education, which was recently established, which has a big vision to remake and reform the early education system for the city of New York. The Mayor's Office of Food Policy, which is a major priority of this Mayor, in case you didn't notice, it is a huge, huge body of work. The newly created Mayor's Office of Equity, which is really breaking ground in many ways in the city. The Mayor's Office of Nonprofit Engagement, I know it's in the house, which is incredibly important. The Mayor's Fund and the list goes on and on. Anna, you are going to be very busy. So kiss, sleep, goodbye. And these are incredibly important initiatives. And I really know firsthand what this role means. That's why we are so proud and so pleased to welcome Anna to a sisterhood of deputy mayors, as well as leaders across the administration. And with that, I want to introduce our Chief Advisor, one of the strongest women we've got, Ingrid Louis Martin. And Anna didn't have to tell me to say that because I am a proud member of the Afro-Latina family. Yes. So we are really happy today. I'm thrilled and delighted to bring remarks about a woman who has become a sister to me in a very short space of time. You know who I am? I'm the Chief Advisor to the Mayor, a chaplain. Many of you know my journey with the Mayor, a long one. I was with him in all of his administrations. And one thing about this Mayor is that in every administration, he has always found quality women to put in leadership positions. Yes, he deserves a hand for that. For the record, in case you don't know it, there are actually more women in New York City than men. Yes, there are. And in leadership, our administration reflects that information. And it's important. As the Brooklyn Borough President, I'll go back. As a New York State Senator in our office, he had the most diverse office in the State Senate and the most women in leadership positions in the State Senate. As the Brooklyn Borough President, he was actually cited by our public advocate as having, again, the most women in his administration. Not only did he have the most women in his administration, we were the highest paid women in the Senate. So our principle understands the importance of bringing together qualified, talented, strong, brilliant women in leadership positions in government. He understands that, and he does just that. He also understands that a lot of times women are underrated, second-guest, and discounted. This administration helps to put it into that. So it does. As someone who participated directly in the interview and hiring process of our next Deputy Mayor of Strategic Initiatives, DMSI, as we call, will call her because we have nicknames. We have a COS, an FDM, a CA. We have, you know, initiatives that we use. It was obvious to me in a very short space of time who the ideal choice was. All of the candidates, every last single one of the candidates were formidable. However, our next DMSI stood out. She had a level of sensitivity that's needed for this particular position. She's an immigrant, and her story as an immigrant is captivating, and I am positive that once you hear from her and you hear her story, that you too will be as impressed with her as we were. She cares about all that she does. She has an illustrious history of giving back. She worked in government for many years, and in the private sector, in the nonprofit point specific. So I am thrilled and delighted today that we're bringing in another sister, an Afro-Latina sister. A sister that gets it. A sister, yes. A sister who will work in partnership with all of the other women in this administration. She has a proven track record, wonderful track record, but I have to say this, women, women and more women, chief of staff, five female deputy mayors, five commissioner, police commissioner, sanitation commissioner, commissioner of D-Cast, yours truly, me. And the list goes on. So we are blessed. We are excited beyond measure that another woman, a sister, again, an Afro-Latina sister, is once again being added to our administration, and she will serve us well. So welcome aboard, Anna. And you may have noticed that our chief of staff, another one of our sisters, isn't here with us. She could not be here with us because she had other obligations, but she asked me to read something on her behalf and I'm honored and humbled to do it. Morning, everyone. I wish I could be here to show my support for a former colleague and now proud member of this administration who the mayor will soon name our next deputy mayor for strategic initiatives. In my work in state government, I saw firsthand a clear demonstration of this person's skill set. She said this person because we weren't supposed to say her name, but since her name has already been shared, I'm just letting you know why. Skill set and most importantly, her character that has prepared her for the role of deputy mayor for strategic initiatives. A tenacity, a drive and a deep sense of care for the people you will serve. She knew how to master the art of government, delivering vital services to New York is most in need, and was a trusted colleague in both moments of crises and harm. Make no mistake though, her experience goes well beyond government with decades of exposure and an expertise across also the private and non-profit sector. She brings a wealth of cross sector knowledge into a position where you need to be able to navigate swiftly, both internally and externally. She is well prepared to follow on the behalf of all New Yorkers. My mistake, she is well prepared to deliver on behalf of all New Yorkers and move our city forward. I'm excited to have her join this team and to call her a colleague once again and welcome her to the Get Stuff Done administration. And that was our chief of staff, Camille, who could not be here today, and she loves you and she asked me to give you a hug. Thank you so much, Ingrid, and that certainly speaks for all of us. And as much as we appreciate all of the strong women, we do appreciate the men as well. And so with that, I'd like to introduce our mayor, Mayor Eric Adams. I'm glad you said that so we men don't feel bad. But also if I can, Penelope, would you come up and stand next to us? Come stand next to us, all right? This is your moment. You're going to remember this, trust me. This is just really an exciting moment. And I think that what is really something that is going to be kind to this administration in history, when we reflect on this administration, even