Structure and Properties of Polymers Essay

Structure and Properties of Polymers Essay Structure and Properties of Polymers Essay C 10 Lecture Notes Freely jointed chain, a â€Å"phantom† chain n links of same length, ak Joints permit completely free rotation Mean squared end to end length = nkak2 Contour (stretched out) length Lc=nkak Persistence length aq=ak/2 What is the size of the blob? For an ideal Kuhn chain RG2 = RL2/6 (approx.) RG: Characteristic radius of blob 3. Non-crystalline Polymer (Physical States of Matter) 3.1 Glass transition temperature Specific volume a) Tg occur in all materials where crystallinity doesn’t get in the way b) Because it is not an equilibrium phase, glass transition is not a thermodynamic transition Melt/Rubber Glass Equilibrium line T 0 Specific volume Specific volume 1. Cool slowly 2. Heat quickly Tg depends on time scale of observation Slow cool Fast heat Anneal 0 T 0 T 3.2 Polymeric states Molecular weight Increase molecular weight to infinity (chemically linked) → All RUBBER in this region Tg Glass Rubber Viscous melt T 1 GPa Glass log E Rubber 1 MPa ~ 10 MPa Viscous creep Temperature Spring: purely elastic, ÏÆ' = EÃŽ µ Dashpot: purely viscous, ÏÆ' = ÃŽ ·ÃŽ µ stiff spring model elasticity of glass (Eg) dashpot controls short relaxation time processes (frees upon reaching Tg) Eg-Er Er ÃŽ ·1(T) ÃŽ ·2(T) weak spring model elasticity of glass (Er) dashpot for longest relaxation time processes (frees for rubber-melt transition) ÃŽ ·1 and ÃŽ ·2 solid → glass: Eg ÃŽ ·2 solid, ÃŽ ·1 free → rubber: Er viscosity, ÃŽ · = ÏÆ'/ÃŽ µ 4.1 Behavior of spring/dashpot models ÏÆ' ÃŽ µ Maxwell element Time tot = E + − CON. EQN ÏÆ' ÏÆ'0 at time t = Ï„, ÏÆ' = ÏÆ'0/e 0 t ÏÆ' ÃŽ µ = ÏÆ'0/E t Voigt element Add stresses, ÏÆ'tot = EÃŽ µ + ÃŽ ·ÃŽ µ − CON. EQN â‘ ¢ Constant ÃŽ µ, ÃŽ µ = 0 ÏÆ' = EÃŽ µ Constant ÏÆ', ÏÆ' = 0 4.2 How realistic? Assumptions: (i) Viscosity Newtonian ÃŽ · ≠  f (ÃŽ µ) Not very good assumption at high strain rate (ii) Only two relaxation processes Ï„1 Ï„2 LHS controls Tg Relaxation of molecular chain segments RHS longest Ï„ Unraveling of entangled chain N (Ï„) Relaxation Time Spectrum Ï„ Note: N (Ï„): number of elements with Ï„ between Ï„ and Ï„ + d Ï„, like ‘density of state† 5.1 Modulus of glass Eg ~ E of van der Waals solid (held together by VdW forces), approx. 1 GPa Einorganic glass ~ 65 GPa → combinations of ionic bonding and Si – Si Emetal : steel ~ 210 GPa Al ~ 70 GPa Epolymer chain pulled out ~ 250 GPa 5.2 Viscosity of ÃŽ ·1 dashpot In region of Tg, (a) Time-temperature superposition (Fig 5.1) (b) Superimposed curve, made by shifting data by log aT (Fig 5.2 b) (c) Plot of shift factor aT vs. temperature (Fig 5.2 c) Williams-Landel-Ferry (WLF) found empirical equation to describe (c) Ts ~ reference temperature, works well if Ts = Tg With C1 = 17.4 , C2 = 51.6 K Implication: log aT (i.e. ÃŽ ·1) turns to ∞ when T = Tg – C2 → (Tg – 51.6) K ∠´Creep of polymer glass turns to zero at temperature (Tg – 51.6) K or lower Justification of WLF in terms of free volume Specific volume Occupied volume 0 T Second Input: Doolittle Equation 5.3 Elasticity of Rubber Spring 5.4 Viscosity of dashpot Rubber ⇄ viscous melt? Viscous flow ~ relative motion of centers of masses of molecules A. Reptation Model Molecules effectively confined in tube by entangling neighbours Constraints physical cross-linked points Reptation - Molecule can only escape lengthwise Parameters: Need two other equations: B Above critical molecular weight for

Torture Is Never Justified

Torture Is Never Justified Torture through the History The concept of torture is at the base of many conflicts that take place throughout the country. In fact, it began in ancient times with the Romans and Greeks forcing their prisoners to participate in some of the worst forms of torture we’ve ever known. Since that time, countries around the world have used everything from ‘the rack,’ tar and feathering, stoning, waterboarding and much more to torture others whether for the purpose of gaining information or simply as a method of slowly killing a prisoner. For any purpose, however, torture has never been able to be justified, at any point in our history and most definitely will not be at any point in our future. Torture Is Often Useless Many claim that torture can be justified because it comes down to the safety of the people. They believe that torturing someone in order to gain information that could potentially save lives is acceptable or even reasonable, however, this is not the case. In fact, torture is often used on those labeled as ‘traitors’ for this very purpose but is not often as effective as many would have us believe. This is because those who are being tortured, those who may know something that we would want them to divulge, are also highly trained to ignore the torture and to fight through it as long as they need to until death. As a result, the torture is being done on an individual for no purpose but perhaps a level of sadism on the part of the captor. Despite what we may be told, there is little if anything to be gained by the process. Yet another problem that arises with the concept of torture is at what point does it end? In many countries, torture is allowed for different types of crimes. In the United States, only those accused of being terrorists or prisoners of war are allowed to be tortured, yet only the accusation and not actual proof is needed. In other countries, crimes less than terrorism can be punished by torture and in still others, a crime is not even needed to enact torture on the basis of a simple belief. How could it be possible to even for those who believe in torture in some instances to say that torture is allowed in all  instances per justice? And this is where the struggle begins. Because the more that torture is defended and allowed in one situation, the more others will clamor for it to be allowed in all situations. After all, every criminal situation is looking to help people, to protect people. Want to know more? Go here: When Is Military Force Justified? Single-Parent Children Behaviour Causes of Human Errors in Aircraft Accidents Human Dignity   Sample Essay about Happiness What Is the Value of Human Life? The truth of the matter is that it is not only the government that participates in torture. There are also many instances of vigilante justice where the people of a country or area will join together to enact some type of vengeance on a person they perceive to have done something wrong. These individuals could be tortured with no more evidence against them than public opinion and yet, by attempting to justify torture in some senses, we are opening the door to these types of torture in any sense. The most important matter, however, that arises in this question, is that of human life. The value of human life, of human wellbeing, is written into the Constitution of the United States, ‘the right to life, liberty and the pursuit of happiness.’ The life and ‘pursuit of happiness’ for all people is important to us and has always been. But through torture, we strip individuals of their life and their liberty and their pursuit of happiness with the thought that, because we believe them to have done something bad, they are somehow less human. When viewing this issue of torture it is important to remember that there have been changes to it throughout time. Originally, very little was needed in order to implement torture on anyone. Over time, we have narrowed down the reasons and this is a step in the right direction. However, we have not eliminated the process altogether and this is an important next step for us to take. Torture cannot be allowed to continue in any nation that would call itself civilized because, despite what we may be told, there is no justice to be found in torture.