during a midst of crisis, just think about it. From COVID to the migrant asylum seeker crisis, to making sure our ferries are running correctly to public safety, to dealing with important decisions we're going to have to make around our budget issue, item after item after item. And all the incoming that this administration gets thrown at it all the time of running the most important city on the globe. You just never see this administration cracks or buckles. They're fearless because all of them had to manage difficult moments all their lives. There's something about a woman's ability to manage a multitude of things and at the same time keep forging ahead in innovative ways of just getting things done. And so I'm surrounded by people who probably would have been looked over in high governmental positions because the criterias that others use to bring on leadership is different from mine. And it's going to be a while before people get it. But while they're getting it, I'm going to get stuff done with the leadership that I have. And these first are so important. And don't get it mixed up. Being first does not mean we're just trying to check a box. We took our time and we looked over many resumes. We interviewed many people to make sure we were able to get it right. But it means so much to me that I have the first Indian American to be a Deputy Mayor Amir Joshi as she manages our multitude of infrastructure projects. Every time I walk in a room with my AAPI community and I'm able to talk about the dynamic and fantastic Deputy Mayor Maria Torres-Springer, the first Filipina American to hold this position. And when I made the decision of these important areas that I wanted to address, I went to someone that I trust who led my team of bringing in the talent with Sheena Wright as the first DMSI and now the first Deputy Mayor. Everyone knows the long relationship I've had with my Chief Advisor who has advised me on all of my campaigns and has basically been there for me, my right hand in government. These are real people who are doing real things helping real New Yorkers. And to add to this was a conversation that I had. One of the first people I spoke with was my good brother, Congressman Esmeralda. I told him what my needs were, the balance, my balance of showing the diversity that was important to the city but bringing the right talent, the talent based on my definition. Don't tell me about being academically smart if you're not emotionally intelligent. I won both and I've said that from day one of my administration, he brought me several different names and we looked over them, the team looked over them, and we assembled a real system of betting on who was going to meet both criteria. We looked far and wide. We did not allow voting to be done because with Anna's nine siblings, they would have voted anyone. But we wanted to make sure the balance that we need, that portfolio that Deputy Mayor Wright went over, they're at the heart of what's important to me. Healthy food. How do we really help our nonprofits? They have been denied for so many years and we wanted to make sure they receive the support that they deserve. Our Mayor's Fund, which is crucial, we saw how important it was after the fire in the Bronx to be able to step up and administer the resources that were needed. And so today, I'm proud as we bring on board the new member of our team who's really coming with a wealth of experience, dedication, and her story speaks for itself. We're announcing New York City Next Deputy Mayor for Strategic Initiative and Amazon. And I want to thank her family and friends, and I really wanted her mom to be standing next to her as we did this. I always wanted my mother to be there when I was sworn in. The Mayor I carried her photo, but Anna's story and her mother's story of raising 10 children who are all contributors to our society and what she represents and what it means. This is an American story. These mothers watch their children go on to great heights, but we don't realize what it takes to be a mommy and just want the best for their children and family. And that's what she did.  All of Anna's siblings are just prominent in their own right. And here you have a woman who speak little English, but can communicate from our heart. And now we're seeing the benefits of that. And the beauty of this country and my role as Mayor, I am not the Mayor for only English speakers. I'm the Mayor for every language in this city. And we are really the example for the entire country that you can come to this country and work hard instill the values of family and your children. And no matter how challenging it is, you can arrive at the position of being the Deputy Mayor of one of the most important city on the globe. Man, that's an American story. And so before I get into Anna's long impressive set of accomplishment, I want to acknowledge our whole team here. Many of them are behind us of what we are going to accomplish from leading what we have done from leading the historic child care blueprint of what Deputy Mayor, First Deputy Mayor Sheena Wright did in this role and included securing billions around child care, helping launch my city and cleaning, clearing the ACS of voucher weightless. She unlocked over $4.5 billion for New York City's nonprofits in the first few weeks in office. And she oversaw a major expansion about summer youth employment program. First time 100,000 young people, the summarizing program that she oversaw as well. She set a high bar for this role, creating historic partnership to solve major challenges for everyday New Yorkers. And I remember when I appointed her to Deputy Mayor's strategic initiative, people said, well, she never roped in government before. And I said, that's the plus. That's the plus. Because there's been a lot of professional government to officials that have been in place and still 40% of the young people or family men and women on Rikers Island are dyslexic. There's been a lot of people that roped in government and we had a real housing crisis. A lot of people roped in government and we were unable to educate our children. I think it's time now to start looking outside of government to have not those who don't believe, but those who do believe. And Sheena lived up to that and I'm proud that she's now my first Deputy Mayor. This is more than, this is no more, this is an important time, I should say. And it's important time to have someone like Anna now in this position. For more than a decade, Anna has built bridges between nonprofits and government. Most recently, she served as a Director of Community Relation at the Mother Cabrini Health Foundation, where she led, wrote to improve health outcomes in diverse communities. This is something we must tackle. Health is wealth and health brings prosperity. Before that, she was Chief of Staff to the New York State Inter-Agency Coordinator for Non-profits. In this role, she spearheaded media campaigns across the state, oversaw a $25 million poverty reduction initiative, and helped expand the Empire State Poverty Reduction Initiative to more than 15 cities. Early in her career, she worked with the National Association of Latino Elected Officials, engaging members of the Latino community in the policymaking process. She has gotten a lot done in her career. She has helped a lot of New Yorkers. But in this administration, it's not just about what you've done. It's also about who you are. Anna knows how to get stuff done for New Yorkers, because a story looks like those, the stories of so many New Yorkers. Family moved from Santa Domingo to Dominican Republic in search of the American Dream. She's a proud CUNY alumni, dedicated her life to serving others. This agency has been, the agencies that she's going to be in charge of have been often overlooked, but they're important to the infrastructure of our city. She's joining an administration New Yorkers that look like New York City. And she's a strong Latina, and her representation is such an important part of our city. We are so proud to have her as the first Dominican to serve in the role of the Deputy Minister. And Anna continues in this administration's tradition of leadership by strong women, side by side with the men that understand we're part of the men who get the club. We have to do it together and leave no one behind. And Anna, you are more than prepared to take on this challenge. And I can't wait to work with you, I can't wait to work with the team as we continue to get stuff done for these, for New Yorkers during these most difficult times with so many things happening at once. But we wake up every day excited and thankful that we have the obligation to do what's best for New Yorkers. And we don't run away from the problems. Winners want the ball when the game is on the line. And right now, we have a real winner that we're going to turn the ball over to because the game is on the line and she will score. Thank you, Anna. What a beautiful room. Not just the architecture. Everyone here. Good morning, everyone. And thank you, Mr. Mayor, for that introduction. Thank you, thank you, Chief Advisor Ingrid for the beautiful word. And who's the first opinion major? She's not right for that beautiful, beautiful remarks. I am thrilled to be the next deputy mayor for strategic initiatives. Thank you. And I'm short. My New York story started when I was 17 years old and immigrated to Bushwick, Brooklyn from the Dominican Republic. Brooklyn, indeed. Growing up in the Dominican Republic, every Dominican learns about three things. Faith, baseball, and politics. My family knew the importance of our strong faith, the value of public service, and the significance of staying civically engaged. As a child, they showed me the meaning of hard work that fuels me to this day. My dad was the definition of hard work. He never needed an alarm clock because he said his body always knew when to get up and work. My mother pushed me, and yes, my nine siblings, to strive for excellence. She never, never let us waver, especially when things got hard as they often do. When we arrived to the U.S., we came seeking not just the American Dream, but the New York City Dream. I came here not knowing one word of English and working a factory to help my family. However, thanks to the support from my non-profit in Brooklyn, El Puente, in Williamsburg, where I enrolled in an adult learning class, I was able to learn English and eventually become a proud CUNY graduate. It is the experience that I bring to this role. I know firsthand the value of a CUNY degree, the local non-profit talents at hand, and the fundamental role government can play in providing opportunities. It was a service that I received both from the public and non-profit sectors that turned my American New York City dream into a reality. Now, I am fortunate, as the major mentioned, and so did the first deputy major, to be overseeing the very agencies and offices that helped me reach this moment. Professionally, and as the major mentioned earlier, I bring to this position over two decades of experience but on all public, private, and non-profit sectors. I have spent six years as a chief of staff to the New York State non-profit interagency coordinator for non-profit. I messed that up. I'm going to go back and say it again. Supporting the sector and providing oversight for a $25 million and poverty reduction initiative. I also saw the rollout of that program, and as the major mentioned, that expanded to 15 cities. Before that, I work at the National Association of Latino Elected and Appointed Officials Naleo Educational Fund, mobilizing Latinos to become civically engaged in American politics and executing grassroots campaigns. Finally, before taking this role, I work with Mother Cabrini Health Foundation to deliver, there we go, to deliver clinically needed healthcare funding to underserved communities. I want to end by thanking my family, my loved ones who helped me reach this moment in my life, and who has supported me through my journey, through my friends. There are so many. It is hard to count, and I have nine siblings, so counting, I know how to do. But to Jenny, who's here today, to K.S. Dordin, to Shannon, to Myra, to Jennifer, and to Libria, and to Angela, who's right behind us. You have gone above and beyond to support me in my career, and to my dear friend, Dr. Rosengueo. Thank you. I promised my sister I wouldn't do it. To my nine siblings, to my nieces, to my nephews, every day you inspire me to do better, to be better. We all wish Papi was here today, to my beloved husband. Thank you for your unconditional support. You made my world better. This role is personal to me. I want New Yorkers to know that you have an immigrant, Latina, who came to this city with a dream, who worked in the service industry, whose first degree is from Hostos Community College, a proud CUNY school, and who understands firsthand the role government can and must play to work for hard-working people. I want to express my excitement to Mayor Adams, my excitement to continue my New York City story to Mayor Adams, and the amazing group of women leading this administration from our first Deputy Mayor, to our Chief Advisor, to my fellow Deputy Mayor, as well as our Chief Staff, who is now with us today. I want to express my excitement because I cannot wait along you to get stuff done. Thank you, and as my mom just said, the American dream, the New York City dream is still alive, and it is still well. Thank you. I don't see her, but I know she's the role of our Deputy Mayor and Williams Eisen, who has just really, really navigated many of the social service aspects of the city. We want to, our final speaker, is just a real friend and a pioneer himself, who first Dominican congressman from here, not think of history all the time, sitting in the classroom as a child, not able to speak English, but just continue to move forward. He's just a real friend and advisor on so many of these issues, and I know this is a proud moment for you, and I want to bring on my friend, Congressman Adjana Esviar. Thank you, Mayor Adams. Not only for getting the job done, but for keeping your word. You said that you would take on crime, and crime is going down, in the 34th precinct, which used to unfortunately average over 100 homicides in the 80s and 90s. Today, there's zero homicides. Even with all the obstacles and hurdles, you have completed the mission and continued the mission of the city to be a beacon of hope and opportunity for immigrants. So we thank you for that. And you pledged to have a diverse administration that reflected the composition of the city of New York, and led by women. Once again, you have kept your word by bringing yet another capable woman as a deputy mayor. This time, the first Dominican American deputy mayor in the city of New York. Thank you. Thank you. Thank you for keeping your word. And to Ana and her family, the mayor spoke about his love for his mom. Many of you know my mom, the love that I have for her. She's never short of an opinion either. But to see your mom here and your family here makes this a majestic moment. It makes this a New York City moment. It makes this a historical moment. And it is an act that will strengthen the fabric of the city to bring an immigrant woman from Brooklyn. I wish you would have been from Washington Heights. It would have been a perfect story if she came from Washington Heights. But such is life. And that's true. I bet you you're from Brooklyn, too. But, you know, we're so happy to have Ana as the deputy mayor and to bring her skills to this city, this great city that provides continues to be, you know, if it was the 1960s, I would say or 70, a factory or dream, but it's an incubator of opportunities, right, mayor. And so we will continue to work with your administration and we will work with Ana at the federal level to ensure that we do better for the city of New York. But we want to remember today as some majestic moment put forward by a mayor that not only gets things done, but that keeps this work. Thank you. Thank you, everyone. I think that that on top.


In this lecture number 11, we will continue discussion on spreading contact angles, work up addition, not only in context of smooth surfaces, but also on rough and composite surfaces. And as mentioned last time, we will take recourse to free energies considerations rather than surface tension, because first free energies are difficult to measure for solids and they are not a precise concept to define in terms of solid surface tensions. To keep this lecture complete in itself, we go a few slides back and resume from the discussion on magnitudes of contact angles of liquids on solids. We had seen that Young's equation allowed the contact angle theta to be related to the work up addition between the liquid and solid and the work up cohesion for the liquid which is trying to spread on to the solid. And if it fails to do so, it would be restrained in the form of a finite lens in its equilibrium shape. So, Young's equation would relate the contact angle to WSL and WL which is the work up cohesion of liquid and you know that is twice the surface tension of the liquid. And we had seen that for a given surface tension the contact angle would increase as the addition between the liquid and the solid decreased and that was indicated by three pictures in which the contact angle made by the tangent to the surface of liquid at the three phase contact line made an acute angle for the greatest work up addition. That was 90 degrees angle when the work up addition was relatively less and the angle became obtuse when the work up addition for the liquid on solid decreased further. And one could take that argument further to determine what would be the maximum contact angle possible, how obtuse can it get theoretically one may expect a contact angle of 180 degrees. However, in all real liquid solid systems this would not be achieved. Having said that we will actually use a contact angle of 180 degree in one of the examples to follow in the later parts of this lecture. So, in practice you have mercury resting on steel giving you a contact angle of about 154 degrees. If you place a water drop on paraffin wax the theta could be measured up to 110 degrees that would indicate the work up addition from Young's equation as WSL equal to 48 Ergs per centimeter square. That is pretty close to 43 Ergs per centimeter square measured for liquid paraffin wax liquid paraffin in contact with water that is pretty close to the work up addition for the solid wax that we have cited here. On the other hand water resting on polyethylene will give you a theta of 94 degrees. High theta or contact angle is also attainable on surfaces which are normally hydrophilic. I hope this statement is clear to you. Once we say that we are looking at water and a solid, if the solid surface is hydrophilic then the necessary implication is that contact angle would be very small. If water has a positive spreading tendency on this hydrophilic surface the contact angle should be 0. However, what we are trying to imply here is that it is possible to attain a high contact angle by modifying this otherwise hydrophilic solid surface. So, we take the example of glass clean carefully with hot chromic acid that would give theta equal to 0 degrees per water. However, a very thin layer of silicone or a derivative of dimethylsilane would completely alter the weighting properties. What now happens could be shown in the form of diagram. Here we can see what would happen if you have a very thin layer of dimethyl dichlorosilane laid on top of the hydrophilic glass surface. So, if this is a clean glass surface this should be hydrophilic. If we had to spread water or place a drop of water on this surface it would just flatten out into a thin film of water right across this hydrophilic surface. However, if you look at the structure of this surface you would have a silicate lattice which gets chemically modified if we were to place on the clean glass surface this dimethyl dichlorosilane. What this does is that the OH groups on the outside of the clean glass surface would get reacted with dimethyl dichlorosilane releasing HCl and then bonding this group over here. So, this is a case of chemical bonding this unit is repeated all over the surface what will the drop of water placed on top of this chemically modified surface C it would see the methyl groups that is about it. What has happened the clean hydrophilic glass surface has been rendered completely hydrophobic now because of these hydrocarbon groups methyl groups even a monolayer of dimethyl silane will render glass or steel completely hydrophobic or completely lipophilic. That means now the glass will be weighted by oil this knowledge is used often in preparing suitable rings or dropping tips for surface tension measurements. When we go into the details of surface tension measurements will be spending quite some time on the procedures preparing our equipment and surfaces for actual measurements. So, we continue in this lecture the concentrations of contact angles and spreading also into rough surfaces. This is what I have just explained dimethyl dichlorosilane attaches so strongly to the surface of glass that now you would not have contamination of liquids which are brought in contact with such a modified surface. They were certainly other options possible for example, heavy metal soaps and long chain fatty acids and amines could also produce similar effect rendering and otherwise hydrophilic surface hydrophobic. But there is a risk involved here because these compounds are not chemically bonded to the surface. So, they may actually contaminate the liquids which are being studied for their spreading tendencies contact angles etcetera. They have been commercial products available under various trade names Tadol trifilm M441 of ICI these were the materials available which could be applied from solution in carbon tetrachloride making the silicate lattice now hydrophobic. The conclusion here is that silicone and silane treatments are preferable because they would necessarily avoid contamination of adjacent liquids. We talked about Teflon a few lectures ago this polytetra fluoroethylene PTFE also known as Fluon or Teflon you would know is strongly water repellent. I had mentioned that nothing sticks to Teflon. With respect to water the contact angle is 108 degrees which is about 14 degrees higher than for polyethylene. The higher contact angle is again a reflection of less work of addition or less tendency of water to adhere to Teflon compared to polyethylene. But it does not mean that Teflon surface cannot be made wettable with water. But you need an intervention like a strong wetting agent like sodium, dioptylsulfo succinate to be used along with water. If you make a solution of STOS then the aqueous solution can actually wet Teflon. At this point we logically move into a somewhat more difficult question that is with the observation that so far we have restricted ourselves to only smooth surfaces. We only talked of smooth solid surfaces. What would happen if we were to have a rough surface? Same liquids that we have been talking about in terms of contact angles or works of addition or spreading cohesions how would these magnitudes get changed? What principles would govern this and maybe some of the common observations that we make in everyday life perhaps the answer could lie in the reality of rough surfaces. I intend to take you through the very fundamentals of these considerations for rough surfaces. So we may go slow here but hopefully we will get a hang of what are the chief considerations which make rough surfaces different from smooth surfaces. I already primed this thought that contact angles would depend on roughness of surface. Rough surfaces will be perhaps also have accompanied adsorption of impurities of water maybe even air and if we have these adsorbed impurities especially compounds like water we might even have the possibility of solid surface molecules reorienting themselves. These aspects would have to be addressed in at least some sense. Let us see how far we go how far we can go into these details. First to note is this very broad observation made by Ray and Bartel in 1953. Surface of a surface makes contact angle further from 90 degrees. What it means is if on a smooth solid you get a contact angle greater than 90 degrees if you take a rough equivalent of that solid same composition except that surface is roughened then the contact angle will become even more greater than 90 degrees. However if the smooth solid has a contact angle for a given liquid less than 90 degrees then the roughness will decrease that contact angle further. So it is like a situation the contact angle relative to 90 degrees if greater than 90 degrees it swings further away is less than 90 degrees again swings further away from 90 degrees that is the way roughness seem to seems to affect the contact angle could we quantify this. It is fine as a matter of experimental observation but we would need theoretical substantiation too. So if this is clear to you clear enough also to remember we can move further. Let us look at some magnitudes. If we take smooth paraffin wax for water the contact angle is above 110 degrees roughen the wax surface and the contact angle will become about 132 degrees it has taken theta further away from 90 degrees is an application to this while measuring contact angles and surface tensions using a method called Willem's plate method we actually use roughening. This will ensure that the contact angle of thin mica plate in contact with the surface active solution is always close to 0. We need it fine there are applications in measurements of contact angles measurements of surface tensions. So we can keep this in mind as a way of ensuring whenever we deal with solid liquid systems and we need the solid to be weighted by the liquid as one possible avenue in order to get the weighting of the solid by the liquid. Next we come to the question that before we can exemplify the effect of roughness on contact angle we got to quantify roughening. We must be able to define the roughness or roughening in some quantitative manner. So the way to do that is we define a factor called rugosity or roughness simply as roughness as the ratio of the real surface to apparent surface. Let me explain this supposing we have a smooth solid surface alright and we are looking at an equivalent which is rough. So let me draw some kind of roughness equivalent here the same solid but rendered rougher. Now how do we define the roughness here quantitatively? So we define this rugosity r as the actual surface which will be corresponding to this crevices and valleys here as it is. How we measure is a different matter we might use a BET apparatus to know whatever is the actual surface area which is again based on adsorption. How much gas is adsorbed and knowing the molecular cross section using the BET theory we can estimate what is this area. Apparent area that we have in this context is whatever is the area which is the area of projection. Looking from top if we were to look at just unit area which is projected then between these boundaries look from top we will have 1 centimeter square apparent area 1 centimeter by 1 centimeter square is what we are looking at. But the same apparent area corresponds to much larger area because of this roughness. So the rugosity is the real to that projected or apparent area. This is what we could use as a means of quantifying the roughness of a solid surface. So the question next is what would be the contact angle for the same liquid on the same solid but with rougher surface. Historically this relation was given by Wenzel in 1936 and the relationship is as simple as this cosine of contact angle for a rough surface is equal to the rugosity times cosine of angle for a smooth solid surface. So we have cos theta bar corresponding to the rough surface theta bar is the contact angle for rough surface, theta is the contact angle for the same liquid for smooth solid r is this rugosity real to apparent surface area ratio or real to projected area ratio. We should be able to derive this though. So that is our next task to show that Wenzel's relation is actually logically possible to derive. So let us prove Wenzel's relation for rough surface the contact angle is theta bar and for smooth surface the contact angle is theta. What we use a starting point here is the equation for infinite simul change in an equilibrium system on similar lines as we had addressed last time too. But now remember that we are dealing with rough surfaces we are actually referring to the same expression or same kind of equation which for infinite simul change in equilibrium system adds up the free energy change and work done. Infinite is the same diagram we are referring to we have a solid plate immerse in a liquid and inclined to the horizontal at angle theta such that the liquids meniscus is planar right up to the three phase contact line ok. So maybe I can show you that again. This is the same diagram we have the liquid surface and we have the solid plate deliberately inclined to make angle theta here with respect to the horizontal. This angle is theta and the liquid surface is planar right up to the three phase contact line. We do not worry about this part and in our thought experiment we say that this plate will be immersed through a differential length delta L and in the process some work done by the contact angle by the surface tension component acting at an angle corresponding to contact angle will tend to pull the plate inside ok. So that is in this case surface tension is trying to assist the immersion. So gamma L a cos theta will tend to help immersion associated with this work also is the change in energy because initially one into delta L unit width in the direction perpendicular times delta L that area which was in contact with air is now finally in contact with liquid. So there is a surface energy change for smooth solid we had made the balance which now has to be modified because now this surface is no longer smooth that is the only difference otherwise this same picture is valid for our concentration here. So how do the concentrations change? We can look at the next slide where we find that the first term FSLS the final interfacial energy between liquid and solid minus FSAS the surface free energy of solid in contact with air is now multiplied by 1 into delta L and that area apparent area 1 unit width times delta L now needs to be replaced by the real change in area and that will be real by apparent into the apparent that is R into 1 into delta L this real change in area should replace 1 into delta N in original equation. When we do this since we are now dealing with the solids which are rough we would necessarily replace theta by theta bar. So those are the two changes we have made we replaced 1 into delta L by R into 1 into delta L and we replace theta by theta bar. So new equation that we have here would appear this way we are careful here in noting that this would be justifiable only if the roughening is small scale which means we might still be able to think of some contact angle for the rough surface. This will not be true at all scales of roughening for the time being let us say that the roughening is able to permit application of this method of virtual displacement of three phase contact line. We will add a few explanatory sentences here a short while later, but at this stage if we simplify this cancel of delta L from these two terms and we get R equal to FSLS minus FSAS plus gamma LA cos theta bar right. Sir due to the roughening when the FSLS and FSAS change I mean not in terms of magnitude but in terms of direction. Please remember that now we are talking of energies. So it is a scalar ok. These are only magnitudes works per centimeter square ok. The only difference we are conceiving here is of solid either being smooth or rough that is it ok. This is another merit of method of virtual displacement or the alternative of speaking in terms of the surface energies rather than tensions because with tensions you would have immediate difficulties. So just note that the dimensional equivalence of tensions and pre energies should guide you as a reliable shortcut a mental shortcut, but do not take that analogy very far. Once we decide to drop the concept of tension we not only get rid of the imprecision about the idea of tension for solids but we also now switch over to more general free energies which can be measured and they are scalar so we do not have to worry about those. So I am not saying that the tensions should not be thought of but they should be at a subconscious level guiding a mental check on what we are doing. The precision like will lie in working with the free energies alright. So your question I will take further and say that will roughening change the free energies and my response to that is that since roughening is not altering the chemical composition the free energies should remain same ok or if the changes are there they are minuscule we are not giving much weightage to those changes right ok. So we have now a new relation which brings in the contact angle effective or apparent contact angle for rough surfaces theta bar in relationship with rugosity or roughness R this is it. Now is it possible to establish a relation between theta bar R and theta that is what Wenzel's relation states we need to relate theta bar not only to R but also to theta. So that is here that we can take help of this equation which was written for smooth surfaces.  Once we substitute for the difference required here the energy difference is same.  Now this will bear out all your expectations as to what roughing would do experimentally in relation to the magnitude of contact angle against 90 degrees. Now I add that explanation for the caveat that the surface presumed here is necessarily submicroscopic in the scale of roughing. Why is it necessary? This is not difficult to see. If we were to think of a solid which is roughened to a very coarse level what difficulties will we have? Close to the solid the liquid boundary will necessarily become ragged with one more consequence that the contact angle theta would not be constant independent of delta l and that was the assumption in the derivation of Wenzel relation. So we require the roughing to be of micro scale. This leads to a further thought. If there is a pattern roughing as often happens in practice I will just ask you to think of rough surfaces in everyday experience that you come across and when you think of the different rough surfaces you can think of the patterns of roughing. In most of the rough solids manmade solids we see a regular pattern. If there is a pattern of roughing and if there is any grooving then one may require to know how that pattern of roughing is or how that grooving has been done. What is the periodic variation of the surface with respect to the planar and grooved parts? If there are only a few grooves on the surface of Teflon the mean contact angle is still given by Wenzel's relation. But we may not always be so lucky we might have patterns which are experimentally possible to measure or quantify but they may not be as periodic or as less frequent as we may want in the normal Wenzel relation. So it is here we think about one more complexity. The surface might be composite. First we talk about a smooth composite surface and we consider a finely constituted smooth composite surface which means we have two or more kinds of components making up the surface. Let us limit ourselves to only two components and the composite surface is finely constituted in the sense the length scales over which these different solids occur at the surface that scale is small it is a fine scale. In addition when we look at the contact angle of a given liquid on this composite surface which is smooth let us say the contact angle is defined as theta prime what is indicated here on the left hand side and if we were to take these solids separately the contact angles that the liquid will exhibit on these solids will be theta 1 and theta 2 ok.  The reality forces us to look at more complex situations. Once again the idealization of a smooth composite surface might no longer be true what if we have finely constituted rough surface for a composite.    Let us see whether this simple relation can help us understand some nice observations that you get to make in practice even in nature. Let us take the case of air solid composite. What I mean here is that the solid surface has a porosity and the pores within the solid are occupied by air. So, if you have a part of surface composed of air spaces like on a porous solid what does our relation for composite rough surface yield to us. There is a mention here of theta to equal to 180 degrees. I had made a tangential reference to that theoretical expectation of contact angle equal to 180 degrees and that will not be possible for any liquid and real solid surface, but since a water drop in air is spherical one may say with relation to air the contact angle of water is 180 degrees. So, cos theta 2 if 2 is air in our rough composite surface with the roughness is actually air spaces cos of 180 degrees minus 1.  Cos 180 degrees minus 1.  Let us put some numbers here. If most of the surface consists of air spaces and you see that I am sure you have thought of certain textiles you can easily get most of the surface occupied by air and it actually is an interesting fact made use of by certain plants and insects to remain unwetted. Theta prime can easily become of the order of 150 degrees even when the basic contact angle for the solid theta 1 is only 90 degrees. All it will require is f 1 is equal to 0.134. So, you can design surfaces or textiles by using the patterns occupied by air spaces to make a fabric unwetable by common liquids. You just take away the contact angle to the region where we achieve unwetable surface. It is here that we are forcing ourselves to consider a certain interesting experimental fact that is related to the hysteresis of contact angle. In an experiment similar to what we imagined in the method of virtual displacement, one may be able to measure the contact angle between the liquid and solid while the plate is getting immersed into the liquid. So, there is a part of cycle in which we are moving forward with immersion. We would measure a certain contact angle and in the other part we might have withdrawal of the plate. So, if we measure the contact angle while advancing the plate into the liquid and we measure the contact angle again when we withdraw the plate from the liquid, the contact angles seem to be different. The difference is illustration of hysteresis of contact angle. So, the fact is that cleaner the surface smaller is the hysteresis of contact angle. We might want to understand this theoretically. Advancing contact angle is generally larger, receding contact angle is smaller and the hysteresis is lesser if we have a cleaner surface. So, we can think of possible explanations for this. In the advancing cycle when we measure the advancing contact angle, we might have to begin with the plate with some material adsorbed on it. So, there may be a film of some material which prevents the liquid from adhering to the solid. We will see how this complexity can develop further even when accidentally you are extremely careful. So, if the liquid cannot adhere to the solid, we will measure a larger contact angle. Then what is actually likely to be the real contact angle if the material will were clean. But after contact with the liquid in the forward or immersion cycle, this film may be either completely or partially get removed. If that happens, then the receding cycle will see a cleaner solid surface in contact with the same liquid. But now that the film is gone on the surface, the liquid will be able to adhere to the solid better and therefore, the contact angle will get smaller. This is the general explanation for hysteresis contact angle. And if you use cleaner material, then of course, this effect is lesser. So, that will be in tune with the experimental observations. Can we rationalize this? That is the next question. We may be able to do this in terms of the concentration of the Helmholtz free energy per area FSLS between the liquid and solid. This may become reduced. We can offer the following argument to explain the hysteresis contact angle. We may say that in the advancing cycle, part of cycle, the adsorb film is spontaneously getting removed. If this happens, FSLS will decrease. Therefore, cos theta must become greater.  So, in the forward cycle, the film spontaneously leaves making from free energy concentrations the effective FSLS for the receding cycle smaller, which will mean that the receding cycle will see a smaller FSLS. And therefore, FSAS minus FSLS will be higher and therefore, cos theta will be higher and theta smaller. So, in the receding cycle, you have a reduction in the contact angle. So, that is how the hysteresis of contact angle could be explained. Let us see whether we can stretch this understanding to a finer level. The adsorb solid, adsorb material on the solid is in the form of film. When you bring this film covered solid in contact with the liquid, this film leaves the solid liquid interface and occupies the air liquid interface. It leaves spontaneously. When it leaves this solid, it means that this is a spontaneous process and therefore, the solid surface energy must diminish. Everything happens in direction of decreasing free energy. So, that means now FSLS is lower, FSAS minus FSLS is higher, therefore, cos theta is higher. If gamma L A has not changed much and therefore, theta must have become reduced. So, in the receding part of the cycle, we will see a more complete contact or lesser value for the contact angle. Clear? If the film consists of a greasy material adsorbed in small traces from air, we could confirm whether this happens. We are little bit ahead of these lectures, but we will see later that it is possible to measure the potential surface and interfacial potentials to detect these impurities at clean water surface. So, by measuring potentials after a few minutes of exposure of a clean air water surface, we may be able to confirm that there is a adsorbed film on solid which is leaving it and occupying the air water surface. And because it is a spontaneous thing, it is indicating a preferential adsorption of this material, greasy material at the air liquid surface. So, what effect can this have? This could cause the surface tension of water to diminish. After all, this film has come spontaneously to the surface, so it must have also reduce the surface energy of the liquid. Therefore, next part of argument is gamma LA will be reduced. And then again, by the same equation we can say if gamma LA is reduced, FSL is reduced. Actually, this quantity has become higher, we will require cos theta higher. So, that means theta must be reduced. So, this is a consistent rationalization which can explain the hysteresis of contact angle. Are there practical examples which can substantiate these kind of phenomena? In the literature on floatation, you see that in practice if solid surface is covered, even up to the extent of about 10 percent using a monolayer of long chain compounds, it can drastically increase theta. So, one commonly makes use of this understanding in floatation practice. Taken together, we may say that this explanation of hysteresis is reasonable. The liquid surface in such extents must be very carefully cleaned. And this older practice of taking the mean of advancing and residing contact angle has practically nothing to recommend it. They are actually two different contact angles. The solid surface with adsorbed impurities is actually a different solid surface. We cannot take an average. This is the last slide for today. Even if we are extremely careful in removing the contamination, we may still observe the advancing contact angle to be too large. How could that happen? That may be result of adsorption of a film of air on rough solid. Especially rough solids will have larger area, so greater probability of adsorption of air. That would decrease the work of addition between the liquid and this air covered rough surface solid. And if WSL decreases, then that may make the contact angle too large. Remember Wenzel's relation. This is the last slide for today. WSL is gamma L a cos theta plus 1. By adsorption of air, WSL between the given liquid and solid is reduced. That is what this arrow is supposed to tell you. And therefore, we require cos theta to decrease. If this relation is to be obeyed, cos theta has to be decreased, which corresponds to theta increase. So, in practice we might have much larger observed contact angle even when you carefully treated the liquid surface and the solid surface to get rid of impurities, but the ambient air still can play a part. So, very clean and very smooth solid surfaces are shown to display very little or no hysteresis of contact angle. We will stop here for today and resume our discussion further considering the nature of solids and the way you cut out a solid surface before you make measurements on contact angles. So, we will stop here for today.